Abstract
The objective of this paper was to study the transport and deposition of non-spherical oblate and prolate shaped particles for the flow in a tube with a radial suction velocity field, with an application to experiments related to composite manufacturing. The transport of the non- spherical particles is governed by a convective diffusion equation for the probability density function, also called the Fokker–Planck equation, which is a function of the position and orientation angles. The flow is governed by the Stokes equation with an additional radial flow field. The concentration of particles is assumed to be dilute. In the solution of the Fokker–Planck equation, an expansion for small rotational Peclet numbers and large translational Peclet numbers is considered. The solution can be divided into an outer region and two boundary layer regions. The outer boundary layer region is governed by an angle-averaged convective-diffusion equation. The solution in the innermost boundary layer region is a diffusion equation including the radial variation and the orientation angles. Analytical deposition rates are calculated as a function of position along the tube axis. The contribution from the innermost boundary layer called steric- interception deposition is found to be very small. Higher order curvature and suction effects are found to increase deposition. The results are compared with results using a Lagrangian tracking method of the same flow configuration. When compared, the deposition rates are of the same order of magnitude, but the analytical results show a larger variation for different particle sizes. The results are also compared with numerical results, using the angle averaged convective-diffusion equation. The agreement between numerical and analytical results is good.
Highlights
Transport of particles in cross-flow configurations has many important applications in natural, biomedical, and industrial systems such as groundwater flows, filtering techniques, flows in the processing of composite materials, flows in the body, protein separations, and tissue engineering.Often the cross-flow geometry consists of a fluid flowing in a tube containing particles with porous walls
First the suction velocity is assumed to be uniform along the x-axis, whether theory
First the suction velocity is assumed to be uniform along the x-axis, whetherthis thisisisaacorrect correct assumption assumptioncan canonly onlybe beunderstood understoodififthe thephysics physicsof ofthe thesurrounding surroundingporous porousmedium mediumisistaken takeninto into account
Summary
Transport of particles in cross-flow configurations has many important applications in natural, biomedical, and industrial systems such as groundwater flows, filtering techniques, flows in the processing of composite materials, flows in the body, protein separations, and tissue engineering. The purpose of the present work is to develop a theory for the transport of non-spherical nano-sized particles in cross-flow geometry using the Fokker–Planck approach and with an application to the flow configuration considered in the work of reference [3] It extends and corrects some of the results of that paper. As in that paper [3] in this first work the effect of the porous medium is only to provide a radial suction out of the tube This means that the much more complicated case of transport of the non-spherical particles into the porous medium is not considered here and will be left for further studies.
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