Universal expression for the drag on a fluid sphere.

D A Barry,J.-Y Parlange

doi:10.1371/journal.pone.0194907

Abstract

An expression was developed for prediction of drag coefficients for any spherical particle, drop or bubble in an infinite, homogeneous liquid. The formula reproduces the limiting cases for gas bubbles and solid spheres, as well as the exact Hadamard-Rybczynski solution. The accuracy of the expression, which is valid for Reynolds numbers up to a few hundred, was confirmed by comparison with published numerical predictions of the drag coefficient for a range of physical circumstances.

Highlights

Bubbles, drops and particles are widespread in science and engineering phenomena
Wegener et al [2] recently provided a comprehensive review of theory, experimental data and pertinent approximations describing the dynamics of single drops in fluid systems
The steady rate of movement of spherical particle, drops and bubbles is quantified by the drag coefficient, Cd

Summary

Introduction

Drops and particles are widespread in science and engineering phenomena. Knowledge of the behavior of single bubbles and drops is directly relevant to many applications; it supports understanding of the corresponding swarms, e.g., [1]. For laminar flow (i.e., oscillations of the particle do not occur), Harper and Moore [13] as well as Parlange [14] obtained approximate expressions for the drag for this case, . In both [13] and [14], it was observed that, to a first approximation, flow inside the particle is described by a Hill’s vortex, and outside by a potential flow. Both approaches give drag predictions that are “numerically indistinguishable” [14].

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Conclusion