advanced lab course in physics
TRANSCRIPT
Technical University of MunichFaculty of PhysicsChair of Physics of Biological Sys-tems
Advanced Lab Course in Physics
Construction and Operation of aMicrofluidic Device
Supervisor: Anna Jakel
ZNN 2.012
Contents
Nomenclature 2
1 Introduction 3
2 Theoretical Background and Methods 32.1 Microfluidics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 The Navier Stokes Equation . . . . . . . . . . . . . . . . . . . . . 32.3 Dimensionless Hydrodynamics . . . . . . . . . . . . . . . . . . . . 42.4 Microfluidic Circuits . . . . . . . . . . . . . . . . . . . . . . . . . 52.5 Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.6 Lithographie . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.7 Materials Used for Microfluidic Experiments . . . . . . . . . . . . 72.8 Preparation of a PDMS Chip . . . . . . . . . . . . . . . . . . . . 92.9 Filling of a Microfluidic Chip . . . . . . . . . . . . . . . . . . . . 92.10 Fluorescence Microscopy . . . . . . . . . . . . . . . . . . . . . . . 11
3 Experimental Part 113.1 Preparation of a PDMS Chip . . . . . . . . . . . . . . . . . . . . 113.2 Bond PDMS to a Glassslide . . . . . . . . . . . . . . . . . . . . . 113.3 Fill Microfluidic Device . . . . . . . . . . . . . . . . . . . . . . . 113.4 Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4 Information for Your Report 12
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Nomenclature
ddH2O Double distilled water
FITC Fluorescein isothiocyanate
PDMS Polydimethylsiloxane
Re Reynolds number
Si Silicon
SU-8 Epoxy-based negative photoresist
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1 Introduction
Microfluidics refers to the science and engineering of systems in which fluid be-havior differs from conventional flow theory primarily due to the small lengthscale of the system [1, p. 1]. Thus, the key feature of microfluidic devices is theuse and the manipulation of small fluid amounts (10 · 10−9 to 10 · 10−18 L) inchannel structures with dimensions of tens to hundreds of micrometers [1, p. 1].First successes in this field were the development of a gas chromatograph basedon a silicon chip [2] and the development of an inkjet printer [3].
Objective of the Lab Course
In this lab course you will produce and operate a microfluidic device. Thisdevice will be used to conduct a diffusion experiment, from which the diffusionconstant of FITC in agarose can be calculated.
2 Theoretical Background and Methods
In this section, the theoretical concepts which guide the experiment are intro-duced.
2.1 Microfluidics
The used fluids in microfluidic applications show significant deviations in theirbehavior from those of liquids in the macro world. They are dominated byinterfacial tension, electrostatic, and electrokinetic forces, whereas the macroworld is dominated by inertial forces and gravity [4, p. 1]. Also, other effectslike laminar flow play a role when working with microfluidic devices. As longas the Reynolds number (ratio of inertial forces to viscous forces within a fluid)Re < Recritical the flow is dominated by laminar flow and shows no turbulence.Laminar flow describes a type of flow where the fluid travels smoothly on regularpaths with no irregular fluctuations or mixing between the different layers (Fig.1). Such conditions, in combination with controlled diffusion, can create anenvironment for temporally and spatially highly resolved reactions with littlereagent consumption [5]. Steady-state conditions can be achieved trough theaccurate control and manipulation of fluids which provides a great environmentto study biochemical reactions.
2.2 The Navier Stokes Equation
The motion of viscous fluid substances can be described by a set of partialdifferential equations which solution is a vector field v(r(t), t), the flow velocity.Because of mass conservation (no annihilation or creation of atoms) in a closedfluidic system
δtρ+ div(ρv) = 0 (1)
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Figure 1: Laminar flow profile in a cylindrical tube. The arrows depict theinfinitesimal parallel layers of the flow with no disruptions between them. Aparabolic fluid profile follows.
follows, where ρ is the mass desity. When applying now Newton’s 2nd law, theforce on a region W is:
F =
∫W
fd3r (2)
with the force density:
f = ρv(r(t), t) = ρ(δtv + (δtri)δiv) = ρ(δt + v · ∇) =: ρDtv, (3)
whereDt denotes the total time derivative. There are two types of forces, surfaceforces and external forces like gravity. Surface forces emerge from a pressure pand viscous drag which is described with the drag tensor [σij ]:
Fg =
∫W
gρd3r, (4)
Fs = −∫W
∇pd3r +
∫W
∇[σij ]d3r. (5)
When there is no viscous drag the forces can be inserted in equation 3 and
ρDtv = −∇p+ ρg (6)
results. When there is viscous drag the viscous stress can be described by
σij = CijklVkl +O(V 2), (7)
with Vkl being the rate-of-strain tensor. The isotropic tensor Cijkl can be sim-plified for isotropic fluids and when using the Stokes hypothesis λ = − 2
3η theNavier-Stokes equation for a Newtonian fluid follows:
ρDtv = ρg −∇p+1
3η∇(∇ · v) + η∆v. (8)
2.3 Dimensionless Hydrodynamics
The Navier Stokes equation (Eq. 8) can not be solved analytically. For certainproblems approximations can be made, because some terms might be dominant.
