micro flows: an introduction michael shusser
DESCRIPTION
MICRO FLOWS: AN INTRODUCTION Michael Shusser. SIZE RANGES OF MACRO, MICRO, AND NANO DEVICES. FLUID FLOW AND HEAT TRANSFER IN SINGLE-PHASE FLOW OF A NEWTONIAN FLUID IN A MICRO-CHANNEL. NO MULTIPHASE FLOW NO POLYMERS OR BIO-FLUIDS NO COMPLEX GEOMETRIES NO ELECTRO-KINETIC FLOWS. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/1.jpg)
1
MICRO FLOWS: AN INTRODUCTION
Michael Shusser
![Page 2: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/2.jpg)
2
SIZE RANGES OF MACRO, MICRO, AND NANO DEVICES
![Page 3: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/3.jpg)
3
FLUID FLOW AND HEAT TRANSFER IN SINGLE-PHASE
FLOW OF A NEWTONIAN FLUID IN A MICRO-CHANNEL
• NO MULTIPHASE FLOW• NO POLYMERS OR BIO-FLUIDS• NO COMPLEX GEOMETRIES• NO ELECTRO-KINETIC FLOWS
![Page 4: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/4.jpg)
4
IS EVERYTHING
DIFFERENT OR JUST
SMALLER?
![Page 5: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/5.jpg)
5
IS THE CONTINUUM APPROXIMATION VALID?
POSSIBLE NON-CONTINUUM EFFECTS:
• SLIP AT THE BOUNDARY• STRESS/RATE OF STRAIN
RELATION IS NONLINEAR• CONTINUUM APPROXIMATION
FAILS
![Page 6: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/6.jpg)
6
FOR THE TIME BEING WE ASSUME THAT THE
CONTINUUM THEORY IS VALID
• LIQUIDS
• GASES FOR L > 5 μM
![Page 7: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/7.jpg)
7
MANY OF STUDIES OF BASIC HEAT AND FLUID FLOW PROBLEMS IN
BASIC GEOMETRIES FOUND LARGE DEVIATIONS FROM EXPECTED
RESULTS
• FRICTION FACTOR f
• NUSSELT NUMBER Nu
• CRITICAL REYNOLDS NUMBER ReC
5.3f
f5.0
MACRO
MICRO
16Nu
Nu2.0
MACRO
MICRO
43.0Re
Re13.0
MACRO,C
MICRO,C
![Page 8: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/8.jpg)
8
LAMINAR FLOW OF AN INCOMPRESSIBLE FLUID WITH CONSTANT PROPERTIES IN A
CIRCULAR PIPE
• FRICTION FACTOR
• REYNOLDS NUMBER
• POISEUILLE NUMBER
dx
dp
r
ur
rr
1
Du
Re mD
2u
Ddx
dp
f2m
DRefPo
![Page 9: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/9.jpg)
9
DRe
64f 64Po
![Page 10: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/10.jpg)
10
SCALING EFFECTS• THE EFFECTS THAT CAN BE
NEGLECTED IN MACRO SCALES BUT ARE IMPORTANT IN MICRO SCALES ARE CALLED SCALING EFFECTS
• PROVIDED THE CONTINUUM APPROXIMATION REMAINS VALID, ALL THE DISCREPANCIES BETWEEN MICRO AND MACRO FLOWS CAN BE EXPLAINED AS SCALING EFFECTS
![Page 11: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/11.jpg)
11
• ENTRANCE EFFECTS
• VISCOUS HEATING
• TEMPERATURE- AND PRESSURE DEPENDENT PROPERTIES
• WALL ROUGHNESS
• COMPRESSIBILITY
• CONJUGATE HEAT TRANSFER
• AXIAL HEAT CONDUCTION
![Page 12: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/12.jpg)
12
ENTRANCE EFFECTS
FOR LAMINAR FLOW IN A CIRCULAR PIPE
