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Fluids 2016, 1(4), 36;

Hydrodynamics of Highly Viscous Flow past a Compound Particle: Analytical Solution

Department of Mathematics, Applied Mathematics and Statistics, Case Western Reserve University, Cleveland, OH 44106, USA
Academic Editors: Mehrdad Massoudi and Ashuwin Vaidya
Received: 23 September 2016 / Revised: 6 November 2016 / Accepted: 7 November 2016 / Published: 12 November 2016
(This article belongs to the Special Issue Mechanics of Fluid-Particles Systems and Fluid-Solid Interactions)
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To investigate the translation of a compound particle in a highly viscous, incompressible fluid, we carry out an analytic study on flow past a fixed spherical compound particle. The spherical object is considered to have a rigid kernel covered with a fluid coating. The fluid within the coating has a different viscosity from that of the surrounding fluid and is immiscible with the surrounding fluid. The inertia effect is negligible for flows both inside the coating and outside the object. Thus, flows are in the Stokes regime. Taking advantage of the symmetry properties, we reduce the problem in two dimensions and derive the explicit formulae of the stream function in the polar coordinates. The no-slip boundary condition for the rigid kernel and the no interfacial mass transfer and force equilibrium conditions at fluid interfaces are considered. Two extreme cases: the uniform flow past a sphere and the uniform flow past a fluid drop, are reviewed. Then, for the fluid coating the spherical object, we derive the stream functions and investigate the flow field by the contour plots of stream functions. Contours of stream functions show circulation within the fluid coating. Additionally, we compare the drag and the terminal velocity of the object with a rigid sphere or a fluid droplet. Moreover, the extended results regarding the analytical solution for a compound particle with a rigid kernel and multiple layers of fluid coating are reported. View Full-Text
Keywords: Stokes flow; stream function; axisymmetric flow; compound particle; fluid coating Stokes flow; stream function; axisymmetric flow; compound particle; fluid coating

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Zhao, L. Hydrodynamics of Highly Viscous Flow past a Compound Particle: Analytical Solution. Fluids 2016, 1, 36.

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