This dissertation will focus on my work in biophysics, and my work in mean field games and glucose predictive analysis will not be presented. Several problems relating to the effects of thermodynamic coupling and hydrodynamic coupling within the membrane stack system are discussed. Three theoretical approaches are employed and proposed to study the membrane stack system: a diffuse-interface approach is utilized for numerical simulations; a coarse-grained sharp-interface approach is utilized to provide physical understanding of various kinetics; a hybrid intermediate sharp-interface approach is adopted to study the domain coalescence in the absence of diffusion.
In the first part of the thesis, we discuss the thermodynamic coupling in membrane stack systems. Comprehensive analyses are presented to understand the accelerated coarsening kinetics with respect to single layer and long-range alignment. Numerical simulations are conducted for three systems, namely a diffusion dominated system, an advective interlayer friction dominated system, and an advective membrane viscosity dominated system. Experimental results regarding the advective interlayer friction dominated system are supported by simulations. We investigate the mechanism of the enhanced coarsening kinetics in membrane stack systems and the relationship between the coarsening process and vertical alignment. An intuitive understanding along with analytical explanations are further presented. Moreover, numerical results regarding the critical mixture are also discussed.
We then investigate the interfacial fluctuation behavior within membrane stack systems. The hydrodynamic coupling is found to play a significant role and several physical length scales are found to be crucial. Both a sharp-interface approach and a diffuse-interface approach are employed to numerically simulate decay of interface fluctuations in representative two-membrane systems.
To measure the thermodynamic coupling in experiments, the hydrodynamic force needs to be quantified, especially for the non-circular domains. In the last part of this thesis, the drag coefficient relating domain velocity and force acting on the domain is calculated using perturbation theory within two limits: the first limit refers to a domain much larger than the hydrodynamic screening length; the second limit refers to a domain that is much smaller than the hydrodynamic screening length.
|Advisor:||Haataja, Mikko P.|
|Commitee:||Stone, Howard A., Stone, James M.|
|Department:||Applied and Computational Mathematics|
|School Location:||United States -- New Jersey|
|Source:||DAI-B 79/07(E), Dissertation Abstracts International|
|Subjects:||Mathematics, Physical chemistry, Biophysics|
|Keywords:||Coupling, Drag coefficient, Hydrodynamics, Interface fluctuation, Phase separation in membrane, Phase-field method|
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