Dhyd,fd Re05.0
D
X PrRe05.0
D
XD
therm,fd
![Page 13: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/13.jpg)
13
WATER FLOW IN A 2D CHANNEL – CFD/EXPERIMENT
ReD
xx
h
![Page 14: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/14.jpg)
14
• ENTRANCE EFFECTS ARE NOT ALWAYS NEGLIGIBLE IN MICRO FLOWS
• DEVELOPING FLOW IS STRONGLY INFLUENCED BY THE INLET VELOCITY PROFILE
• THERE IS NOT ENOUGH DATA ON ENTRANCE EFFECTS FOR VARIOUS CROSS-SECTIONS
![Page 15: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/15.jpg)
15
VISCOUS HEATING
ENERGY EQUATION FOR FLOW IN A PIPE
VISCOUS HEATING
(VISCOUS DISSIPATION)
Tk
uBr
2m
2
2
2
dr
du
PrRe
Br
r
Tr
rr
1
x
T
PrRe
1
x
Tu
![Page 16: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/16.jpg)
16
BRINKMAN NUMBER• THE IMPORTANCE OF THE VISCOUS
HEATING TERM IS DETERMINED BY THE BRINKMAN NUMBER
• FOR EXAMPLE, FOR CONSTANT HEAT FLUX
• IN MACRO FLOWS VISCOUS HEATING IS IMPORTANT ONLY FOR VERY VISCOUS FLUIDS OR VERY HIGH VELOCITIES
Br229.0
1
Br4811
48Nu
![Page 17: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/17.jpg)
17
• IN MICRO FLOWS BRINKMAN NUMBER IS USUALLY VERY SMALL
• WATER: μ = 8.55·10-4 kg(m·s) k = 0.613 W/(m·K)
ΔT = 1 ºC um = 0.1 m/s Br ≈ 1.4·10-5
• AIR: μ = 1.846·10-5 kg(m·s) k = 0.0263 W/(m·K)
ΔT = 1 ºC um = 1 m/s Br ≈ 7·10-4
• THE INFLUENCE OF VISCOUS HEATING ON HEAT TRANSFER IN MICRO FLOWS IS USUALLY NEGLIGIBLE
Tk
uBr
2m
![Page 18: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/18.jpg)
18
VISCOUS HEATING CAN BE IMPORTANTDUE TO VERY STRONG DEPENDENCE OFLIQUID VISCOSITY ON TEMPERATURE
WATER T = 300 K ν = 8.576·10-7 m2/s T = 310 K ν = 6.999·10-7 m2/s
TEMPERATURE RISE OF 10 K CAUSES18% DECREASE IN KINEMATIC VISCOSITYWHICH RESULTS IN CORRESPONDINGINCREASE OF THE LOCAL Re NUMBERAFFECTING THE FRICTION FACTOR
![Page 19: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/19.jpg)
19
THERMAL EXPLOSIONTHE MOMENTUM AND ENERGY
EQUATIONS FOR FULLY DEVELOPED
FLOW IN A CIRCULAR PIPE ARE
FOR EXPONENTIAL DEPENDENCE OF
LIQUID VISCOSITY ON THE
TEMPERATURE
dr
dur
dr
d
r
1
dx
dp
20
0
000 RT
TTEexp
RT
Eexp
RT
Eexp
0dr
du
kdr
dTr
dr
d
r
12
![Page 20: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/20.jpg)
20
INTRODUCING NEW VARIABLES
THE ENERGY EQUATION REDUCES TO
IT HAS NO SOLUTION FOR
NO FULLY DEVELOPED FLOW!
20
2
r
r
20
0
RT
TTE
0ed
d1
d
d2
2
01 0d
d
0
const
2
![Page 21: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/21.jpg)
21
ISOPROPANOL FLOW IN A SQUARE MICRO CHANNEL
• L = 11.4 cm; D = 74.1 μm; (L/D = 1543)
• FOR Re ≈ 300 Tin - Tout =6.2 oC
![Page 22: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/22.jpg)
22
EXAMPLE OF A CFD RESULT
• INLET CONDITIONS
D= 20 μm; T = 300 K ν = 8.576·10-7 m2/s
Re = 2000 V = 85.76 m/s !
