Couette creeping flow past a sphere in non-Newtonian power-law fluids
- PDF / 1,569,389 Bytes
- 7 Pages / 595.276 x 790.866 pts Page_size
- 25 Downloads / 194 Views
(0123456789().,-volV)(0123456789(). ,- volV)
TECHNICAL PAPER
Couette creeping flow past a sphere in non-Newtonian power-law fluids Asterios Pantokratoras1 Received: 4 July 2020 / Accepted: 30 August 2020 Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The flow past a sphere, rigidly held between two parallel plates (Couette flow), was studied in a non-Newtonian, power-law fluid, numerically. The three momentum equations have been solved under the following conditions: creeping flow with Re \ 1; power-law index 0.2–1; distance of sphere center from the plates 1.15–10; sphere position between the plates 0.1–0.9. Diagrams have been produced for the direct calculation of the force acting on the sphere. The numerical forecast shows a significant disparity between Newtonian and non-Newtonian fluids. All in all, the wall effect in power law fluids is less extreme than in Newtonian fluids. Furthermore, in non-Newtonian fluids, the force changes linearly when the sphere approaches the upper plate.
1 Introduction Modelling the motion of small particles in a viscous fluid close to a wall is useful for various applications, such as in the field-flow separation technique, the movement of silt in river beds, dust removal from surfaces, the lubrication of spherical bearings and the motion of biological fluid cells. Here, we consider a spherical particle small enough to be low on the Reynolds number of the fluid flow, so that creeping flow equations are applied. It is stated here that when the number of Reynolds is very small the flow is called Stokes flow or creeping flow where the inertial forces are small when compared to viscous forces or the length scales of the flow are very small. The creeping flow equations are linear when the fluid is Newtonian but nonlinear for a non-Newtonian fluid like that in the present work. Historically the creeping flow was first studied to understand lubrication. Goldman et al. (1967) considered the case of a sphere held fixed in a shear flow near a single wall, combining their earlier results with the Lorentz reciprocal theorem to derive expressions for the forces acting on the sphere. This formal solution is complemented by two asymptotic solutions: (i) a lubrication-theory-like approximation & Asterios Pantokratoras [email protected] 1
School of Engineering, Democritus University of Thrace, 67100 Xanthi, Greece
applicable in cases where the sphere is very close to the wall; (ii) an approximation ‘‘method of reflections’’, valid for the opposite case. Tozeren and Skalak (1977) studied a uniform shear stream past a plane wall with a single spherical particle. A set of solutions and the mean speed and stress field were developed and calculated for a forcefree and couple-free sphere as well as for spheres with couples used by external means. The particle’s translation velocities and the distribution of stress on the particle’s surface were calculated. The mean stress on a plane parallel to the wall is shown to decrease the value of Einstein when the distance from t
Data Loading...
