The force on a bubble, drop, or particle in arbitrary time-dependent motion at small Reynolds number

Abstract

The hydrodynamic force on a body that undergoes translational acceleration in an unbounded fluid at low Reynolds number is considered. The results extend the prior analysis of Lovalenti and Brady [to appear in J. Fluid Mech. (1993)] for rigid particles to drops and bubbles. Similar behavior is shown in that, with the inclusion of convective inertia, the long-time temporal decay of the force (or the approach to steady state) at finite Reynolds number is faster than the t-1 2 predicted by the unsteady Stokes equations.

Velocity fidelity of flow tracer particles

“…For unsteady motions, the history force also exists on a clean bubble besides the quasi-steady force and the added-mass force (Auton et al 1988;Drew and Layhey 1990), as was demonstrated in Chen (1970), Sy et al (1970), Kim and Krilla (1991), Yang and teal (1991), Mei and Klausner (1992), Lovalenti and Brady (1993b), and Mei et al (1994). While Lovalenti and Brady's (1993b) equation for the unsteady force on a fluid bubble or drop is accurate, it is only applicable for Re < 1.…”

Dynamics of Two Charged Particles in a Creeping Flow

“…In the present paper we consider a motion of two electrically charged particles in different setups taking into account gravity/buoyancy force, electrostatic force and viscous drag forces. The effect of viscosity is taken into consideration through the SD force and BBD force which depends on the motion prehistory [4][5][6]8]. We also take into account a reciprocal influence of particles on the drag force which depends on the particle configuration [9].…”

“…It has been demonstrated that in the case of a transient flow the influence of Boussinesq-Basset drag (BBD) force [4][5][6] is very important. It provides different character of particle motions in comparison with the well-known Stokes drag (SD) force [7,8].…”

Resonance properties of forced oscillations of particles and gaseous bubbles in a viscous fluid at small Reynolds numbers

“…Particle motion is caused by the influence of an external harmonic force having the amplitudeà and frequencyω. A corresponding equation of motion in a one-dimensional case in the creeping flow regime is 1,5,13 r + 1 2…”

“…In this equation, the second term in the left-hand side describes the quasi-stationary Stokes drag (SD) force, while the integral term describes the well-known BBD force. 1,14 The added mass effect for a spherical particle is accounted for through the coefficient 1/2 within the bracket in the left-hand side of the equation. 14 We assume that a particle being at rest commences with an instantaneous motion at t = 0 with the initial velocity V 0 , i.e., its velocity experiences a sudden jump from zero to V 0 and then varies in accordance with the equation of motion (1).…”