![Page 23: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/23.jpg)
23
• VISCOUS HEATING HAS USUALLY NO INFLUENCE ON HEAT TRANSFER IN MICRO FLOWS
• ITS INFLUENCE ON FRICTION FACTOR CAN BE IMPORTANT DUE TO VERY STRONG DEPENDENCE OF LIQUID VISCOSITY ON TEMPERATURE, ESPECIALLY FOR LONG CHANNELS
![Page 24: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/24.jpg)
24
VARIABLE PROPERTIES• DUE TO LARGE GRADIENTS IN MICRO
FLOWS THE DEPENDENCE OF PROPERTIES ON PRESSURE AND TEMPERATURE IS IMPORTANT
• LIQUIDS SHOULD BE MODELED AS INCOMPRESSIBLE WITH TEMPERATURE-DEPENDENT VISCOSITY
• SOMETIMES PRESSURE-DEPENDENCE OF VISCOSITY SHOULD ALSO BE TAKEN INTO ACCOUNT
![Page 25: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/25.jpg)
25
LIQUID FLOW AT 30 MPa
![Page 26: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/26.jpg)
26
COMPRESSIBILITY EFFECTS
• THE FRICTION-INDUCED PRESSURE DROP PER TUBE LENGTH COULD BE LARGE IN FLOW THROUGH A NARROW CHANNEL
• COMPRESSIBILITY EFFECTS CAN BE IMPORTANT IN GAS FLOWS EVEN FOR LOW MACH NUMBERS
![Page 27: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/27.jpg)
27
PRESSURE AND DENSITY VARIATIONS ALONG THE TUBE AT DIFFERENT INLET
MACH NUMBERS
![Page 28: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/28.jpg)
28
WALL ROUGHNESS• ROUGHNESS LEADS TO INCREASING
FRICTION FACTOR AT THE SAME Re NUMBER AND DECREASING VALUE OF THE CRITICAL Re NUMBER (EARLIER TRANSITION FROM LAMINAR TO TURBULENT FLOW)
• THE INFLUENCE OF THE ROUGHNESS IS DETERMINED BY ITS GRAIN SIZE ks AND FRICTION VELOCITY v* (OR WALL SHEAR STRESS τw)
w*v
0rrw r
u
![Page 29: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/29.jpg)
29
FLOW REGIMES FOR ROUGH PIPES
HYDRAULICALLY SMOOTH
LAMINAR
TURBULENT
TRANSITION TURBULENT
COMPLETELY
ROUGH
TURBULENT
Reff 5vk
0 *S
70vk
5 *S
70vk *S
Re,Re
kff s
Re
kff s
![Page 30: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/30.jpg)
30
• FOR LOW Re (D < 100 μm) SOME EXPERIMENTS OBSERVED DEVIATIONS FROM THE CLASSICAL THEORY INCLUDING THE INFLUENCE OF ROUGHNESS IN LAMINAR FLOW
• ONE POSSIBLE REASON FOR THE DISCREPANCY IS NON-UNIFORMITY OF THE ROUGHNESS
• THERE IS NOT ENOUGH DATA ON INFLUENCE OF ROUGHNESS ON HEAT TRANSFER
![Page 31: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/31.jpg)
31
CONJUGATE HEAT TRANSFER• IN MICRO FLOWS THE RELATIVE
THICKNESS OF THE CHANNEL WALL s/Dh IS USUALLY MUCH LARGER THAN IN MACRO FLOWS
