Resistance functions for spherical particles, droplets and bubbles in cylindrical tubes

• Published in: Journal of fluid mechanics Vol. 298; pp. 193 - 210
• Main Authors: Higdon, J. J. L., Muldowney, G. P.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 10.09.1995
• Subjects: Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Laminar flows; Laminar flows in cavities; Laminar suspensions; Physics; Bubbles; Low Reynolds number; Algorithms; Two-phase flow; Numerical simulation; Droplets; Wall effects; Spherical particle; Particle suspension; Boundary element method; Hydrodynamic drag
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/S0022112095003272

Numerical computations are performed to evaluate the resistance functions for low Reynolds number flow past spherical particles, droplets and bubbles in cylindrical domains. Spheres of arbitrary radius a and radial position b move with arbitrary velocity U within a cylinder of radius R. The undisturbed fluid may be at rest, or subject to a pressure-driven flow with maximum velocity U0. The spectral boundary element method is employed to compute the resistance force for torque-free bodies in three cases: rigid solids, fluid droplets with viscosity ratio λ = 1, and bubbles with viscosity ratio λ = 0. A lubrication theory is developed to predict the limiting resistance of bodies near contact with the cylinder walls. Compact algebraic expressions are developed which accurately represent the numerical data over the entire range of particle positions 0 < b/(R − a) < 1 for all particle sizes in the range 0 < a/R < 0.9. The resistance functions are consistent with known analytical results and are presented in a form suitable for further studies of particle migration in cylindrical vessels.