James Feng

Bio-mimicking microfluidic devices have been developed to provide a biologically relevant framework for drug development and toxicological studies. This dissertation aims to describe three case studies in the area of particle and cell transport in bio-mimicking microfluidic devices using finite-element simulations.In the first study, we model the deposition of submicron particles on the epithelial layer of a well-established lung-on-a-chip device. As main results of the study, our simulations predict enhanced submicron particle deposition during physical exercising, subject to opposing effects of elevated air volume and breathing frequency. Moreover, the deposition efficiency varies non-monotonically with particle size, due to the distinct effects of gravitational settling and Brownian motion.In the second case study, we propose a biomechanical model for the passage of a tumor cell through the endothelial cells monolayer. Based on prior in vitro observations, we assume that the tumor cell extends a protrusion between adjacent endothelial cells that adheres to the extracellular matrix. Inside the protrusion, a contractile element composed of stress-fibers and focal-adhesions pulls the nucleus through the endothelial opening. We modeled the chemo-mechanics of the contractile element as well as the elastic deformation and cytosolic flow during transmigration process. Using physiologically reasonable parameters, our model shows that the contractile element can produce a force on the order of 70 nN, which is sufficient to deform the endothelial cells for transmigration. The third project deals with the tenertaxis hypothesis. During immune reaction, leukocytes transmigrate either directly through the body of an individual endothelial cell (the transcellular route) or from the junction between adjacent endothelial cells (the paracellular route). What determines the usage of one route over the other is ambiguous. A recently proposed tenertaxis hypothesis claims that leukocytes choose the path with less mechanical resistance against leukocyte protrusions. Our simulations results show that the required force to breach the endothelium through the transcellular route is greater than paracellular route (22 pN versus 15 pN). Moreover, experiments have demonstrated that manipulation of the relative strength of endothelial resistance can make the transcellular route preferable. Our simulations have confirmed this reversal, and thus tentatively confirmed the hypothesis of tenertaxis.

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During tissue morphogenesis forces at the cellular level cause deformation of tissues. Through complex interactions organs are able to develop from epithelial sheets. This work explores the role that sub-cellular organization of signalling proteins, force generation at the cellular level and collective cell behavior have during tissue morphogenesis. Using a class of biophysical model for cellular mechanics known as the vertex model, biological questions concerning two developmental processes are explored. In the first study, a two-dimensional vertex model for drosophila dorsal closure predicts the mechanics of cell oscillation and contraction from the dynamics of the PAR proteins. Using experimental observations of PAR protein dynamics, a system of differential equations models their behavior. By coupling to the vertex model for cellular mechanics, it is shown how the oscillation of cell area results from an intracellular negative feedback loop that involves myosin, an actomyosin regulator, aPKC and Bazooka. In the slow phase, gradual sequestration of apicomedial aPKC by Bazooka causes incomplete disassembly of the actomyosin network over each cycle of oscillation, producing a ratcheting effect. The fast phase of rapid cell and tissue contraction arises when aPKC is no longer able to antagonize the actomyosin network. From experimental observations, the mechanochemical model can account for all major mechanical outcomes of dorsal closure and the transition between three distinct phases. In the second study, a three-dimensional vertex-based model is presented for the study of salivary gland invagination. It is shown how the forces that drive cell shape changes within a flat epithelial sheet, results in the buckling and invagination of a tubular organ. Modelling the epithelial sheet with a 3D model allows for the quantification of how apically patterned forces cause cell shape changes in the basal compartment of the cells. It is shown how cellular constriction leads to the formation of a pit, circumferentially patterned arcs drive the invagination process and the importance of a supracellular actomyosin cable. The model is able to quantify the role that topological transitions have in invagination. The novel 3D model is able to quantify cell mechanical behavior and analyze the effect of different forces during invagination.

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This thesis aims to develop and apply modern computational techniques to study the interfacial dynamics involving complex fluids, where the underlying microstructure strongly affects the behaviour of the fluid. In particular, we have chosen two case studies that are significant to the current state of knowledge in specific fluids.In the first problem, we investigate the interaction between a pair of ferrofluid drops subject to rotating magnetic fields. Through direct numerical simulation using a volume-of-fluid method, we classify four different regimes of the ferrofluid drop interaction. We closely examine the planetary motion regime and identify hydrodynamic interaction to be dominant over magnetic dipole interactions. We also discover a new interaction regime called drop locking, which is confirmed in experiments inspired by our study.In the second problem, we first develop a phase-field method to compute elasto-capillary flows of nematic liquid crystals. The new formulation is able to simultaneously achieve a consistent description of structures of topological defects in the material, as well as an accurate recovery of macroscopic interfacial forces including surface tension and liquid crystal anchoring stress. This is made possible by incorporating a hydrodynamic theory of liquid crystals based on a tensor order parameter in a phase-field formalism approximating the sharp-interface limit. Then the method is applied to the drop retraction problem. We characterize a variety of different cases and examine their dynamics. Our numerical results reveal quantitatively that the drop deformation is a hallmark of competition between bulk distortional elasticity of the liquid crystal and surface tension. The new computational framework opens doors to a large class of fundamental problems concerning colloidal interaction in coupled elasto-capillary fields.

