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Numerical Simulation On Multiphysics Coupling Field Of Microfluidics Chips

Posted on:2007-12-17Degree:DoctorType:Dissertation
Country:ChinaCandidate:P ZhangFull Text:PDF
GTID:1118360182497122Subject:Mechanical design and theory
Abstract/Summary:PDF Full Text Request
The structure characteristics of microfluidic phenomena are the microchannel network,and its main application object is life science. And its main work principal is to control theflow in the microchannels. Aiming at the multiphysics field coupling problems ofmicrofluidics chips, the computer numerical simulation technology is adopted to investigatethoroughly the rules of the flow transportation phenomena in microchannels. The researchcontents of this dissertation are as following:In the first part, the actuality of oversea and inland microfluidics chips research isanalyzed. The structure and characteristics of microfluidics chips are introduced. Thencategories of the driving and controlling the microflow are introduced. And the advantages anddisadvantages of electroosmotic and pressure-driven flow needed to be studied in thedissertation are discussed in detail. And the basic problems of the miroflow dynamics arepointed out. Due to the difference between the micro and macro scale, the micro flow involvesscale effects, surface effects and multiphase/multiphysics coupling problems. The study datumof oversea and inland electroosmotic flow are summarized and analyzed. And the existentproblems at present are pointed out. There are much domestic and oversea information aboutmicro flow, but there is no integrate theory to guide the practice. So the numerical simulationmethod is adopted in the dissertation to study the electrokinetic theory of the micro flow. Andit is used to guide the designs of the pressure-driven pumping, electroosmotic pumping andmicrofluidic chip, to optimize their parameters of design and improve their performance. Atlast, the research contents of this dissertation are assured according to the existent problems ofmicrofluidics at present, and the research method and technical scheme are presented.In the second part, the electrokinetic theory in microchannels is investigated. Theelectrokinetic effects are the important phenomena of the microflow. The electrokineticphenomena can be divided into four categories: electroosmosis, electrophoresis, streamingpotential and sedimentation potential. The two kinds of electrokinetic phenomena ofelectroosmosis and streaming potential are investigated in this dissertation. When the surfacesof the disperse system bear electric charges, it will attract the ions of opposite charges to thatof the solid surface in the electrolyte solution, and the whole system is electrically neutral.Thus the "electrical double layer" (EDL) is formed. The key to the quantity description of theEDL lies in the EDL model. The shape of microchannel made by modern micromachingtechnology is mostly rectangular. The research object is rectangular channels, and thetwo-dimensional EDL governing equation is studied. In order to obtain easily the numericalsolution, the governing equation is dimensionless. Then the form mechanism of electroosmoticflow is introduced. The electric field force due to the interaction between net charge density inthe EDL regime and the applied electric field is considered, the governing equation ofelectroosmotic flow is obtained, i.e. the modified Navier-Stokes equation. Thetwo-dimensional steady and transient state equations governing electroosmotic flow arepresent in detail. At last, the main simplifying assumptions and approximations involved inthis dissertation are given.In the third part, the discretized equations based on the finite control volume method areinvestigated. Considering that the equations needed to be solved in this dissertation aretwo-dimensional, nonlinear, partial differential equation, the corresponding discretizedequations of problems are detruded using the finite control volume method which isintroduced in the Patankar's book. And they are the steady two-dimensional discretizedequations involving diffusion term and non-linear source term (e.g. Poisson-Boltzmannequation) and the transient two-dimensional discretized equations involving diffusion term(e.g. modified Navier-Stokes equation). Take example for a microchannel between the twoparallel plates, the linear Debye-Huckel approximate analytical solution is used to validate theprogram. The results show that the linear approximation analytical solution can not reflectpreferably the changes of the potential and velocity in the EDL close to the wall for the case ofbigger zeta potential. And this may result in an error in modeling the electrokinetic flowbehavior in microchannels if the linear approximation is used to solve the Possion-Boltzmannequation. The linear Debye-Huckel approximation is not used in solving thePossion-Boltzmann equation in this dissertation. Then the program of solving thePossion-Boltzmann equation is compiled by means of Matlab, and the profile of potential inmicrochannels is obtained. The influences of electrokinetic