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Numerical evaluation of stresses acting on particles in high-pressure

microsystems using a Reynolds stress model

S. Beinert n, T. Gothsch, A. Kwade

Institute for Particle Technology, TU Braunschweig, Volkmaroder Strasse 5, 38104 Braunschweig, Germany

H I G H L I G H T S

We investigate the multiphase ow elds of different micro-channels by CFD.

A new model to calculate acting stresses on particles was used. Based on the Reynolds stress tensor and a stationary particle tracking a quantication of acting stresses was possible. Effect of steam and cavitation was reproduced. Peak stress seems to be the leading breakage mechanism in turbulent microchannels.

a r t i c l e i n f o

Article history:

Received 28 August 2014

Received in revised form

17 October 2014

Accepted 22 October 2014

Available online 30 October 2014

Keywords:

Simulations

Multiphase

Reynolds-stress model

Stress analysis

Dispersing

a b s t r a c t

In the present study a model was developed which enables to calculate the stress acting on particles

induced by the uid ow in microchannels. Computational uid dynamics (CFD) was used to simulate

the ow eld in ve different microchannel geometries. With the help of aReynolds-stress model and a

stationary particle tracking a quantication of stresses in different geometries at varying pressure

differences is possible. Furthermore, the effect of cavitation which occurs if the uid expands to ambient

pressure was investigated. The mass ow rates determined by the simulations are in good agreement

with the ones determined experimentally. Except for the z-channel the computed stresses are in good

agreement with previously conducted dispersion experiments. Additionally, the computed uid stresswas compared with the calculated Kolmogorov length scale to validate the results.

& 2014 Elsevier Ltd. All rights reserved.

1. Introduction

In the last couple of years the impact and inuence of

numerical methods for process design and optimisation largely

increased. Simulations are used to get a better understanding

of different processes, for the prediction of the results or as a

additional tool to investigate acting mechanisms. Due to the

increased computational power new, more detailed simulationscan be conducted which improved the understanding of unit

processes. Especially, if experimental methods are not applicable

or if they are expensive (in time and costs) simulations become

more and more the method of choice. In this work simulations

were used as they are (often) faster, reliable and enable informa-

tion which cannot be fetched out of experimental investigations.

They were used to compute different types of microchannel

geometries and to identify the dominant stress mechanism for

the breakage of agglomerates or aggregates (in the following

named particles).

The usage of microchannels in chemical and pharmaceutical

engineering offers a couple of advantages, like high energy input

per volume, high efciency, narrow residence time distributions

and reproducible results. As nanoparticles have become more and

more important for industrial applications the microchannels areused to produce particles with a dened size and a dened,

narrow size distribution. As the geometry of these devices is very

exible investigations to optimise the geometry are required.

The number of possible designs is extremely high and, hence,

simulations are required to get a understanding of the leading

breakup mechanism. If the mechanism for the breakage of the

particles in a microchannel is known the geometry can be adapted

in a way which supports this mechanism.

Wengeler and Nirschl (2007)andWengeler (2007)investigated

the dispersion behaviour in nozzles with a circular cross-sectional

area. They used a stress model with four different kinds of stresses

Contents lists available atScienceDirect

journal homepage: www.elsevier.com/locate/ces

Chemical Engineering Science

http://dx.doi.org/10.1016/j.ces.2014.10.042

0009-2509/&2014 Elsevier Ltd. All rights reserved.

n Corresponding author. Tel.: 49 531 391 9621; fax: 49 531 391 9633.

E-mail address:[email protected](S. Beinert).

Chemical Engineering Science 123 (2015) 197206
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(compressive, shear, tensile and turbulent stress) for a two-

dimensional simulation to evaluate the acting stress. This model

was enhanced to three dimensions and extended with a stationary

particle tracking to enable a quantication of different microchan-

nel geometries (see Beinert et al., 2012). Furthermore, in these

previous published results a k model was used to calculate the

ow elds and compute the stresses acting on the particles.

As the dispersion of solid particles in microchannels is a

relatively new process and not yet common in industrial applica-tion there is not much research done on it. Many research projects

were done in the eld of (laminar) mixing and chemical reactions

in micro-devices and particle laden gas ows. The laminar mixing

of different species and a possible reaction is based on the

diffusion process and the interface which is very large in such

micro-devices. Particle laden uid ows, especially turbulent

ows, are very common for diesel injection, soliduid transpor-

tation or uidized beds.

1.1. Mixing and chemical reactions in micro- and macro-devices

Among others, micro-devices are used for continuous mixing

and/or for continuous chemical reactions. Due to the fact that

laminar ows are volitional only low uid velocities, low forcesand low pressures occur. Therefore, established experimental and

numerical methods for laminar ow can be used to characterise

and improve the geometry of the micro-devices. Pennella et al.

(2012) investigated a new designed micromixer by the help of

particle image velocimetry (PIV) and computational uid

dynamics (CFD). They showed that the current methods can be

used to largely improve the geometry in terms of mixing quality,

costs and energy input. On the other hand the micro-scale of

reactive ows was investigated. For example Porta et al. (2012)

looked at the global reaction rate and the spacetime distributions

in dependency of dimensionless quantities like Peclet or Dam-

koehler number.

In the work ofMakowski et al. (2012) large eddy simulations

(LES) were used to calculate the mixing process of particles in arectangular channel reactor. The results were compared with

different simulations and experimental data. They showed that

for high Reynolds numbers and low concentration the k model

offers similar results. With decreasing Reynolds numberand

higher concentration large scale inhomogeneities and non-linear

effects have to be taken into account and, therefore, the usage of a

LES is required.

Similar investigations were performed in Gradl et al. (2006)

and Gradl and Peukert (2009). They investigated a t-mixer with

the help of experimental and numerical methods. They used

coupled direct numerical simulations (DNS) and population bal-

ance equations (PBE) to model the inuence on the resulting

particle size distribution. With the help of a derived micro-mixing

model they were able to predict the particle size distribution inthe precipitation process. For unstable conditions they extended

their coupling with the DLVO theory which improves the possibi-

lities to stabilise the production of particles.

1.2. Particle ladenows

In contrast to the work shown above a lot of investigations have

taken place in the eld of particle laden turbulent ows in non-

micro-devices. In Messa et al. (2013, 2014) different process para-

meters for turbulent ows were computed and compared with

experimental data. They compared their computed results based on

a turbulence model including physical mechanisms with experimen-

tally measured pressure drops, solid volume fractions or spatial

particle distributions and particle velocities. Furthermore, DNS can

be used to calculate micro- and macro-time scales (compare the

work ofWang and Manhart, 2012).