• THEREFORE CONVECTIVE HEAT TRANSFER IN THE FLUID AND HEAT CONDUCTION IN THE WALL MUST BE ACCOUNTED FOR SIMULTANEOUSLY
• THIS CONJUGATED HEAT TRANSFER IS USUALLY NEGLIGIBLE FOR MACRO FLOWS
![Page 32: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/32.jpg)
32
EXPERIMENT
• LAMINAR FLOW Re ≈ 50 L/D ≈ 160
• CONSTANT WALL HEAT FLUX
![Page 33: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/33.jpg)
33
THEORETICAL SOLUTION
• WALL TEMPERATURE
• BULK TEMPERATURE
• NUSSELT NUMBER
constcm
q
dx
dT
p
ww
constcm
q
dx
dT
p
wm
36.411
48
k
D
TT
qNu
mw
w
![Page 34: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/34.jpg)
34
EXPERIMENT - RESULTS
![Page 35: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/35.jpg)
35
CFD – CONJUGATE HEAT TRANSFER INCLUDED
![Page 36: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/36.jpg)
36
AXIAL CONDUCTION NUMBER
• THE IMPORTANCE OF THE CONJUGATE HEAT TRANSFER IS GIVEN BY THE AXIAL CONDUCTION NUMBER M
VceL
ek
Mf
ss
conv
//cond
![Page 37: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/37.jpg)
37
• THE NUMBER M IS USUALLY VERY LOW FOR MACRO CHANNELS (HIGH V, SMALL eS/ef, LARGE L) BUT CAN BE LARGE FOR MICRO CHANNELS (LOW V, eS/ef IS NOT SMALL, SMALL L)
• FOR LARGE M THE WALL HEAT FLUX BECOMES STRONGLY NON-UNIFORM: MOST OF THE HEAT IS TRANSFERRED TO THE FLUID NEAR THE ENTRANCE TO THE CHANNEL
![Page 38: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/38.jpg)
38
AXIAL HEAT CONDUCTIONENERGY EQUATION FOR FLOW IN A PIPE
AXIAL HEAT CONDUCTION
• AXIAL HEAT CONDUCTION CAN USUALLY BE NEGLECTED UNLESS PECLET NUMBER IS VERY LOW
r
Tr
rr
1
x
T
Pe
1
x
Tu
2
2
50PrRePe
![Page 39: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/39.jpg)
39
• OILS: Pr >>1 LIQUIDS: Pr ~ 5
GASES: Pr ~ 0.7 LIQUID METALS: Pr << 1
• IN MACRO FLOWS THE AXIAL HEAT CONDUCTION IS NEGLIGIBLE EXCEPT LIQUID METAL FLOWS
• IN MICRO FLOWS THE AXIAL HEAT CONDUCTION SOMETIMES MUST BE TAKEN INTO ACCOUNT
![Page 40: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/40.jpg)
40
TURBULENCE IN MICRO FLOWS
• MICRO FLOWS ARE USUALLY LAMINAR (Re < 2000)
• MOST EXAMPLES OF TURBULENT FLOW ARE USUALLY FOR RELATIVELY LARGE DIAMETERS (D > 300 μm)
• FOR LARGE PRESSURE DIFFERENCE, GAS FLOWS CAN BE TURBULENT EVEN FOR SMALL DIAMETERS
![Page 41: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/41.jpg)
41
CFD: PIPE FLOW• D = 50 μm; PIN ≈ 20 atm; POUT ≈ 2 atm
• VISCOUS COMPRESSIBLE TURBULENT FLOW
• INLET: VX ≈ 125 m/s Re ≈ 25,000
• DO STANDARD TURBULENCE MODELS (LIKE k-ε) WORK IN THIS CASE?