parameter, K, solutionconcentration and zeta potential on the potential contribution are discussed. When theconcentration of solution decreases which implies the electrokinetic parameter becomes small,the thickness of EDL is comparable to the size of the microchannel. The electrical doublelayers between the walls will reciprocity, and the charge density in the centerline ofmicrochannel is not zero. The EDL field will influence the whole microchannel, and result inthe potential in the centerline of microchannel is not zero. The aspect ratio effect on thepotential distribution is studied for the same hydraulic diameter. As can be seen from thepotential contour, the corner effect becomes obvious with the increase of the aspect ratio. Andthe corner effect on the potential is maximal when the aspect ratio is one.In the fourth part, the electrokinetic effects on pressure-driven flow in microchannels areinvestigated. The pressure-driven flow in microchannels is investigated using theelectrokinetic theory model. And the electrokinetic theory is enriched and perfected. Thepressure-driven flow can result in streaming potential, and it builds up a reverse electric field.The electric field force due to the interaction between net charge density in the EDL regimeand the induced electric field is considered, so the equation governing the pressure-driven flowinvolves the induced electric field and pressure-driven flow field coupling. And it is solved bymeans of the finite control volume method. With consideration of electrokinetic effects, themaximal velocity in the centerline of microchannels becomes smaller due to the presence ofelectroviscous effects. The electroviscous effects become stronger with the decrease of theionic concentration of the liquid which implies the zeta potential increases. At the micro scale,the velocity distribution, volumetric flowrate and friction coefficient are significantlyinfluenced by the EDL field with consideration of electrokinetic effects and hence deviatefrom the results described by classical fluid mechanics. The effects of the size and the shape ofmicrochannels, the concentration of solution and the applied pressure gradient on the averagevelocity, volumetric flow rate, streaming potential and friction coefficients are discussed withconsideration of electrokinetic effects. The conclusions can be obtained as following:Firstly, for a fixed hydraulic diameter, the volumetric flowrate of the pressure-driven flowin microchannels decrease as the aspect ratio (i.e. the geometric ratio of channel height towidth) increases, but the average velocity increases at the same time. In the case of a fixedaspect ratio, the average velocity and volumetric flowrate all increase with the increase of thehydraulic diameter. As the hydraulic diameter increases, the volumetric flowrate can reach theorder of the ml/min magnitude, and the electrokinetic effects become weaker. In the samemicrochannel, the volumetric flowrate and average velocity all increase with the increase ofthe concentration of solution. If the concentration of solution is higher, which implies that theDebye-Huckel parameter is larger, namely, the EDL thickness is smaller, less ions are carriedto the downstream with the flow and hence lower charge accumulation at the ends of thechannel occurs. So the induced streaming potential becomes smaller, and this results in thelarger volumetric flowrate and average velocity. The volumetric flowrate and average velocityall increase linearly with the pressure gradient.Secondly, for a fixed hydraulic diameter of the microchannel, the streaming potential isincreased with the increase of the aspect ratio. And as the aspect ratio approaches one (for asquare channel), the streaming potential is maximal. In the case of a fixed aspect ratio themicrochannel, the streaming potential increases linearly with the increase of hydraulicdiameter. In the same mircrochannel, the streaming potential decreases as the concentrationincreases, and the induced streaming potential increases linearly with the increase of thepressure gradient. In the absence of an externally applied electric field, when a fluid is forcedto flow through a channel under a hydrostatic pressure difference, the ions in EDL region arecarried to the downstream. The ion concentration difference between the upstream and thedownstream of the microchannels results in an induced electrokinetic potential. A largerpressure difference will generate a larger volume transport and hence more ions are carried tothe downstreame of the channel. Therefore, the induced streaming potential becomes largerwhen the pressure difference increases.Thirdly, the friction coefficients predicted by the model with consideration ofelectrokinetic effects are higher than that by the classical fluid mechanics. When the hydraulicdiameter is the same, the friction coefficients predicted by the model with consideration ofelectrokinetic effects and by the classical fluid mechanics all decrease with the increase of theaspect ratio. And as the aspect ratio approaches one, the friction coefficient has the minimum.Unlike that the friction coefficient for a rectangular microchannels