(Gui et al., 2010) simulated the particlevortex interaction in

turbulent, swirling jets with the help of DNS and studied the

inuence of the particles on a plane jet in Gui et al. (2013). They

showed that the DNS is a good method to simulate those interac-

tions if the Reynolds number is not to high due to the rapidly

increased computational costs. Furthermore, they pointed out that

for high volume fractions of the dispersed phase the two-wayinteractions between the uid and the particles have to be taken

into account.

1.3. Stress mechanism in dispersion processes

A general overview of the acting stresses on particles in a uid

is given in Raasch (1961) and a general overview of dispersion

experiments in different dispersing devices is given by Schilde

et al. (2010, 2011).

Investigations of dispersion and aggregation behaviour of parti-

cles in non-uniform shear ows were performed and described by

Masuda et al. (2013b) (backward facing step) and Masuda et al.

(2013a) (parallel plates). These investigations were performed for

lowReynolds numbers and two-dimensional

ow simulations. Theyintroduced a model which enables the prediction of size distribution

of particle clusters (based on coagulation and breakup) and com-

pared the gained results with experimental data.

Rotorstator devices are often used for the production of disper-

sions or emulsions as they produce high shear stresses. Jasiska et al.

(2013, 2014)simulated the three-dimensional ow in a rotor stator

with the k model to predict the power input and turbulence

within the ow and/or linked it with the population balance

equations to predict the droplet size distribution over time.

CFD coupled with the discrete element method (DEM) can be

used to evaluate the stress acting on agglomerates in an pharma-

ceutical dry powder inhaler. Tong et al. (2013)used this approach

to identify agglomerate-device impacts as the dominant stress

mechanism beside multiple impacts between agglomerates. A

similar approach to describe the dispersion progress in a stirred

media mill is shown in Beinert et al. (2014). Coupled CFD-DEM

simulations were performed to evaluate the contacts between

grinding media to estimate with the help of PBE the particle

size distribution over time.

2. Methods and models

In the rst section the microchannels, experimental set-up

and material properties are described. Further information on

the experimental part of this project are given in Gothsch et al.

(2011, 2014). The second part describes the software and used

boundary conditions while the third part describes the turbulent

model. The fourth part denotes how the acting stress is calculated,while the last section takes the effect of turbulence on particles

into account.

2.1. Experimental set-up

A uid was pumped through the microchannels (containing

particles) with a pressure difference up to p 500 bar andexpanded to ambient pressure or into a pressure vessel at various

pressures. These microchannels were manufactured by the Insti-

tute for Microtechnology of TU Braunschweig (compare Lesche

et al., 2011). The pressure in the vessel is called backpressure

while the difference between the inlet and the outlet is called

pressureor pressure difference. The backpressure experiments

were performed to investigate the inuence of cavitation. Two

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different types of experiments were used to compare the results

with the numerical gained data: mass ow measurements (with or

without backpressure) and dispersing experiments. These results

were performed in ve different microchannels which are shown

in Fig. 1. The upper four geometries are microchannels of older

designs which were investigated in previous works. The acting

stresses based on a k model were computed (compareBeinert

et al., 2012) and are used in this work to evaluate the new model.

As the previous experimental results showed that the orice

channel was the most effective one, a new geometry (the lowest

one inFig. 1) was fabricated in silicon and stainless steel to gain

higher pressures. All microchannels of the rst generation offer a

height ofh 68m while the second generation offers a height ofh 50m.

In order to simulate the ow in a correct manner material

properties have to be known. In Table 1 all required material

properties are listed. For the dispersion experiment aluminium oxide

Al2O3 (Aeroxides

AluC, Evonik) produced by pyrolysis was used.

The solid density of aluminium oxide (Al2O3) cannot be used as

the particle's density. They consist of primary particles which are

formed to aggregates (solid strong bonds) and/or agglomerates

(solid or liquid weak bonds) with a fractal shape due to the

pyrolysis production process. This shape can be quantied by the

fractal dimension d. According toStiess (2009)the fractal dimen-

sion is dened as

n ra

rp d

; 1

where n is the number of primary particles, ra the radius of

gyration of the agglomerate or aggregate and rp the radius of the

primary particles. A fractal dimension ofd 1 represents a row of

primary particles while a fractal dimensiond 3 represents a solid

sphere. This relation can be used to calculate the volume ratio of

solid v within a sphere with the radius ra:

v ra

rp

d 3: 2

The fractal dimension of aluminium oxide (Aeroxides AluC,

Evonik, was used, too) was determined as d 2.7 (compare

Capitaine and Hill, 2012). Therefore, the density of spherical

particles which represents the investigated aluminium oxide

particles with the radius of the agglomerates ra 115 nm (the

mass-weighted measured median particle size is x50 230 nm,

compare Gothsch et al., 2011) and the radius of the primary

particlerp 13 nm (taken from producers data sheet) is

a H2O ra

rp

d 3 Al2O3 H2O

2179 kg=m3: 3

This density was used to depict the shape of the agglomeratesas only a spherical drag law was used for the stationary particle

tracking. The reduced density is comparable to a higher drag

coefcient which is caused by the fractal dimension of the

agglomerates.

2.2. Numerical set-up

The simulations were performed with the commercial software

package ANSYSs Fluents

14.0.0 based on block structured meshes

created with ANSYSs ICEM CFDs 14.0. The mesh of the micro-

channels of the 2nd generation is resolved ner to improve the

quality of the simulations (four million cells increased to seven

million cells). To reduce computational cost the symmetry of

microchannels was taken into account. As turbulence model aReynolds-stress model was used. The pressure difference between

inlet and outlet was specied and the uid ow was calculated.

Due to the fact that the uid expands to different pressures

including ambient pressure cavitation occurred. To include the

effect of cavitation the mixture model was used and as interaction

between steam and water the ZwartGerberBelamri modelwas

applied. The simulations were transient to enable non-steady

behaviour of the different microchannels. If a stationary value

occurred a stationary particle tracking was conducted to measure

acting stresses, uid and particle velocity (hence, the relative

velocity) and volume fraction of surrounding steam. To quantify

the dispersing behaviour of the different geometries the seeding

points were spatial distributed all over the inlet (distance between

two seeding points: d 8:7 m, leading to 10,201 seeding pointsover the entire inlet). The normal uid velocity component at

every seeding point was used to weight the tracked values. The

stresses acting on the particles were calculated by variables of the

uid as described in the following.