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For many cells, their biomechanical properties are important to their biofunctions. This thesis contains three computational studies of cellular dynamics under mechanical deformation.When infected by malaria, infected red blood cells (iRBCs) become less deformable and tend to block microcapillaries. Microfluidic channels have been used to investigate the deformability of iRBC at different infection stages. In my first project, I applied a discrete iRBC model to simulate the traverse of iRBCs through a microfluidic channel and investigated the progressive loss of the cell deformability due to three factors: the membrane stiffening, the cell surface-volume ratio reduction, and the parasite growing inside the cell. The results indicate that the growth of the parasite clusters play the most significant role in causing the channel blockage.Recent experiments have investigated the response of neutrophils after passing through microfluidic channels. The results indicate that neutrophils may be activated by mechanical deformation. Mechanical deformation causes disassembly of the cytoskeletal network of the neutrophils, which results in a sudden drop of the cell elastic modulus (termed fluidization). The fluidization is followed by either activation of the neutrophils with formation of pseudopods or uniform recovery of the cytoskeletal network without pseudopod formation. The former only occurs when the neutrophils' transit rate is slow. I proposed a chemo-mechanical model for the fluidization and activation processes, based on the polarization of the Rac protein through a wave-pinning mechanism. The model captures the main features of the experimental observation.The third project investigates the response of smooth muscle cells to transient stretch-compress (SC) and compress-stretch (CS) maneuvers. Prior experimental results indicate that the transient SC maneuver causes a sudden fluidization of the cell while the CS maneuver does not. To understand this asymmetric behavior, I built a biomechanical model to probe the response of stress fibers to the two maneuvers. The model couples the cross-bridge cycle of myosin motors with a viscoelastic Kelvin-Voigt element. Simulation results point to the sensitivity of the myosin detachment rate to tension as the cause for the asymmetric response of the stress fiber to the CS and SC maneuvers.

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Using a shear cell device, we have studied four associatedproblems in foam by experiments: Bubble-bubble coalescence insheared two-dimensional foam; lateral migration of a single largebubble in an otherwise monodisperse foam; size segregation ofbubbles in sheared bidisperse foam; and the effect ofnon-Newtonian rheology of foam on lateral migration of bubble. Forbubble-bubble coalescence in sheared two-dimensional foam, weobserved a threshold of shear rate beyond which coalescence ofbubbles happens. The most promising explanation was the modelbased on the centripetal force with qualitative agreement withexperimental results.Next we studied the dynamics of monodisperse foam in the presenceof a single bubble whose size is different from the neighboringbubbles. We reported the lateral migration of a larger singlebubble away from the wall. We also reported thresholds of shearrate and bubble size ratio beyond which migration occurs. In thisstudy we modified the Chan-Leal model and predicted theexperimental trajectories of migrating bubbles.For bidisperse foams, we reported evolution in foam structure to asize segregated structure, in which large bubbles accumulate atthe middle of the gap whereas smaller ones close to walls. Then,we adopted a model based on convection-diffusion equation toaccount for both lateral migration and shear induced diffusion.Finally, we extended the second work by widening the gap ofCouette coaxial cylinder geometry. Similar to the second work, wefound that large bubble migrates laterally to an equilibriumposition close to the inner wall. We believe this new mechanism isthe non-Newtonian feature of foam. We characterized our foam bymeasuring its degree of shear thinning and also estimated itselasticity based on the literature data on foam. Then, we foundout for a shear thinning fluid bubble migrated to position evencloser to the inner wall than in the foam while a bubble in Bogerfluid migrated to a position closer to the outer cylinder.Therefore, for a viscoselastic fluid which has the same featureone would expect to see bubble migration to a position betweenthese two for two fluids.