by the classical fluidmechanics is dependently only on the aspect ratio, the friction coefficients predicted by themodel with consideration of electrokinetic effects are dependent of the microchannel size.When the hydraulic diameter decreases, the friction coefficients increases and theelectroviscous effects become stronger for the same aspect ratio of the microchannel. As theconcentration of solution decreases which implies that the zeta potential increases in the samemicrochannels, the friction coefficient increases and the electroviscous effects becomestronger. The friction coefficients for the rectangular microchannels predicted by the modelwith consideration of electrokinetic effects are independent of the pressure gradient, and this isthe same as that from the classical fluid mechanics.And the relationship between the pressure gradients and Reynolds numbers in threemicrochannels for three concentrations of solution is numerically computed usingelectrokinetic theory models. The predictions of electrokinetic flow model have a goodagreement with the experimental datum. So the electrokinetic flow model in the dissertationproves to be right and reliable. The numerical results show that the friction coefficients of thepressure-driven flow in three microchannels with consideration of electrokinetic effects underthe micro scale are higher than that without consideration electrokinetic effects under themacro scale. The zeta potential and the concentration of solution have impacts on the frictioncoefficients. In the same microchannel, the lower the concentration of solution is, the higherthe friction coefficient is. And the friction coefficients are independent of Reynolds numberson the whole.In the fifth part, the influence factors of electroosmotic flow in a microchannel areinvestigated numerically. After solving the two-dimensional Poisson-Boltzmann equation, themodified Navier-Stokes equation is solved farther. In the steady state, the dependence of thepotential, velocity, average velocity and volumetric flowrate on the aspect ratio, hydraulicdiameter, liquid properties and the applied electric field is analyzed in detail. The fittingpolynomials of the relationships between volumetric flow, average velocity and influencefactors are presented. And they are used to guide us design the microfluidics chips andelectroosmotic pumping, and to optimize their parameters of design. The conclusions can beobtained as following:Firstly, for a fixed hydraulic diameter, the volumetric flowrate decreases as the aspectratio increases and the average velocity shows no dependence on the aspect ratio. In particular,as the aspect ratio approaches one(i.e. the square microchannel), the flowrate is minimal. Thisis because of the corner effect become more significant as the square channel geometry isapproached. The same volumetric flowrate is achieved when the channel was rotated by 90degrees, demonstrating that the orientation of the channel is not significant as long as theelectric field is applied tangentially to the channel.Secondly, when the hydraulic diameter decreases, the velocity and potential in the regionvery close to the microchannel wall drop off slowly for a fixed aspect ratio. The volumetricflowrate increased with approximately the square of hydraulic diameter for a fixed aspect ratio.So when larger pumping flowrate is desired, larger diameter channels would seem to be abetter choice at the microscale. However, caution should be used in choosing large channelsbecause the increase of average velocity is not obvious.Thirdly, the concentration of solution has much impact on the potential, velocity andvolumetric flowrate in the same microchannel. When the concentration of solution decreases,the potential close to the wall drops off slowly. From the fitting polynomial, it can be seen thatthe average velocity and volumetric flowrate decrease linearly with the logarithm of theconcentration of solution.Forthly, when the concentration of solution is fixed in the same microchannel, thepotential has no change basically in the range of researchful electric field strength. There is alinear variation in the average velocity and volumetric flowrate with the applied electric fieldstrength. It should be noted that the upper limit for the applied electric field should beconsidered, because the potential temperature increase caused by the heat generated with theapplied voltage which has not been included in this model.The numerical results show that the needed time that the electroosmotic flow gets to thesteady state is the order of millisecond magnitude when the hydraulic diameter is 48μm andthe applied electric field strength is 105V/m. The mechanism of momentum transfer of thetransient electroosmotic flow is analyzed. To begin with, the ions in the EDL are driven by theelectric field forces and drag its surrounding liquids from zero (no-slip velocity) rapidly to getto the maximum. As the time elapsed, the momentum transfers to the center of themicrochannel and the electroosmotic flow gets to the steady state. And the electroosmotic flowin the center of the microchannel moves with a fixed velocity. The effects of