The time step size varied between t 2 10 92 10 8 sdepending on the pressure difference p as it is nearly propor-tional to the maximum velocity. The Courantnumber was partly

above 1 without any stability issues. For all channels, expect the

straight channel, the mass ow rate over time behaves like an

under- or an overdamped system (a maximum of 150,000 time

steps were required). As convergence criteria the absolute value of

the residuals for every solved equation had to be lower than 104,

which was only critical for the rst couple of time steps.

2.3. Numerical models

In this model the uid stress is taken as an indicator for

breakage. For very small particles the validation of this assumption

has to be proven (compare Section 2.5), for very large particles and

high volume fraction of the particles the uid ow would be

inuenced which is not taken into account. The investigated

particles are small and the volume fraction is very low

(x50 230 nm and m 0:010 which is v 0:003, compare

Gothsch et al., 2011).

If the uid is incompressible the NavierStokes equations are

uit

xjuiuj

pixi

xj

uixj

ujxi

ki: 4

Fig.1. Geometries of the four microchannels of the 1st generation (upper four) and

the orice channel of the 2nd generation (lowest one).

Table 1

Properties of used materials.

Material Density(kg/m3) Viscosity(Pa s) Vapour pressure(Pa)

Watera 997.05 8.901 104 3230

Steama 0.023 9.867 106

Al2O3b 3270

a Values taken fromVDI (2013).b Values taken from producers data sheet.

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To reduce computational costs it is common to use turbulence

models which need additional transport equations. With higher

amount of additional transport equations the computational costs

and the accuracy increase. Reynolds proposed an averaging to

reduce the effects of turbulence in the Reynolds-stress tensor

(RST). Therefore, the velocity u and the pressure p are split into

an average and a uctuation value:

ui ui u0i and pi p i p

0i: 5

With these new quantities theNavierStokes equations could be

transformed into the Reynolds-averaged-NavierStokes equations

(RANS equations):

uit

xjuiuj u

0iu

0j|fflffl{zfflffl}

RST

0B@

1CA p i

xi

xj

uixj

ujxi

ki 6

The Reynolds-stress tensorin index notation is

u0iu0

j

u01u01 u

01u

02 u

01u

03

u02u01 u

02u

02 u

02u

03

u03u01 u

03u

02 u

03u

03

0BB@

1CCA: 7

It is easy to observe that the Reynolds-stress tensoris symmetric

and, hence, six additional transport equations are required to solvethe Reynolds stresses. Furthermore, the diagonal elements are

tensile stress while the others represent shear stress. To receive

the acting stresses at every place in the solution area the stresses

out of the averaged velocity and due to the Reynolds-stress

tensor is required. The resulting stress tensor is

sij

2uixi

u0iu0i fori j

uixj

ujxi

u0iu

0j foriaj

8>>>>>:

8

2.4. Stresses on particles

In this work only spherical particles are investigated and,hence, the differentiation between tensile and shear stress is not

useful as a different coordinate system will lead to different tensile

and shear stresses. The principal axis transformation can be used

to transform sij into a tensor tij which consist only of diagonal

elements. This is done by the Jacobi method and leads to

tij

11 0 0

0 22 0

0 0 33

0B@

1CA: 9

11, 22 and 33 are the principal stresses and can be used to

detect material failure. It is a common method (compare max-

imum shear stress criterion) to calculate if a material breaks. It can

be useful to reduce the stresses to one value. Hence, the principal

stresses are used to dene a vector s! which norm could be usedas acting stress:

s!

11

22

33

0B@

1CA and

s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

211 222

233

q : 10

2.5. Turbulent stress on particles

The next section discusses the stress acting on the particles.

First, it is interesting to compare the stress induced by turbulence

and the stress induced by the averaged velocities as proposed in

this model. Second, it is useful to compare the stress acting on a

particle taking the ratio of the size of the particles and the size of

the smallest eddies into account. Third and last, it is necessary to

consider the character of the stress (like inertia or viscous stress).

2.5.1. Order of turbulent stress

In this section the order of the turbulent stress is compared

with the order of the stress induced by averaged velocities. For

every Reynolds-stress model the averaged velocity gradients and

the uctuation of every velocity component are calculated. The

turbulent stress su0 and the stress induced by the averaged

velocitiess u are

su0 =k

1=2and su

uixi

: 11

where kis the Kolmogorov time scale, the turbulent dissipation

rate and the kinematic viscosity. The ratio is

su0

su

ffiffiffiffiffiffiffiRet

p

u0il

1

ui=xi; 12

if the turbulent dissipation rate , which is dened using the

velocity uctuationu 0i and the scale of the larger eddies l,

k3=2

l pu0i3

l ; 13

and the turbulent Reynolds number

Ret u0i l

14

is used. One can take u0i=l ui=xi as the frequency of large eddies

and the frequency of the mean ow should be equal or at least

similar. Therefore, the ratio of the stresses is

su0

su

ffiffiffiffiffiffiffiRet

p 15

and it is easy to observe that for fully turbulent ow the stresses

induced by the mean ow are negligible. In this work different

pressure differences and different geometries are investigated.Some ows are not fully turbulent and, hence, it is necessary to

take both kinds of stresses into account. Nevertheless, the turbu-

lent stress should be the dominant one.

2.5.2. Order of turbulent stress on particles

The turbulent stress acting on particles su0 ;p in dependency on

the particle's diameter dp can be estimated using the uid's

density and the turbulent dissipation rate :

su0;p dp 2=3

16

The ratio between the turbulent stress acting on particles su0;pand the stress induced by averaged velocitiessu can be estimated

in the following manner:

su0;psu

ffiffiffiffiffiffiffi

Retp

su0;psu0


Retp

dp 2=3

= 1=2


Retp

dp

k

2=3with k

3

1=417

This leads to the conclusion that with increasing turbulence

and with increasing ratio of particle size and size of the smallest

eddies the turbulent stress will become dominant. As the range of

investigated ows includes laminar ows and ows in transition

as well as particles with different size the uid stress due to

gradients of the averaged velocity is still necessary to take into

account. Again, the expected turbulent ow leads to the assump-

tion that the turbulent stress is the important one.