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Using the Cahn-Hilliard diffuse-interface model, I have studied three interfacialdynamic problems for incompressible immiscible two-phase flows. Asthe first problem, capillary instability of a liquid torus is computed. Themain differences between the torus and a straight thread are the presenceof an axial curvature and an external flow field caused by the retraction ofthe torus. We show that the capillary wave initially grows linearly as on astraight thread. The axial curvature decreases the growth rate of the capillarywaves while the external flow enhances it. Breakup depends on thecompetition of two time scales: one for torus retraction and the other forneck pinch-off. The outcome is determined by the initial amplitude of thedisturbance, the thickness of the torus relative to its circumference, and theviscosity ratio.The second problem concerns interfacial dynamics and three-phase contactline motion of wicking through micropores of two types of geometries:axisymmetric tubes with contractions and expansions of the cross section,and two-dimensional planar channels with a Y-shaped bifurcation. Resultsshow that the liquid meniscus undergoes complex deformation during itspassage through contraction and expansion. Pinning of the interface at protrudingcorners limits the angle of expansion into which wicking is allowed.Capillary competition between branches downstream of a Y-shaped bifurcationmay result in arrest of wicking in the wider branch.As the third problem, auto-ejection of drops from capillary tubes is studied.This study focuses on two related issues: the critical condition for autoejection,and the role of geometric parameters in the hydrodynamics. Fromanalyzing the dynamics of the meniscus in the straight tube and the nozzle,we develop a criterion for the onset of auto-ejection based on a Weber numberdefined at the exit of the nozzle and an effective length that encompassesthe geometric features of the tube-nozzle combination. In particular, thiscriterion shows that ejection is not possible in straight tubes. With steepercontraction in the nozzle, we predict two additional regimes of interfacialrupture: rapid ejection of multiple droplets and air bubble entrapment.

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Recent technological developments in microfluidics and fuel cellshave given special significance to interfacial dynamics in smallpores. Using a diffuse-interface model and a finite-element code,I have simulated three associated problems numerically: gas-liquidflow regimes in micropores; relative permeability for two-phaseflow through a model porous medium; and dynamics of sessile dropsunder the simultaneous action of a wettability gradient and anexternal flow. For two-phase flows in corrugated microchannels driven by apressure drop, a number of flow regimes were observed: gas flow,blockage, liquid flow, bubble-slug flow, droplet flow, annularflow and annular-droplet flow. Some of the regimes are known fromprior studies in macroscopic pipes, but the others are new andspecific to the micropores. Then a map of flow regimes has beenconstructed in the plane of the liquid saturation and the imposedpressure drop. The transitions among certain flow regimes showsignificant hysteresis, largely owing to the pinning of theinterface at sharp corners in the flow conduit. As an extension of the above study, I computed the relativepermeability of a model porous media made of corrugated tubes,using an averaging scheme over a pore-size-distribution of a realporous medium. I discovered that the flow rates vary nonlinearlywith the pressure gradient, and that the extended Darcy's law doesnot hold in general. In the third project, I found that for each prescribed wettinggradient, there is a narrow range for the cross flow within whicha stationary drop can be achieved. The drop motion exhibits stronghysteresis, i.e. sensitivity to initial conditions and forcinghistory. Two drops merge or separate depending on the competitionbetween wettability and external flow. In general, the wettabilitygradient favors catch-up and coalescence while the external flowfavors separation. These numerical simulations have demonstrated that novelinterfacial dynamics can be produced in micropores where capillaryforces and contact line dynamics play more important roles than inlarger spatial dimensions. The numerical results may serve asguidelines to future experiments and technological development inmicrofluidics and lab-on-chip devices.

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The connection between certain human diseases and changes in the mechanical properties of living cells is well established, e.g. in the cases of malaria and cancer. However, the mechanism for the mechanical modifications, which tend to facilitate the pathogenesis of such diseases, is not always clear. For instance, the overall loss of deformability of malaria-infected red blood cells (RBCs) corresponds to a 10-fold increase in the rigidity of the cell membrane. On the other hand, micropipette aspiration has only measured a 3-fold increase in the elastic modulus. In this thesis, a particle-based model is developed to explore the interplay between the underlying microstructures and the behavior of the cell as a whole. The research consists of three related projects. The first project deals with the long-standing problem of Smoothed Particle Hydrodynamics (SPH) method with open boundaries and solid walls. We propose a "rotational pressure-correction scheme" with a consistent pressure boundary condition that leads to a large improvement in accuracy of calculated pressure and the drag coefficient on solid obstacles. The second and third projects concern developing a 2D and then 3D particle-based model for RBCs to explore the parasite-driven changes in malaria-infected RBCs. In our models the cell membrane is replaced by a set of discrete particles connected by linear or nonlinear springs. In addition, a linear bending elasticity is implemented using the deviation of the local curvature from the innate curvature of the biconcave shape of a resting RBC. The cytoplasm and the external liquid are modelled as homogeneous Newtonian fluids, and discretized by particles as in standard SPH solution of the Navier-Stokes equations. The malaria parasite is modelled as an aggregate of particles constrained to rigid-body motion. We argue that the discrepancy in the estimated elastic modulus of the membrane is caused by the presence of the rigid parasite particles inside infected cells, and have carried out numerical simulations to demonstrate this mechanism. Our three-dimensional simulation of RBC stretching tests by optical tweezers accurately demonstrates the compensating effects between the existence of malaria parasites and the elevated stiffness of the membrane on the overall deformability of infected RBC.