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For convenience and also to describe the systems behavior independently of scalethe Navier Stokes quation is often written in dimensionless form. Dimensionlessvariables can be defined as
r′ =r
L0v′ =
v
v0t′ =
t
t0p′ =
p
p0
g=
g
|g|, (9)
with the characteristic scales for length L0, time t0, pressure p0, and the averageflow velocity v0. The Reynolds number is probably the most famous one:
Re :=ρv0L0
η. (10)
It describes the ratio between the inertial and the viscous drag forces. There isa threshold, the critical Reynolds number Rec which defines the transition fromlaminar to turbulent flow. Below this value viscous drag damps any fluctua-tions and as a result the flow is laminar. Above Rec the inertia term becomespredominant and the flow is turbulent. For microfluidic channels a typical flow
rate of v0 = 400µLh−1
(20µm)2 ≈ 300mms−1 can be estimated. With L0 = 10µm,
ρ = 1gcm−3, and η = 1mPas a Reynoldsnumber of ≈ 3 can be obtained. Thisis smaller than the critical Reynoldsnumber of 2300 which can be estimated forcylindrical pipes with the radius L0 [6].
2.4 Microfluidic Circuits
Microfluidic circuits are in their description very similar to electric circuits. Inboth cases, the circuits are configurations of components through which eitherelectricity or fluids are allowed to flow. The circuits can be composed of re-sistors, capacitors, inductors, or transitors. Thereby microfluidic devices cancontrol flow rates, flow directions, particle separation, mixing and reactions ofchemicals. [7]
Because the viscous forces are dominant over the inertia of the fluids inmicrofluidic channels the flow becomes laminar (Fig. 1). As a result turbulenceeffects cannot be used to control flow. Thus, most microfluidic devices usedfor pressure-driven flow are based on fluid resistance. The impedance of thefluid path or the mass flow rate can be changed to regulate the fluid. Thefluidic impedance or fluidic resistance can be calculated by dividing the pressuredifference ∆P by the flow rate Q:
R =∆P
Q(11)
For a planar channel (Length L x width W x heigth H) the fluid resistance isgiven by
R = 12µL
WH3(12)
where µ is the viscosity of the fluid [7].
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Figure 2: Illustration of diffusion along a concentration gradient in an enclosedsystem. In (1) two sorts of particles are separated by a barier. As soon thebarrier is removed (2) the particles diffuse along their concentration gradient,which leads to total mixing of the two substances (3). The undirected randommotion (brownian motion due to their thermal energy) is indicated by the redarrow. [8]
2.5 Diffusion
Diffusion describes the movement of particles along a concentration gradient dueto brownian motion. This process leads to entirely mixing of different materialsin enclosed systems. The flux of particles can be described with Fick’s first law:
J = −D ∂c
∂x, (13)
where c denotes the concentration of a particle species, x denotes the distancethat the particles travel along, and D is called the diffusion constant. Wheninserting the continuity equation 1 into Ficks first law the second law can bederived:
∂c
∂t= D
∂2c
∂t2. (14)
Through separation of the variables the diffusion constant can be calculatedwith:
D =< x2 >
2t. (15)
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2.6 Lithographie
For the construction of microfluidic devices lithography normally would be thefirst step in the microfabrication. There exist several lithographic techniquesas electron-beam lithography, greyscale lithography, X-ray lithography, focusedion-beam lithography, or holographic lithography. All these techniques do havein common that they include low speed processes and therefore are not suitablefor mass production. But they can be used to fabricate reverse 3D microstruc-tures as molds that can then be used to produce the final devices by casting [9].Silicon substrates are often used as molds for the final devices, but also polymersas SU-8 have widely been used as substrates due to their biochemical compat-ibility and ease of fabrication. Various 3D mold fabrication techniques havebeen developed in recent decades. They include photoresist reflow, inkjet print-ing, and unconventional lithographic methods. One of them is the grayscalelithography which uses locally modulated exposure doses to manufacture themold for the microfluidic device. For grayscale litography the epoxy-based neg-ative photoreist SU-8 can be used. It becomes cross-linked after an exposure toultraviolet (UV) light. It is called a negative photoresist because only the mi-crofluidic structures get to be exposed so that they crosslink and the remaindercan be washed away after exposure due to the fact that it stays soluble. [10]The next step in the production of microfluidic devices is the transfer of thestructure from the mold to another polymer. Also here several techniques areavailable for selection, among them soft litography (Fig. 3). It is probably theeasiest and most intuitive one. The polymere material is casted directly ontothe mold and polymerized then by heat or UV light. After polymerization itcan be peeled of and bonded to a substrate like glass.The bonding of the polymer and the substrate can be achieved through plasma-activated bonding, for this oxygen is one of the most common used gases. Withinseconds hydroxy-group can be integrated in the treated surface. The hydroxy-groups can then react with other chemical groups in the surface of the secondmaterial, so that strong e.g. Si-O-Si groups can be formed [11, p. 218].