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2.5.3. Order of inertial turbulent stress

The inertial stress acting on a particle is the energy input of the

active uidEfper volume of the uid itselfVf. The energy input is

caused by the smallest eddies which dissipate the uids energy

due to viscous effects. It can be written as

su0 ;i EfVf

mf u

2

mf=

u2p dpk

2

d2p: 18

Therein, mf is the mass of the active uid and k is the

Kolmogorov time scale. As the inertial effects on a particle can

only be based on eddies of at least the same magnitude the acting

velocity should be proportional to the diameter of the particle and

theKolmogorov time scale. Comparing these inertial uid stresses

with the turbulent stress due to viscous effects leads to

su0 ;isu0

d

2p

1=2 dpk 2

19

Hence, with decreasingdp=k the inertial uid stress decreases

and becomes negligible for dp=k{1. In the following these

different conclusions have to be proven and will be an indicator

to evaluate if the model is sufcient to describe the acting stresses.

3. Results and discussion

3.1. Massow and spatial distributions

Due to the fact that the pressure difference is specied the

resulting mass ow can be used to validate the macroscopic

quality of the simulations and used models. In Fig. 2 the mass

ow of water for the four different microchannel geometries of the

1st generation is shown (simulations: pressure difference of

p 50, 100, 200, 300 and 500 bar; experiments: varying pres-

sure differencep). Furthermore, a comparison of thekand theReynolds-stress model with experimental data is shown.

It can be seen that the more sophisticated Reynolds-stress

modelimproves the quality of the simulation. The y-channel is

again in a very good agreement. Additionally, the straight (up to

100 bar, for higher pressures the ow in the straight channel did

not become stationary) and z-channel are in very good agreement

with theReynolds-stress model and justify the increased computa-

tional costs. The difference between calculated and experimentally

measured mass ow in the orice channel is reduced but still

distinct. This could be induced due to small inaccuracies in the

production of the microchannel geometry or the dimensions

of these microchannels. Nevertheless, overall the comparison of

the experimental data with the simulation results based on the

Reynolds-stress modelis in good agreement. Fig. 3 shows the

velocity distribution of the uid at a plane with the height of

h 34m (half of the microchannel height) for the four differentgeometries at a pressure difference between in- and outlet of

p 500 bar.As the pressure difference is responsible for the uid ow

the geometry denes the occurring uid velocity. For the same

pressure in the z- and straight channel only moderate velocities

are reached. The long small channel creates a continuous decrease

in pressure and, hence, a relatively constant average velocity. The

orice and y-channel offer partially very narrow channels and due

to the rapid decrease in pressure high velocities occur. Behind the

narrow parts of the microchannel and in the widening at the end

of the channels regions with very low velocities occur. At these

regions cavitation can develop due to the fall of the static pressurebelow the evaporation pressure. The steam distributions for these

four channels are shown inFig. 4.

If the colour differs from dark blue cavitation leads to steam

until only steam is present for red coloured regions. The steam

distribution of the z- and straight channel and of the orice and

y-channel are similar. For the z- and straight channel steam occurs

at the widening at the end of the channel. For the orice and

y-channel the steam occurs after the narrow section and increases

at the widening at the end. The steam leads to a decreased energy

dissipation due to the reduced density and viscosity. Hence, it

enables the forming of free jets by the meaning of an expansion

into the gas phase (not into vacuum as in other cases).

These gained ow elds can then be used for a stationary

particle tracking. This stationary particle tracking is based on the

Fig. 2. Comparison of the mass ow for the different microchannels and for

different pressure differences.

Fig. 3. Velocity distribution of the uid for the four different geometries at a

pressure difference ofp 500 bar.

Fig. 4. Steam and water distribution for the four different geometries at a pressure

difference ofp 500 bar.


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previously described equations and requires the averaged velocity

gradients and the Reynolds-stress tensor.

3.2. Evaluation of the new model

To characterise different microchannel geometries the values of

the different parameters along every possible path are required.

As a Reynolds-stress model is used which is based on the RANS

equations the averaged velocity u and the uctuating velocity u0

are constant at every place. Therefore, it is possible to reduce the

number of tracked particle paths. In Fig. 5the tracked parameters

along a path of a particle with a diameter of dp x50 230 nm

released at the centre of the orice channel for a pressure

difference ofp 500 bar are shown. Therein velocity is theuid's velocity, relative velocity is the difference between the

particle velocity and the uid velocity (negative values represent

the case of a particle which is faster than the uid), steam

fraction is the fraction of steam in the region surrounding the

particle and stress represents the acting stress according to

Eq.(10).

It can be seen that the uid's velocity is very low before the

particle reaches the orice. Short before the orice a rapid increase

in the uid's velocity occurs leading to a continuously deceleration

until the widening is achieved. The relative velocity is an indicator

for the acting stress as the difference in velocity causes forces

acting on the particles. The largest difference occurs when the

uid is accelerated rapidly. The peak difference is vrel 8 m=s.

After the orice the particle is continuously decelerated by the

uid. The steam fraction in the volume surrounding the particle

increases after the orice and remains high until the particle

leaves the microchannel. When the local minimum is reached the

widening of the channel begins.The main stress along the entire path of the particle is tracked,

too. It can be seen that the peak value occurs in the orice itself,

but after the peak value of the relative velocity. Due to the

turbulence after the orice the main stress is higher compared

to the laminar region before the orice. Furthermore, it can be

seen that the relative velocity is an indicator if locally high uid

stress occurs. Due to the fact that a Reynolds-stress model is used,

the stress induced by turbulence cannot be tracked or charac-

terised by the relative velocity. As these stresses could be larger

the main stress has to be used.

To quantify different geometries at different pressures the

peak values (like relative velocity, stress, etc.) of every tracked

path are calculated and weighted by the normal velocity compo-

nent at the inlet of the seeding point. In Fig. 6the probability of a

particle to face a maximum relative velocity for the four micro-

channel geometries for a pressure difference of p 500 baris shown.

The z- and the straight channel offer a similar relative velocity

distribution. Due to the redirections within the z-channel slightly

higher values occur. Expectedly, the y- and, especially, the orice

channel prevail higher relative velocities. Due to the narrow parts

the uid's acceleration at a very limited space leads to higher

differences. If the acceleration or the deceleration of the particles

by the surrounding uid is the leading breakage mechanism

(excluding shear stress due to velocity gradients and turbulence)

the orice channel should offer the best results while the z- and

straight channel should be more inefcient; the y-channel should

be between them.

To predict the dispersion efciency of different microchannel

geometries the acting stresses on a particle were tracked and the

resulting distributions for the orice channel at ve different

pressures (see Fig. 7) and for the four different investigated

geometries at two different pressures (seeFig. 8) are presented.

