(14f) Linear Response of Finite Thickness Membranes

Lipid bilayers are fundamental to a plethora of cellular phenomena, often displaying unique physics owing to their behaving as in-plane fluids and out-of-plane elastic solids. Typically, a direct two-dimensional approach is used in order to obtain a computationally and analytically tractable theory. However, such an approach cannot capture some experimentally and computationally observed phenomena such as Kelvin-Helmholtz-like instabilities or electromechanical coupling in lipid bilayers.

Here, we apply an “effective” two-dimensional framework recently developed by the authors that explicitly includes membrane thickness while retaining the amenability of previous theories. In particular we consider the response given quiescent bulk and Couette flow base states. We find that accounting for the thickness slows the linear response of lipid bilayers to external perturbations. Inclusion of thickness alters the behavior of the fluctuation spectrum in the short wavelength regime, where bending effects are important. In addition, we observe the existence hydrodynamic circulations exterior to the bilayer in response to high frequency excitations that two-dimensional theories cannot capture.