2.7 Materials Used for Microfluidic Experiments
The Microfluidic devices used here are fabricated with PDMS. PDMS belongsto a group of polymeric organosilicon compounds that are commonly referredto as silicones. Due to its properties as being chemically inert, thermally stable,permeable to gases, being optically clear and its low costs it can be used for avariety of applications. Also, it is ”simple to handle and manipulate, exhibitsisotropic and homogeneous properties ..., and can conform to submicron featuresto develop microstructures” [13].PDMS is well suited for the fabrication of microfluidic devices via soft litographyas suggested by Whitesides [14][15], due to its advantages like the resolution of20µm [15] and that tubing can be directly plugged in after using a biopsy punch.Also, the low autofluorescence behavior in the visible spectrum is beneficial forreal time imaging [16].
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Figure 3: Single steps of oftlithography. A Si wafer with the wanted structureon top, made from SU-8, is used as a mold. PDMS is casted on top of the waferand baked afterwards. The resulting PDMS chip and a substrate (here glass)are bonded together after treating the surfaces with O2 plasma. [12]
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2.8 Preparation of a PDMS Chip
For the preparation of the microfluidic devices, PDMS and a curing agent (Syl-gard 184, Dow Corning) have to be mixed in a 10:1 ratio. Thorough mixingfor 1 min has to be performed. For 2 inch wafers, 12 g of PDMS and 1.2 g ofcuring agent should be used, to achieve a height of ∼ 4 mm. The mixture willbe poured on a clean silicon wafer and transferred into a desiccator. It has tobe degased for 15 min and baked afterwards for 1 h at 80 ◦C. The PDMS chipcan then be detached from the wafer after cooling down to room temperature(25 ◦C) and the devices can be cut to size with a scalpel. Holes for the tubinghave to be punched with a biopsy punch (diameter = 0.5 mm). Afterwards thedevices have to be cleaned with scotch magic tape. Glass object slides (75.77 mmx 25.78 mm x 1 mm), used as substrates, will be cleaned in an ultrasonic bathwith Hellmanex for 15 min and in a ddH2O bath for 5 min, and then dried inan oven for 30 min at 80 ◦C. Eventually, the PDMS and object slide surfaces,that should stick together, will be activated by an exposure to O2 plasma for0.7 min. The two pieces will be placed on each other with the prepared sidesfacing each other and bonded with a soft touch. To ensure propper bonding,the devices will be baked at 80 ◦C for 1 h.
2.9 Filling of a Microfluidic Chip
The microfluidic devices (Fig. 4) will be operated in an IX71 microscope. Theflows can be regulated with a syringe pump (typical flow rates 50 µl
h ). As sam-ple reservoirs, 1.5 mL Eppendorf tubes were used, which were filled typicallywith around 20µL of 2 % SLM agarose (Super low melt agarose, Roth), or120µL sample solution. The sample reservoirs can be connected with the de-vices through flexible plastic tubing (TygonR© ND 100-80 tubing, Saint-Gobain),which can be plugged into the devices with metal pins as connectors. The metalpins were turned off from syringe needles (0.6 mm ID). The devices will first beflushed with the agarose mixture after ensuring a vacuum in the side chan-nels through sucking the air out with a syringe. The filling of the sidechannelstakes usually around 5 min. When every sidechannel is filled, the device will beflushed through the feeding channel with air to ensure a free channel. Only thefeeding channel will be cleared by the air and the sidechannels will still be filledwith the agarose mixture. After another 5 min, the device will be connected tothe sample reservoir. Flow through will be collected in an Eppendorf tube. Atime-lapse observation of the diffusion can be performed with an Olympus IX71or a Nikon Ti-2 inverted fluorescence microscope.Agarose is commonly used for gelelectrophoresis to determine the length of DNAwith concentrations varying from 0.7 % to 2 %. Here, it is used as a medium forFITC to observe its diffusion.
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Figure 4: Sketch of the used microfluidic device. The main channel is calledfeeding channel. It is used in a first step to fill the sidechannels, called gelchannel, with gel and afterwards used to flush the device with FITC. There aretwo channels on the side used to create a vacuum to facilitate the filling of thesidechannels with gel, this works because the PDMS is air permeable.
