Loop subdivision surface boundary integral simulations for vesicles in shear and extensional flows
Abstract/Contents
- Abstract
- Vesicles are fluid droplets enclosed by a deformable lipid membrane. The most prominent features of vesicles fluids problems are the incompressibility of the membrane and a membrane bending energy that requires a smooth and accurate determination of curvature. In this thesis we use boundary integral simulations with curvature determined via Loop subdivision surfaces to model vesicles in fluid flow. This method ensures that curvature is measured on a surface that is guaranteed to be at least C1 continuous everywhere. We are able to examine vesicles that are highly non-spherical in shape. When vesicles are placed in a shear flow they undergo motions of tank treading, trembling, and tumbling. We validate our code versus spectral simulations and extend the vesicle phase diagrams to vesicles of increasing aspect ratio. In addition to the prolate shape family of vesicle shapes, we present simulations of biconcave and stomatocyte vesicles. We show that reduced volume 0.65 vesicles experience different responses to the same viscosity ratio and capillary number depending on whether their initial shape is prolate or biconcave. We investigate how the presence of a wall near a vesicle gives the vesicle a lift velocity and how the wall affects the phase diagram. We find vesicles far from a wall experience an induced lift velocity inversely proportional to the square of the height of the centroid of the vesicle and proportional to the wall normal component of the particle stresslet. The presence of a nearby wall also requires a higher critical viscosity ratio for the vesicle to advance from tank treading to trembling or tumbling motions. Finally, we re-examine over a wider range of reduced volumes the instability originally reported by Zhao and Shaqfeh in 2013 of a vesicle placed in an extensional flow. At sufficiently high aspect ratio and capillary number, we find the steady elongated dumbbell shape is unstable to odd perturbations and the vesicle's dumbbell ends become unequal in size. We also find that the critical capillary number as a function of reduced volume is similar between uniaxial and planar extensional flow. We simulate vesicles with an aspect ratio of up to 10:1 and compare to experimental results. Observing the continuation of this instability from modest to high aspect ratio vesicles helps us reconcile the asymmetric nature of the reported instability with the apparently symmetric appearance of high aspect ratio experiments.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2013 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Spann, Andrew |
|---|---|
| Associated with | Stanford University, Department of Computational and Mathematical Engineering. |
| Primary advisor | Shaqfeh, Eric S. G. (Eric Stefan Garrido) |
| Thesis advisor | Shaqfeh, Eric S. G. (Eric Stefan Garrido) |
| Thesis advisor | Darve, Eric |
| Thesis advisor | Spakowitz, Andrew James |
| Advisor | Darve, Eric |
| Advisor | Spakowitz, Andrew James |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Andrew Spann. |
|---|---|
| Note | Submitted to the Department of Computational and Mathematical Engineering. |
| Thesis | Ph.D. Stanford University 2013 |
| Location | electronic resource |
Access conditions
- Copyright
- © 2013 by Andrew Paul Spann
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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