Next Article in Journal
Unconfined Unsteady Laminar Flow of a Power-Law Fluid across a Square Cylinder
Next Article in Special Issue
Fundamental Rheology of Disperse Systems Based on Single-Particle Mechanics
Previous Article in Journal
Laser-Induced Motion of a Nanofluid in a Micro-Channel
Article Menu

Export Article

Open AccessArticle
Fluids 2016, 1(4), 36; doi:10.3390/fluids1040036

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)
View Full-Text   |   Download PDF [1098 KB, uploaded 12 November 2016]   |  

Abstract

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
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

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

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Fluids EISSN 2311-5521 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top