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Drag force on a liquid domain moving inside a membrane sheet surrounded by aqueous medium

Published online by Cambridge University Press:  18 August 2015

V. Laxminarsimha Rao  and
Sovan Lal Das
V. Laxminarsimha Rao
Affiliation:
Mechanics and Applied Mathematics Group, Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India
Sovan Lal Das*
Affiliation:
Mechanics and Applied Mathematics Group, Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India
*
†Email address for correspondence: sovandas@iitk.ac.in
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Abstract

We compute the drag on a circular and liquid microdomain diffusing in a two-dimensional fluid lipid bilayer membrane surrounded by a fluid above and below. Under the assumptions that the liquids are incompressible and the flow is of low Reynolds number, Stokes’ equations describe the flow in the two-dimensional membrane as well as in the surrounding three-dimensional fluid. The expression for the drag force on the liquid domain involves Fredholm integral equations of the second kind, which we numerically solve using discrete collocation method based on Chebyshev polynomials. We observe that when the domain is more viscous than the surrounding membrane (including the rigid domain case), the drag force is almost independent of the viscosity contrast between the domain and the surrounding membrane, as also observed earlier in experiments by other researchers. The mobility also varies logarithmically with Boussinesq number ${\it\beta}$ for large ${\it\beta}$. On the other hand, for a less viscous domain the dimensionless drag force reduces with increasing viscosity contrast, and a significant change in the drag force, from that when there is no viscosity contrast or when the domain is rigid, has been observed. Further, the logarithmic behaviour of the mobility no longer holds for less viscous domains. Our method of computing the drag force and diffusion coefficient is valid for arbitrary viscosity contrast between the domain and membrane and any domain size (subject to ${\it\beta}\geqslant 5$).

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Low-Reynolds-number flows: Low-Reynolds-number flows Biological Fluid Dynamics: Membranes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 779 , 25 September 2015 , pp. 468 - 482
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Copyright
© 2015 Cambridge University Press 

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