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Interfacial flows in complex fluids are an important subject, scientifically rich and technologically important. The main scientific attraction comes from the fact that the microstructure of the bulk fluids may evolve during interfacial flow, and thereby generating non-Newtonian stresses that act on the interface. Thus, interfacial motion and conformation of the microstructure are coupled. Such flow situations arise in many industrial applications, including processing of polymer blends, foaming, and emulsification.In this thesis, I describe three projects aimed at exploring interfacial dynamics of viscoelastic polymeric liquids. The first project consists of finite-element simulations of drop deformation in converging flows in an axisymmetric conical geometry. The moving interface is captured using a diffuse-interface model and accurate interfacial resolution is ensured by adaptive refinement of the grid. The drop experiences a predominantly elongational flow. The amount of deformation sustained by the drop depends, besides the geometry and kinematics of the flow, on the rheology of both the drop and the matrix fluids. The second and third projects concern the same process of selective withdrawal, in which stratified layers of immiscible fluids are withdrawn from a tube placed a certain distance from the interface. We have chosen to work with an air-liquid system, with the suction tube embeddedin the Newtonian or viscoelastic liquid. The second project is an experimental study, where we used video recording and imaging processing to analyze how the interfacial deformation is influenced by the non-Newtonian rheology of the liquid. We discover three regimes, subcritical, critical and supercritical. The third project consists of sharp-interface, moving-grid finite-element simulations of selective withdrawal for Newtonian and viscoelastic Giesekus liquids. The experiments and computations are in reasonable agreement.The work of this thesis has led to two main outcomes. The first is a detailed understanding of how viscoelastic stress can lead to unusual and sometimes counter-intuitive effects on interfacialdeformation. The second is a potentially important new method for measuring elongational viscosity of low-viscosity liquids. This is worth further investigation considering the poor performance ofexisting methods.

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A diffuse-interface finite-element method has been applied to simulate the flow of two-component rheologically complex fluids. It treats the interfaces as having a finite thickness with a phase-field parameter varying continuously from one phase to the other. Adaptive meshing is applied to produce fine grid near the interface and coarse mesh in the bulk. It leads to accurate resolution of the interface at modest computational costs. An advantage of this method is that topological changes such as interfacial rupture and coalescence happen naturally under a short-range force resembling the van der Waals force. There is no need for manual intervention as in sharp-interface model to effect such event. Moreover, this energy-based formulation easily incorporates complex rheology as long as the free energy of the microstructures is known. The complex fluids considered in this thesis include viscoelastic fluids and nematic liquid crystals. Viscoelasticity is represented by the Oldroyd-B model, derived for a dilute polymer solution as linear elastic dumbbells suspended in a Newtonian solvent. The Leslie-Ericksen model is used for nematic liquid crystals，which features distortional elasticity and viscous anisotropy. The interfacial dynamics of such complex fluids are of both scientific and practical significance. The thesis describes seven computational studies of physically interesting problems. The numerical simulations of monodisperse drop formation in microfluidic devices have reproduced scenarios of jet breakup and drop formation observed in experiments. Parametric studies have shown dripping and jetting regimes for increasing flow rates, and elucidated the effects of flow and rheological parameters on the drop formation process and the final drop size. A simple liquid drop model is used to study the neutrophil, the most common type of white blood cell, transit in pulmonary capillaries. The cell size, viscosity and rheological properties are found to determine the transit time. A compound drop model is also employed to account for the cell nucleus. The other four cases concern drop and bubble dynamics in nematic liquid crystals, as determined by the coupling among interfacial anchoring, bulk elasticity and anisotropic viscosity. In particular, the simulations reproduce unusual bubble shapes seen in experiments, and predict self-assembly of microdroplets in nematic media.

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