The left part of Fig. 7 shows the probability for a particle to

suffer a specic peak value of the stress at ve different pressure

differences. It can be seen that an increase in pressure difference

leads to an increased probability to sustain the same stress or it

leads to an increased possibility to sustain a higher stress. To

investigate the dependency of the peak stresses s on the pressure

difference the stress is normalized by the pressure difference:

sn s

p: 20

The probability to face a specic normalized stress is shown

in the right part ofFig. 7. As the shown curves differ for varying

pressure differences it can be stated that there is now lineardependency of the stress on the pressure. The dependency is less

than linear meaning that a doubled pressure difference does not

lead to an doubled stress value or probability.

The comparison between the different microchannel geome-

tries is shown in Fig. 8. For the lower pressure difference

p 100 bar all channels exhibit peak values for every trackedpath within a close range. While the z-channel offers highest peak

values, the three remaining channels behave very similar. For a

pressure difference ofp 500 bar the results differ. The straightchannel offers the lowest peak values and is about one decade

lower than the other channels. While the occurring peak values in

the z-channel are all-over despite the comparatively low relative

velocities the highest, the maximum stress occurs in the orice

and y-channel. This leads to the conclusion that the relative

Fig. 5. Velocities, stress and steam fraction for a single particle passing the orice

channel for a pressure difference of p 500 bar (the axes are assigned to the

colours of the four variables). (For interpretation of the references to colour in this

gure caption, the reader is referred to the web version of this paper.)

Fig. 6. Peak value distribution of the relative velocity between uid and particle for

the four microchannels for a pressure difference ofp 500 bar.


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velocity, which is based on the averaged uid velocities, might not

be the dominating dispersion quantity.

Beside the peak values of the acting stress the energy input on

the particle or at the surface of it might be the leading dispersing

quantity. Therefore, the energy input per surface Esalong the path

which is dened as

Es E

S

Z lull

sdl with l l andlu f sc 21

was tracked. The critical stress sc is the stress which is required to

act on the particles or at least their structure. As it is unknown in

this work two randomly chosen values are used to characterise the

different geometries. If the stress s exceeds the critical stress sc(the chosen values are sc 10

5 Pa and sc 106 Pa) the lower

boundl l was set; if the stress falls below those critical values the

upper bound lu was set. For every path line the highest integral

was used to quantify the surface energy. The probability to face

such an surface energy for both critical values is shown in Fig. 9

(surface energies with a critical stress ofsc 105 Pa are shown in

bright colours while surface energies with a critical stress of

sc 106 Pa are shown in powerful colours).

It can be seen that there are huge differences between both

tracked surface energies. While the straight channel offers the

highest surface energies for the lower critical stress it does not

even reach the higher critical stress, i.e. no curve is shown in Fig. 9.

Due to the constant velocity and turbulence in the entire micro-

channel the product of stress and distance is high as long the

critical stress is smaller than the stress acting in the channel. By

increasing the critical stress sc the other three channels which

offer higher peak values due to higher pressure gradients enable

higher surface energies.

Furthermore, it can be seen that for a critical stress of

sc 106 Pa between 10 and 40% of the particles does not face a

surface stress. Also, the behaviour of the three remaining micro-channel geometries changes. While the z-channel leads to the

highest probability to face a specic stress the order of the orice

and y-channel changes if the critical stress varies. This behaviour

can be used as an indicator to estimate the real critical stress as

both channels behave similar in the dispersing results. Hence, it

can be stated that if the surface energy is the dominant dispersing

parameter its value should be at least above sc 105 (and possibly

above sc 106 Pa).

3.3. Stresses in the microchannels of the 1st generation

Comparing the experimental performed dispersing results leads

to the assumption that the computed stresses of the z-channel are

overestimated. The straight, y- and orice channel behave like the

Fig. 7. Peak value distribution of the maximum stress (left) and normalized maximum stress (right) acting on the particles for the ori ce channel for pressure differences

betweenp 50 and 500 bar.

Fig. 8. Peak value distribution of the main stress acting on particles for the fourmicrochannels for a pressure difference ofp 100 (bright colours) and 500 bar

(powerful colours). (For interpretation of the references to colour in this gure

caption, the reader is referred to the web version of this paper.)

Fig. 9. Probability for a particle to face a specic surface energy above two different

critical values while passing the four different microchannels at a pressure ofp 500 bar (the straight channel offers no stress values above s 106 Pa). (For

interpretation of the references to colour in this gure caption, the reader is

referred to the web version of this paper.)


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experimental results would expect (for peak stresses and surface

energy), while the z-channel defers. Due to the underestimated mass

ow (seeFig. 2) the stress of the orice channel should be under-

estimated, while the others have not to be corrected (correct mass

ow). Compared to the other investigated three channel geometries

the z-channel offers two wide redirections which lead to swirls and

heavily curved streamlines. This behaviour leads to very high

Reynolds stresses which result in higher stresses acting on the

particles and might be the reason for the overestimation.

3.4. Microchannels of the 2nd generation inuence of cavitation

and steam

Another interesting inuence on the dispersing efciency of

different microchannel geometries is the effect of cavitation and,

hence, steam. Therefore, investigations with the orice channel of

the 2nd generation were performed. The effect of cavitation on the

mass ow is presented inFig. 10. For the experimental investiga-

tions an backpressure was applied which increases the static

pressure occurring in the entire channel to a sufcient level which

prevails cavitation and eliminates all steam regions. According to

these results single- and multiphase simulations were performed.

It can be stated that the mass ow is in excellent agreement for

the two investigated pressure differences with or without applied

backpressure. Compared to the results of the 1st generation this

could be based on the ner mesh of the newer microchannel

geometries or the increased dimensions of the channel and the

orice itself (30 68m2 increased up to 80 50m2).In addition, the effect on the mass ow due to the increased

resistance caused by cavitation can be seen, too. The viscosity of

steam is much lower than liquid water and, hence, the inner

friction of the uid is reduced. This would lead to higher mass ow

rates for multiphase systems. But on the other hand, the region

after the orice itself should not inuence the ow before and in

the orice itself. Short before the orice and in the orice the

shear stress of the uid is the highest. The difference in both cases

is that already in the orice cavitation occurs and leads to steam.Even for higher pressures the density of steam is much lower than

in liquid state. Therefore, the creation of steam head to a reduced

cross-sectional area and, hence, to an increased resistance. As long

as steam (created due to cavitation) is present in the orice (but

not in the vena contracta) the mass ow should be lower

compared to the single phase case.

