Abstract
We discuss a continuum-based model describing the deformations of lipid membranes subjected to intramembrane viscosity. Within the frame work of the theory of an elastic surface, the membrane equilibrium equations and the expressions of viscous stress are obtained. The corresponding deformation energy of the membrane is computed via the first and second fundamental form of surface. A compatible linear model is also formulated within the prescription of superposed incremental deformations through which the deformation profiles of the membrane is obtained. It is shown that the intramembrane viscous flow gives rise to straining effects on the membranes. Further, the corresponding dynamic edge conditions reduce to purely elastic boundary conditions in the limit of vanishing viscous effects. Lastly, admissible sets of velocity fields are also examined and are used to formulate membrane shape equations and the associated dynamic boundary conditions.
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