Numerical Simulations of Giant Vesicles in More Complex Stokes Flows and Discretization Considerations of the Boundary Element Method

Charlie Lin, Purdue University

Abstract

Quantifying the dynamics and rheology of soft biological suspensions such as red blood cells, vesicles, or capsules is paramount to many biomedical and computational applications. These systems are multiphase flows that can contain a diverse set of deformable cells and rigid bodies with complex wall geometries. For this thesis, we are performing several numerical simulations using boundary element methods (BEM) for biological suspensions in biomedically relevant conditions. Each simulation is devised to answer fundamental questions in modeling these systems. Part of this thesis centers around the fluid mechanics of giant unilamellar vesicles (GUVs), fluid droplets surrounded by a phospholipid bilayer. GUVs are important to study because they mimic the dynamics of anuclear cells and are commonly used as a basis for artificial cells. The dynamics of vesicles in simple shear or extensional flows have been extensively studied. However the conditions seen in microfluidic devices or industrial processing are not always described by steady shear or extensional flows alone, and require more investigation. In our first study, we investigate the shape stability of osmotically deflated vesicles in a general linear flow (i.e., linear combinations of extensional and rotational flows). We modeled the vesicles as a droplet with an incompressible interface with a bending resistance. We simulated a range of flow types from purely shear to purely extensional at viscosity ratios ranging from 0.01 to 5.0 and reduced volumes (measured asphericity, higher is more spherical) from 0.60 to 0.70. The vesicle’s viscosity ratio appears to play a minimal role in describing its shape and stability for many mixed flows, even in cases when significant flows are present in the vesicle interior. We find in these cases that the bending critical capillary number for shape instabilities collapse onto similar values if the capillary number is scaled by an effective extensional rate. These results contrast with droplet studies where both viscosity ratio and flow type have significant effects on breakup. Our simulations suggest that if the flow type is not close to pure shear flow, one can accurately quantify the shape and stability of vesicles using the results from an equiviscous vesicle in pure extension. Only when the flow type is nearly shear flow, do we start to see deviations in the observations discussed above. In this situation, the vesicle’s stationary shape develops a shape deviation, which introduces a stabilizing effect and makes the critical capillary number depend on the viscosity ratio. Continuing with our research on single vesicle dynamics, we have performed simulations and experiments on vesicles in large amplitude oscillatory extensional (LAOE) flows. By using LAOE we can probe the non-linear extension and compression of vesicles and how these types of deformation affect dilute suspension microstructure in time-dependent flows through contractions, expansions, or other complex geometries. Our numerical and experimental results for vesicles of reduced volumes from 0.80 to 0.95 have shown there to be three general dynamical regimes differentiated by the amount of deformation that occurs in each half cycle. We have termed the regimes: symmetrical, reorienting, and pulsating in reference to the type of deformation that occurs.

Degree

Ph.D.

Advisors

Narsimhan, Purdue University.

Subject Area

Mechanics|Physics

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