According to the work ofGothsch et al. (2014)there is no linear

increasing mass ow rate between a backpressure of pb 0 bar

andpb 175 bar at constant pressure difference between inlet and

outlet p 200 bar. The mass ow increases up to an back-pressure of pb 90 bar and remains constant for higher back-

pressures. It is expected that the mass ow rate will become

constant if no cavitation occurs as the pressure difference between

inlet and outlet is constant. It could be shown that for a back-

pressure ofpb 90 bar cavitation and, hence, steam is only created

in the vena contracta. If the steam remains in the vena contracta

there is no inuence of it on the uid ow due to the decrease in

density. This explanation is supported by the pressure distribution

shown in Fig. 11. It can be seen that the very low (negative)

pressure (which would lead to steam if no backpressure is applied)

is only present in the vena contracta. Therefore, already low

backpressures can reduce regions especially behind the orice

where steam is present.

In Table 2 the required, calculated backpressures to prevent

cavitation and the ratio between backpressure and pressure

difference between inlet and outlet are listed. Additionally, the

required measured backpressures to receive a constant mass ow

rate and the appropriate ratio are listed, too. It can be seen that

higher pressure differences require higher backpressures to get the

same behaviour. The difference between experimental and simu-

lative gained results is based on the described effect (backpressure

inuence on the mass ow). The equation to calculate the lowest

occurring pressurepminin the simulations to suppress cavitation is

pmin 0:505 p1:10 22

and to calculate the experimentally gained backpressure pb to

reach a constant mass ow is

pb 0:076 p1:33: 23

The italic values in Table 2 represent values gained from

Eqs. (22) and (23). It can be seen that the pressure to reach a

constant mass ow and, hence, to allow cavitation only in the vena

contracta (leading to a constant mass ow) increases rapidly

compared to the lowest pressure which would suppress cavitation

in the whole microchannel. The extrapolated value to gain a

constant mass ow for a pressure difference at p 1000 bar isin good agreement with the experimental results (as a constant

mass ow was not reached).

Fig. 10. Experimentally measured and computed mass ow for different inlet

pressures with/without backpressure for the new orice channel.

Fig. 11. Pressure distribution in the 2nd generation orice channel at a pressure of

p 200 bar without cavitation.

Table 2

Applied pressure differences and lowest occurring pressures which suppress

cavitation (received from simulations) and required backpressures to gain a

constant mass ow rate (received from experiments).

Pressure difference (bar) Lowest pressure

(simulations)(bar)

Back pressure

(experiments)(bar)

100 81.7 35

200 175.7 90

300 274.9 150

500 483.4 3001000 1039.3 Z700 755


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In Fig. 12 the particle tracking for the new orice channel is

presented. The stress is normalized by the pressure to enable an

easy comparison between different pressures and between the

single- and multiphase simulation. The powerful coloured lines

represent the previously described computed stress. Due to the

fact that the curves with and the curves without cavitation are

almost identical for varying pressure differences it can be con-

cluded that there is an almost linear dependency on the peak

values of the stress and the pressure. Furthermore, it can be seen

that the reduced mass ow of the multiphase simulations leads to

an reduced level of acting stresses. This is in good agreement with

the experimental data.

3.5. Evaluation of the magnitude of the turbulent stress

In the following two different stresses are investigated: rst the

stress 50% of all particles would face, second the stress only 10%

of all particles would face. Those stress values for a pressure

difference ofp 200 bar without cavitation are used to calculatethe shear strain of the uid:

50 smax;50= 1:29 109 1=s and

10 smax;10= 3:24 109 1=s: 24

Dividing the maximum velocity (which is about vmax 250 m=s)

by the shear strain the radius of the required eddies can be

calculated:

d50 2 vmax=50 388 nm andd10 2 vmax=10 154 nm: 25

If the length scale for the smallest eddies dened byKolmogor-

ov is used, the lower limit of occurring eddies could be calculated

using the turbulent dissipation rate found in the simulation:

k;sim 38 nm 26

The eddy size computed with the dissipation rate out of the

computed Reynolds-stress tensoris in congruence. Again, with the

length scale dened by Kolmogorov it is possible to calculate an

lower limit at which the dissipation of energy due to uid friction

occurs. For the second approach, Eq. (13) with the maximum

occurring velocity vmaxand the lowest length (half of the height of

the channel l 25m) is used to receive an lower limit for this

length scale:

k 3

1=4

3 l

v3max

1=4 33 nm od10od50 27

It can be seen that the computed stresses used by theReynolds-

stress tensor and the maximum velocity seem to be in the range

which could be delivered by the occurred turbulence. To identify

the order of the turbulence stress inFig. 12the stress calculated by

the averaged velocity gradients (brighter colours) is shown, too.These computed velocity gradients are lower than the real stresses

and two to three orders of magnitude lower than the turbulent

stress computed by the Reynolds-stress model . Hence, it can be

stated that the stress is caused by fully turbulent ows. The ratio of

particles and Kolmogorov length scale is about

dpk

230 nm

33153 nm 1: 28

Hence, the turbulence stress could act on the particles and

could be the leading breakage mechanism.

4. Conclusion

In the present study a model to calculate the stress based on

uid velocity gradients and theReynolds-stress tensoris presented.

Based on the Jacobi method a single value which represents the

uid stress can be calculated for every position in the microchan-

nel. With a stationary particle tracking these stresses could be

tracked. Beside the stress the relative velocities and the energy per

surface were tracked. With the normal uid velocity component at

the inlet a weighting of all maximum values for every seeding

point was possible to enable a quantication of different geome-

tries for varying pressure differences. Five different microchannel

geometries were investigated: a straight, a z-, a y- and an ori ce

channel of the 1st generation and a orice channel of the 21nd

generation. The rst ones were used to compare the results with

previously gained results based on simulations with a k model.

The mass ow rate was used as an indicator for the quality

of the simulations. Compared to the k model the results from

simulations based on the Reynolds-stress model are an improve-

ment and offer (partly excellent) agreement with the experimental

results. Only the orice channel of the 1st generation differs a bit.

Due to the increase of the cell number of the mesh, the improved

accuracy of the turbulence model compared to the previous work

and the excellent agreement in mass ow rate for the orice

channel of the 2nd generation it can be stated that further

improvements of model and ner meshes will not lead to the

identical mass ow rate. As the dimension of the orice channel of

the 1st generation is the smallest and the fabrication method

changed from the 1st to the 2nd generation the difference could be

induced due to the different dimensions and/or fabrication inac-curacies. The calculated stresses are in good agreement except for

the z-channel which offers two redirections which lead to swirls

and highly curved streamlines. It could be shown that the max-

imum stress as well as the energy per surface can be the dominant

breakage mechanism (while the maximum stress as leading

breakage mechanism is more reasonable).