influence factorson the needed time that the electroosmotic flow gets to the steady state are discussed under theunsteady state. And the conclusions can be obtained as following:Firstly, the needed time that the electroosmotic flow gets to the steady state is longer asthe aspect ratio decreases for a fixed hydraulic diameter. At the same time, the biggervolumetric flowrate of electroosmotic pumping can be obtained.Secondly, the electroosmotic flow gets to the steady state instantaneously in the case ofthe small hydraulic diameter (i.e. 10μm~20μm). With the increase of hydraulic diameter, ittakes longer time that the electroomotic flow gets to the steady state. But the bigger volumetricflowrate can be obtained.Thirdly, in the same microchannel, the needed time that the electroosmotic flow gets tothe steady state is uniform basically with the different solution concentration. And thevolumetric flowrate dereases as the solution concentration increases.Fourthly, when the concentration of solution and zeta potential are fixed in the samemicrochannel, the smaller the electric field strength, the shorter the needed time that theelectroosmotic flow gets to the steady state. So when larger pumping flowrate is desired undera fixed microchannel, larger electric field strength would seem to be a better choice. However,caution should be used in choosing large electric field strength due to the presence of Jouleheating. And the electric field strength has an upper limit.In the sixth part, Joule heating effect on the electroosmotic flow in the rectangularmicrochannel is numerically investigated. Polymeric materials have recently been reported asan alternative material for the fabrication of microfluidic devices due to the versatility andease of fabrication as compared with glass. Due to the poor thermal conductivity of polymermaterials, the heat transfer of the polymer-based microfluidic systems may become a problem.In order to improve polymeric chip design and thereby extend the capabilities of thesemicrofluidic systems, Joule heating effect on the temperature fields during electroosmosis inglass and PDMS polymer-based rectangular microchannels is numerically investigated withthe finite element method. And the temperature fields in PDMS-based microchannel withdifferent size are compared. The mathematical models on Joule heating effects includePoisson-Boltzmann equation governing the EDL field, the modified Navier-Stokes equationsgoverning flow field and the energy equation governing the temperature field due to Jouleheating. These fields are strongly coupled via temperature-dependent liquid properties. Unlikemomentum and species transport analysis, which is confined to the fluidic domain, the heattransfer problems have to be solved in the solid-liquid coupled regions. According toMacInnes's analysis based on the order of magnitude, the temperature fields and flow fieldsare decoupled. And this method makes the problem become easier greatly. The temperatureincrease due to the presence of Joule heating effects is obtained by means of the decoupledenergy equation. The conclusions can be obtained as following:Firstly, under the same condition, the temperature increment is high up to 70K in aPDMS made microchannel, and the temperature increment is lower than 10K in a glass mademicrochannel. Compared with the temperature increment in a PDMS made microchannel, theJoule heating effect in a glass made microchannel is not significant.Secondly, in a PDMS made microchannel, the temperature increment becomes biggerwith the decrease of the aspect ratio when the solution concentration is 100mM, the electricfield strength is 500V/cm, and the hydraulic diameter is 48μm. When the aspect ratio is 1/4,the temperature increment is high up to 100K.Thirdly, in a PDMS made microchannel, the temperature increment becomes bigger withthe increase of the hydraulic diameter when the solution concentration is 100mM, the electricfield strength is 500V/cm, and the aspect ratio is 1/3. When the hydraulic diameter is 54μm,the temperature increment is high up to 100K.Fourthly, in a PDMS made microchannel with the same size (e.g. the aspect ratio is 1/3and the hydraulic diameter is 48μm), when the electric field strength is 500V/cm, for the dilutesolution(C=1mM), the Joule heating effect may be ignored, and for the higher concentrationsolution(C=100mM), the temperature increment is high up to 70K.Fifthly, in a PDMS made microchannel with the same size (e.g. the aspect ratio is 1/3 andthe hydraulic diameter is 48μm), when the solution concentration is 100mM, for the lowerelectric field strength (E=100V/cm), the Joule heating effect may be ignored, and for thehigher electric field strength (E=500V/cm), the temperature increment is high up to 70K.In the seventh part, it is the summary of the whole dissertation. The main researchachievements and innovative discovers are expatiated. And the future development trends ofthe research are prospected.
Keywords/Search Tags:Microfluidics Chips, Electokinetic Theory, Multiphysics Field Coupling, Numerical Simulation, Finite Control Volume Method
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