MATLAB Code for implementing the series solutions to the membrane hydrodynamics equations of Hughes, Pailthorpe, and White (1981):
Hughes, B.D., B.A. Pailthorpe, and White L. R., "The translational and rotational drag on a cylinder moving in a membrane," J. Fluid. Mech. 110: 349–372 (1981).
The function HPW_drag.m calculates the translational and rotational drag and diffusion coefficients of a membrane inclusion, given input viscosities and the inclusion radius.
HPW_fit.m calculates the best-fit membrane viscosity and inclusion radius, given (measured) rotational and translational diffusion coefficients.
See https://eighteenthelephant.com/2018/09/04/membrane-diffusion-software/ for discussion.
Functions applying the theory of:
\A. J. Levine, T. B. Liverpool, F. C. MacKintosh, "Mobility of extended bodies in viscous films and membranes," Phys. Rev. E 69, 021503 (2004).
LLM_calcD.m calculates the rotational diffusion coefficient and the translational diffusion coefficients parallel and perpendicular to the rod axis as a function of membrane viscosity (eta) and rod length (L).
LLM_fit_viscosity_L.m calulates membrane viscosity and effective rod length for a rod-like membrane inclusion. Uses both D_parallel and D_R, and D_perpendicular and D_R, combining the results from each pair. (October 2021) Note: we've extracted points from the graphs in the Levine et al. 2004 paper, and made simple polynomial interpolations. See notes, 2021, and Jahl and Parthasarathy 2021.