For the orice channel of the 2nd generation the focus was on

the inuence of the cavitation and steam regions. The mass ow

was in excellent agreement with the experimental data. It could be

shown that the simulations can reproduce the cavitation and

steam effects. Additionally, the experiments and simulations sup-

port the explanation for the reduced mass ow: as long as the

steam is limited to the vena contracta the mass ow is constant. If

the steam regions expand into the orice itself a reduction occurs.

Fig. 12. Peak value distribution of the normalized main stress and stress due to

velocity gradients acting on particles for the new orice channels for a pressure

difference ofp 100 and 200 bar with and without cavitation. (For interpretation

of the references to colour in this gure caption, the reader is referred to the web

version of this paper.)


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Furthermore, it was shown that the turbulence ow and the

eddies are in the range which might be responsible for the

breakage of the particles. The stress computed with the developed

model is in the range of reasonable occurring turbulent ows.

Hence, the increased computational costs for solving the six

additional equations for the Reynolds-stress tensorresult in an

improved quality of the owelds and quantication possibilities.

List of symbols

Latin symbols

E energy (J)

d fractal dimension ()

dp m particle diameter

h height, depth (m)

k turbulent kinetic energy (m2=s2)

ki body force, index notation (N/kg)

l length (m)

p pressure (Pa)

b backpressure (Pa)

r radius (m)

s stress (Pa)

sc critical stress (Pa)

sn normalized stress ()

s! stress vector (Pa)

su0 , su stress induced by velocity (Pa)

sij stress tensor (Pa)

S surface (m2)

t time (s)

tij transformed stress tensor (Pa)

ui velocity, index notation (m/s)

vmax maximum velocity (m/s)

V volume (m3)

x50 median particle size (m)

xi coordinates, index notation (m)

Greek symbols

turbulent dissipation rate (m2=s3)

viscosity (Pa s)

k Kolmogorov length scale (m)

kinematic viscosity (m2=s)

density (kg=m3)

ij stress component (Pa)

k Kolmogorov time scale (s)

m mass ratio ()

v volume ratio ()

Acknowledgments

The authors gratefully acknowledge the DFG for nancial

support within the DFG research group 856 Mikrosysteme fuer

partikulaere Life-Science-Produkte (mikroPART) (KW 9/6-2).

References

Beinert, S., Gothsch, T., Kwade, A., 2012. Numerical evaluation of ow elds andstresses acting on agglomerates dispersed in high-pressure microsystems.Chem. Eng. Technol. 35 (11).

Beinert, S., Schilde, C., Gronau, G., Kwade, A., 2014. Cfd-discrete element method

simulations combined with compression experiments to characterize stirred-

media mills. Chem. Eng. Technol. 37 (5) .Capitaine, E.M.R., Hill, J.M., 2012. Determination of the fractal dimension of alumina

using adsorption: challenges of choosing appropriate adsorbates and analysis

methods. Can. J. Chem. Eng. 90 (3).Gothsch, T., Finke, J.H., Beinert, S., Lesche, C., Schur, J., Bttgenbach, S., Mller-

Goymann, C., Kwade, A., 2011. Effect of microchannel geometry on high-

pressure dispersion and emulsication. Chem. Eng. Technol. 34 (3).Gothsch, T., Schilcher, C., Richter, C., Beinert, S., Dietzel, A., Bttgenbach, S., Kwade,

A., 2014. High-pressure micro

uidic systems (hpms):

ow and cavitationmeasurements in supported silicon microsystems. Microuid. Nanouid.,

http://dx.doi.org/http://dx.doi.org/10.1007/s10404-014-1419-6 , online.Gradl, J., Peukert, W., 2009. Simultaneous 3d observation of different kinetic

subprocesses for precipitation in a t-mixer. Chem. Eng. Sci. 64 (4) .Gradl, J., Schwarzer, H.-C., Schwertrm, F., Manhart, M., Peukert, W., 2006.

Precipitation of nanoparticles in a t-mixer: coupling the particle population

dynamics with hydrodynamics through direct numerical simulation. Chem.

Eng. Process.: Process Intensif. 45 (10).Gui, N., Fan, J., Chen, S., 2010. Numerical study of particle-vortex interaction and

turbulence modulation in swirling jets. Phys. Rev. EStat. Nonlinear Soft Matter

Phys. 82 (5).Gui, N., Yan, J., Fan, J., Cen, K., 2013. A dns study of the effect of particle feedback in a

gas-solid three dimensional plane jet. Fuel 106.Jasiska, M., Badyga, J., Cooke, M., Kowalski, A., 2013. Application of test reactions

to study micromixing in the rotor-stator mixer (test reactions for rotor-stator

mixer). Appl. Therm. Eng. 57 (12), 172179. http://dx.doi.org/http://dx.doi.

org/10.1016/j.applthermaleng.2012.06.036 .

Jasiska, M., Badyga, J., Hall, S., Pacek, A.W., 2014. Dispersion of oil droplets inrotor-stator mixers: Experimental investigations and modeling: E. Chem. Eng.

Process. 84, 4553. http://dx.doi.org/10.1016/j.cep.2014.02.008.Lesche, C., Krah, T., Bttgenbach, S., 2011. Microelectro discharge machiningan

innovative method for the fabrication of 3d microdevices. In: Proceedings of

SPIEThe International Society for Optical Engineering, vol. 8066.Makowski, L., Orciuch, W., Badyga, J., 2012. Large eddy simulations of mixing

effects on the course of precipitation process. Chem. Eng. Sci. 77 .Masuda, K., Suzuki, H., Komoda, Y., Hidema, R., 2013a. Aggregation/dispersion

behaviors ofne particles in aow between parallel plates. J. Chem. Eng. Jpn 46

(8).Masuda, K., Suzuki, H., Komoda, Y., Hidema, R., 2013b. Particle dispersion/aggrega-

tion model in a non-uniform shear ow. Nihon Reoroji Gakkaishi 41 (2), 34.Messa, G.V., Malin, M., Malavasi, S., 2013. Numerical prediction of pressure gradient

of slurry ows in horizontal pipes. In: American Society of Mechanical

Engineers, Pressure Vessels and Piping Division (Publication) PVP, vol. 4.Messa, G.V., Malin, M., Malavasi, S., 2014. Numerical prediction of fully-suspended

slurry ow in horizontal pipes. Powder Technol. 256 .

