Modelling and Analysis of Lipid membranes subject to intra-membrane viscous flows and membrane-substrate interactions

• Author / Creator

  Liu,Zhe

• The mechanical responses of the lipid membranes and their mechanisms are of importance in the understanding of essential cellular functions such as budding, fission and vesicle formations. Inside the lipid bilayers, viscous flows play vital roles since they can influence the transportations of elements, the shapes of the lipid membranes and various cellular processes. Within the description of the continuum setting, lipid membranes can be idealized as continuous bilayer sandwich structures. Based on nonlinear elastic thin-film theory, this thesis presents the continuum-based models of lipid membranes subjected to intra-membrane viscous flows as well as interactions with the elliptical-cross-section substrates. The corresponding boundary conditions and shape equations of the membranes are formulated based on the principles of energy equilibrium law and virtual work statement. A careful derivation of the model is presented and utilized to obtain the exact analytical solutions. The solutions of the obtained shape equations in the form of Partial Differential Equations (PDEs) are obtained by using eigenfunction expansion and Mathieu function in the elliptical domain. This thesis also investigates the morphologies of lipid membranes impacted by the uniform, non-uniform and mixed types of viscous flows by modifying the obtained equilibrium equations. Finally, the thickness distension of membranes is considered, and the corresponding analytical solutions are obtained.

• Subjects / Keywords

  • lipid membrane
  • viscous flow

• Graduation date

  Fall 2020

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/r3-xxct-4a40

• License

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