Abstract
Using a hydrodynamic theory that incorporates a momentum decay mechanism, we calculate the drag coefficient of a circular liquid domain of finite viscosity moving in a two-dimensional membrane. We derive an analytical expression for the drag coefficient which covers the whole range of domain sizes. Several limiting expressions are discussed. The obtained drag coefficient decreases as the domain viscosity becomes smaller with respect to the outer membrane viscosity. This is because the flow induced in the domain acts to transport the fluid in the surrounding matrix more efficiently.
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Owing to the reviewer’s comment, we recently came to know that, based on the SD theory, De Koker obtained an integral form of the drag force of a liquid domain which has the same viscosity as that of the matrix. Although this result was not published, we will compare it with our result in sect. conclusion
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Ramachandran, S., Komura, S., Imai, M. et al. Drag coefficient of a liquid domain in a two-dimensional membrane. Eur. Phys. J. E 31, 303–310 (2010). https://doi.org/10.1140/epje/i2010-10577-3
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DOI: https://doi.org/10.1140/epje/i2010-10577-3