![Page 42: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/42.jpg)
42
NON-CONTINUUM EFFECTS - GASES
• THE FLOW IS RAREFIED FOR GASES AND THE WALLS “MOVE”
• TO A CERTAIN DEGREE THE SITUATION IS SIMILAR TO LOW-PRESSURE HIGH-ALTITUDE AERONAUTICAL FLOWS
• HOWEVER, REYNOLDS AND MACH NUMBERS ARE MUCH LOWER
![Page 43: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/43.jpg)
43
MOLECULAR MAGNITUDES• NUMBER DENSITY OF MOLECULES n
• MEAN MOLECULAR SPACING δ
• MOLECULAR DIAMETER dDILUTE GAS: δ/d > 7 AIR:
THE DATA FOR p = 1 atm; T = 0 ºC
Tk
pn
B
325m1069.2n
3/1n m103.3 9
m107.3d 10
![Page 44: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/44.jpg)
44
MEAN FREE PATH• THE DISTANCE TRAVELED BY THE
MOLECULES BETWEEN COLLISIONS IS KNOWN AS MEAN FREE PATH λ
AT p = 1 atm; T = 25 ºC
GAS AIR N2 CO2 O2 He Ar
λ, nm 61.1 60.4 40.2 65.0 176.5 64.4
2nd
12
![Page 45: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/45.jpg)
45
KNUDSEN NUMBER
• THE KEY DIMENSIONLESS PARAMETER IS THE KNUDSEN NUMBER Kn
Kn < 0.01 CONTINUUM
0.01 < Kn <0.1 SLIP FLOW
0.1 < Kn < 10 TRANSITIONAL FLOW
Kn > 10 FREE-MOLECULAR FLOW
Re
M
2LKn
![Page 46: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/46.jpg)
46
LIMITS OF APPROXIMATIONS
![Page 47: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/47.jpg)
47
NON-CONTINUUM EFFECTS - LIQUIDS
• FOR SUFFICIENTLY HIGH STRAIN RATE THE STRESS/RATE OF STRAIN AND HEAT FLUX/TEMPERATURE GRADIENTS RELATIONS BECOME NONLINEAR
HERE τ IS THE MOLECULAR TIME-SCALE
• THE CRITICAL VALUE IS VERY HIGH FOR ORDINARY LIQUIDS BUT NOT SO FOR COMPLEX FLUIDS
2
y
u
![Page 48: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/48.jpg)
48
FUTURE DIRECTIONS OF RESEARCH
![Page 49: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/49.jpg)
49
CONCLUSIONS• PROVIDED THE CONTINUUM
APPROXIMATION REMAINS VALID, ALL THE DISCREPANCIES BETWEEN MICRO AND MACRO FLOWS CAN BE EXPLAINED AS SCALING EFFECTS
• THE MAIN SCALING EFFECTS ARE VARIABLE PROPERTIES, COMPRESSIBILITY, CONJUGATE HEAT TRANSFER
• SOME INFLUENCE OF ENTRY LENGTH, VISCOUS HEATING, AXIAL HEAT CONDUCTION AND ROUGHNESS IS ALSO POSSIBLE
![Page 50: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/50.jpg)
50
REFERENCES1. Bayraktar & Pidugu, Int J Heat Mass Trans, 20062. Cui et al, Phys Fluids, 20043. Gad-el-Hak, Int J Heat Mass Trans, 20034. Gamrat et al, Int J Heat Mass Trans, 20055. Guo & Li, Int J Heat Mass Trans, 20036. Herwig & Hausner, Int J Heat Mass Trans, 20037. Herwig, ZAMM, 20028. Hetsroni et al, Int J Heat Mass Trans, 2005, p. 19829. Hetsroni et al, Int J Heat Mass Trans, 2005, p. 558010. Judy et al, Int J Heat Mass Trans, 200211. Karniadakis & Beskok, Micro Flows, 200212. Koo & Kleinstreuer, Int J Heat Mass Trans, 200413. Maranzana et al, Int J Heat Mass Trans, 2004
![Page 51: MICRO FLOWS: AN INTRODUCTION Michael Shusser](https://reader036.vdocuments.us/reader036/viewer/2022062719/56813256550346895d98e096/html5/thumbnails/51.jpg)
51
THANKS!