Pennella, F., Rossi, M., Ripandelli, S., Rasponi, M., Mastrangelo, F., Deriu, M.A.,Ridol, L., Khler, C.J., Morbiducci, U., 2012. Numerical and experimental

characterization of a novel modular passive micromixer. Biomed. Microdevices

14 (5).Porta, G.M., Thovert, J.F., Riva, M., Guadagnini, A., Adler, P.M., 2012. Microscale

simulation and numerical upscaling of a reactive ow in a plane channel. Phys.

Rev. EStat. Nonlinear Soft Matter Phys. 86 (3).Raasch, J., 1961. Beanspruchung und verhalten suspendierter feststoffteilchen in

scherstroemungen hoher zaehigkeit (Ph.D. thesis). TH Karlsruhe.Schilde, C., Kampen, I., Kwade, A., 2010. Dispersion kinetics of nano-sized particles

for different dispersing machines. Chem. Eng. Sci. 65 (11).Schilde, C., Mages-Sauter, C., Kwade, A., Schuchmann, H.P., 2011. Efciency of

different dispersing devices for dispersing nanosized silica and alumina.

Powder Technol. 207 (13).Stiess, M., 2009. Mechanische VerfahrenstechnikPartikeltechnologie 1, 3rd Edi-

tion Springer, Berlin.Tong, Z.B., Zheng, B., Yang, R.Y., Yu, A.B., Chan, H.K., 2013. Cfd-dem investigation of

the dispersion mechanisms in commercial dry powder inhalers. Powder

Technol. 240.VDI-Gesellschaft Verfahrenstechnik und Chemieingenieurwesen, 2013. VDI-

Waermeatlas. Berechnungsunterlagen fuer Druckverlust, Waerme- und Stof-

fuebergang, 11th Ed. Springer, Berlin.Wang, B., Manhart, M., 2012. Two-phase micro- and macro-time scales in particle-

laden turbulent channel ows. Acta Mech. Sin./Lixue Xuebao 28 (3).Wengeler, R., 2007. Hydrodynamic Stress Induced Dispersion of Nanoscale Agglom-

erates by a High Pressure Process (Ph.D. thesis). TH Karlsruhe.Wengeler, R., Nirschl, H., 2007. Turbulent hydrodynamic stress induced dispersion

and fragmentation of nanoscale agglomerates. J. Colloid Interface Sci. 306 (2).

http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref1http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref1http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref1http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref1http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref1http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref1http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref1http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref1http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref2http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref2http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref2http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref2http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref3http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref3http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref3http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref3http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref4http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref4http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref4http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref4http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref4http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref4http://dx.doi.org/%3Cmac_doitxt%3E10.1007/s10404-014-1419-6http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref6http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref6http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref6http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref7http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref7http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref7http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref7http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref7http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref7http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref7http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref8http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref8http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref8http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref8http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref8http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref8http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref9http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref9http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref9http://dx.doi.org/%3Cmac_doitxt%3E10.1016/j.applthermaleng.2012.06.036http://dx.doi.org/%3Cmac_doitxt%3E10.1016/j.applthermaleng.2012.06.036http://dx.doi.org/%3Cmac_doitxt%3E10.1016/j.cep.2014.02.008http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref13http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref13http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref13http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref13http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref13http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref14http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref14http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref14http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref14http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref14http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref14http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref14http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref14http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref15http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref15http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref15http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref15http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref15http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref17http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref17http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref17http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref17http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref17http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref18http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref18http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref18http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref18http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref18http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref18http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref18http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref19http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref19http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref19http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref19http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref19http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref19http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref19http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref19http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref21http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref21http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref21http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref22http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref22http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref22http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref22http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref22http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref22http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref22http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref22http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref23http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref23http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref23http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref23http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref23http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref24http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref24http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref24http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref24http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref26http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref26http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref26http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref26http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref26http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref28http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref28http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref28http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref28http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref28http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref26http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref26http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref24http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref24http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref24http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref23http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref23http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref22http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref22http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref22http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref21http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref21http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref19http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref19http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref19http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref18http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref18http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref18http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref18http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref17http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref17http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref15http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref15http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref14http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref14http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref14http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref13http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref13http://dx.doi.org/%3Cmac_doitxt%3E10.1016/j.cep.2014.02.008http://dx.doi.org/%3Cmac_doitxt%3E10.1016/j.cep.2014.02.008http://dx.doi.org/%3Cmac_doitxt%3E10.1016/j.cep.2014.02.008http://dx.doi.org/%3Cmac_doitxt%3E10.1016/j.applthermaleng.2012.06.036http://dx.doi.org/%3Cmac_doitxt%3E10.1016/j.applthermaleng.2012.06.036http://dx.doi.org/%3Cmac_doitxt%3E10.1016/j.applthermaleng.2012.06.036http://dx.doi.org/%3Cmac_doitxt%3E10.1016/j.applthermaleng.2012.06.036http://dx.doi.org/%3Cmac_doitxt%3E10.1016/j.applthermaleng.2012.06.036http://dx.doi.org/%3Cmac_doitxt%3E10.1016/j.applthermaleng.2012.06.036http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref9http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref9http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref8http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref8http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref8http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref7http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref7http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref7http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref7http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref6http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref6http://dx.doi.org/%3Cmac_doitxt%3E10.1007/s10404-014-1419-6http://dx.doi.org/%3Cmac_doitxt%3E10.1007/s10404-014-1419-6http://dx.doi.org/%3Cmac_doitxt%3E10.1007/s10404-014-1419-6http://dx.doi.org/%3Cmac_doitxt%3E10.1007/s10404-014-1419-6http://dx.doi.org/%3Cmac_doitxt%3E10.1007/s10404-014-1419-6http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref4http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref4http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref4http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref3http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref3http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref3http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref2http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref2http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref2http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref1http://refhub.elsevier.com/S0009-2509(14)00619-8/sbref1http://re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