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2.10 Fluorescence Microscopy
As meantioned above, microfluidic devices from PDMS can be used for fluo-rescence intensity measurements. These measurements are based on the char-acteristics of fluorescence and are widely used to quantitatively visualize andcharacterize biological reactions. During those measurements, molecules (usu-ally called fluorophores, fluorescent dyes or fluorescent proteins) are used thatemit light, after they absorbed energy from incoming light of a specific wave-length. The wavelength of the emitted light is no longer than the one of theabsorbed light. The emitted light can be detected because the microfluidicstructures from PDMS are optically clear. The measurement of fluorescenceintensity is very useful because the fluorescent molecules are really sensitive andspecific to the studied process [17]. Here, FITC is used.
3 Experimental Part
This section the single steps of the experiment are described. Firstly, a PDMSchip will be prepared, afterwards it will be loaded with the sample and finallya 30 min video will be taken of the diffusing FITC in the agarose gel.
3.1 Preparation of a PDMS Chip
• weight the two components
• mix them together with spatula (for at least 1min)
• prepare a casting mold
• degase chip in a descicator
• bake the chip
3.2 Bond PDMS to a Glassslide
• cut chip to correct size
• clean glasslides with sonicator
• clean glassslides and PDMS with plasma
• bond glass and PDMS together
• bake microfluidic device
3.3 Fill Microfluidic Device
• fill the chip with 2% agarose
• clean the filling channel
• flush the chip with FITC solution
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Figure 5: Microscopy image of the used microfluidic device with a 10x objective.
3.4 Microscopy
• take single pictures every 2min for half an hour
• use brightfield and GFP channel
• an overview of the microfluidic channels is shown in Fig. 5
4 Information for Your Report
The report should contain the following:
• short introduction
• answer the question why PDMS is used for the microfluidic devices
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• analyse the microscopy data: kymograph
• determine the diffusion constant of FITC in agarose
• compare the diffusion constant with theoretical values
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References
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[3] Kurt E Petersen. “Fabrication of an integrated, planar silicon ink-jet struc-ture”. In: IEEE Transactions on electron devices 26.12 (1979), pp. 1918–1920.
[4] Nam-Trung Nguyen. Mikrofluidik: Entwurf, Herstellung und Charakter-isierung. Springer-Verlag, 2013.
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[6] Klaus Gersten. “Hermann Schlichting and the Boundary-Layer Theory”.In: Hermann Schlichting–100 Years. Springer, 2009, pp. 3–17.
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[8] Wikipedia. Diffusion. url: https://de.wikipedia.org/wiki/Diffusion(visited on 05/26/2021).
[9] Ji Fang, Weisong Wang, and Shulin Zhao. “Fabrication of 3D microfluidicstructures”. In: Encyclopedia of microfluidics and nanofluidics. Springer,Berlin (2015), pp. 1069–1082.
[10] Frederik Ceyssens and Robert Puers. “SU-8 Photoresist”. In: Encyclo-pedia of Nanotechnology. Ed. by Bharat Bhushan. Dordrecht: SpringerNetherlands, 2012, pp. 2530–2543. isbn: 978-90-481-9751-4. url: https://doi.org/10.1007/978-90-481-9751-4_360.
[11] Sami Franssila. Introduction to microfabrication. John Wiley & Sons,2010.
[12] Upenn. Softlithography. url: https://www.seas.upenn.edu/~nanosop/Intro_SoftLitho.htm (visited on 04/06/2021).
[13] Alvaro Mata, Aaron J Fleischman, and Shuvo Roy. “Characterization ofpolydimethylsiloxane (PDMS) properties for biomedical micro/nanosystems”.In: Biomedical microdevices 7.4 (2005), pp. 281–293.
[14] J Cooper McDonald, David C Duffy, Janelle R Anderson, Daniel T Chiu,Hongkai Wu, Olivier JA Schueller, and George M Whitesides. “Fabri-cation of microfluidic systems in poly (dimethylsiloxane)”. In: ELEC-TROPHORESIS: An International Journal 21.1 (2000), pp. 27–40.
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[15] J Cooper McDonald, Michael L Chabinyc, Steven J Metallo, Janelle RAnderson, Abraham D Stroock, and George M Whitesides. “Prototyp-ing of microfluidic devices in poly (dimethylsiloxane) using solid-objectprinting”. In: Analytical chemistry 74.7 (2002), pp. 1537–1545.
[16] Philip Wagli, BY Guelat, A Homsy, and NF De Rooij. “Microfluidic de-vices made of UV-curable glue (NOA81) for fluorescence detection basedapplications”. In: Proceedings of the 14th International Conference onMiniaturized Systems for Chemistry and Life Sciences, Groningen, TheNetherlands. 2010, pp. 3–7.
[17] Gea O. F. Parikesit. “Fluorescence Measurements”. In: Encyclopedia ofMicrofluidics and Nanofluidics 2 (2008).
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