The gravity-driven migration of a drop in an unsteady Stokes flow

2021 ◽  
Vol 33 (12) ◽  
pp. 123105
Author(s):  
Y. Qin ◽  
R. Sun
Keyword(s):  
Stokes Flow ◽  
Unsteady Stokes Flow ◽  
Gravity Driven

Motion of slender bodies in unsteady Stokes flow

2011 ◽  
Vol 688 ◽  
pp. 66-87 ◽  
Author(s):  
Efrath Barta
Keyword(s):  
Stokes Flow ◽  
Slenderness Ratio ◽  
Creeping Flow ◽  
Slender Body Theory ◽  
Wide Range ◽  
Unsteady Stokes Flow ◽  
Slender Bodies ◽  
Set Up ◽  
Micro Organisms ◽  
Parameter Values

AbstractThe flow regime in the vicinity of oscillatory slender bodies, either an isolated one or a row of many bodies, immersed in viscous fluid (i.e. under creeping flow conditions) is studied. Applying the slender-body theory by distributing proper singularities on the bodies’ major axes yields reasonably accurate and easily computed solutions. The effect of the oscillations is revealed by comparisons with known Stokes flow solutions and is found to be most significant for motion along the normal direction. Streamline patterns associated with motion of a single body are characterized by formation and evolution of eddies. The motion of adjacent bodies results, with a reduction or an increase of the drag force exerted by each body depending on the direction of motion and the specific geometrical set-up. This dependence is demonstrated by parametric results for frequency of oscillations, number of bodies, their slenderness ratio and the spacing between them. Our method, being valid for a wide range of parameter values and for densely packed arrays of rods, enables simulation of realistic flapping of bristled wings of some tiny insects and of locomotion of flagella and ciliated micro-organisms, and might serve as an efficient tool in the design of minuscule vehicles. Its potency is demonstrated by a solution for the flapping of thrips.

scholarly journals Direct Measurement of Unsteady Microscale Stokes Flow Using Optically Driven Microspheres

2020 ◽  
Author(s):  
Nicolas Bruot ◽  
Pietro Cicuta ◽  
Hermes Bloomfield-Gadêlha ◽  
Raymond E. Goldstein ◽  
Jurij Kotar ◽  
...  
Keyword(s):  
Stokes Flow ◽  
Optical Trap ◽  
Low Frequency ◽  
Phase Lag ◽  
Tracer Particles ◽  
Unsteady Stokes Flow ◽  
Central Particle ◽  
Passive Tracers ◽  
Oscillation Frequencies ◽  
Drag Law

A growing body of work on the dynamics of eukaryotic flagella has noted that their oscillation frequencies are sufficiently high that the viscous penetration depth of unsteady Stokes flow is comparable to the scales over which flagella synchronize. Incorporating these effects into theories of synchronization requires an understanding of the global unsteady flows around oscillating bodies. Yet, there has been no precise experimental test on the microscale of the most basic aspects of such unsteady Stokes flow: the orbits of passive tracers and the position-dependent phase lag between the oscillating response of the fluid at a distant point and that of the driving particle. Here, we report the first such direct Lagrangian measurement of this unsteady flow. The method uses an array of 30 submicron tracer particles positioned by a time-shared optical trap at a range of distances and angular positions with respect to a larger, central particle, which is then driven by an oscillating optical trap at frequencies up to 400 Hz. In this microscale regime, the tracer dynamics is considerably simplified by the smallness of both inertial effects on particle motion and finite-frequency corrections to the Stokes drag law. The tracers are found to display elliptical Lissajous figures whose orientation and geometry are in agreement with a low-frequency expansion of the underlying dynamics, and the experimental phase shift between motion parallel and orthogonal to the oscillation axis exhibits a predicted scaling form in distance and angle. Possible implications of these results for synchronization dynamics are discussed.

scholarly journals Unsteady Stokes Flow through Porous Channel with Periodic Suction and Injection with Slip Conditions

2018 ◽  
Vol 11 (4) ◽  
pp. 937-945 ◽  
Author(s):  
Kaleemullah Bhatti ◽  
Zarqa Bano ◽  
Abdul Majeed Siddiqui
Keyword(s):  
Radial Velocity ◽  
Stokes Flow ◽  
Slip Parameter ◽  
Governing Equations ◽  
Slip Conditions ◽  
Unsteady Stokes Flow ◽  
Flow Through ◽  
Suction Or Injection ◽  
Similarity Method ◽  
Special Case

This work is concerned with the influence of slip conditions on unsteady stokes flow between parallel porous plates with periodic suction and injection. The obtained unsteady governing equations are solved analytically by similarity method. The characteristics of complex axial velocity and complex radial velocity for different values of parameters are analyzed. Graphical results for slip parameter reveal that it has significant influence on the axial and radial velocity profiles. The effects of suction or injection are also observed. The problem of unsteady stokes flow through porous plates with no slip is recovered as a special case of our problem.

scholarly journals The hydrodynamic force on a rigid particle undergoing arbitrary time-dependent motion at small Reynolds number

1993 ◽  
Vol 256 ◽  
pp. 561-605 ◽  
Author(s):  
Phillip M. Lovalenti ◽  
John F. Brady
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Stokes Flow ◽  
Slip Velocity ◽  
Hydrodynamic Force ◽  
Time Dependent ◽  
Rigid Particle ◽  
Flowing Fluid ◽  
Arbitrary Time ◽  
Unsteady Stokes Flow

The hydrodynamic force acting on a rigid spherical particle translating with arbitrary time-dependent motion in a time-dependent flowing fluid is calculated to O(Re) for small but finite values of the Reynolds number, Re, based on the particle's slip velocity relative to the uniform flow. The corresponding expression for an arbitrarily shaped rigid particle is evaluated for the case when the timescale of variation of the particle's slip velocity is much greater than the diffusive scale, a2/v, where a is the characteristic particle dimension and v is the kinematic viscosity of the fluid. It is found that the expression for the hydrodynamic force is not simply an additive combination of the results from unsteady Stokes flow and steady Oseen flow and that the temporal decay to steady state for small but finite Re is always faster than the t-½ behaviour of unsteady Stokes flow. For example, when the particle accelerates from rest the temporal approach to steady state scales as t-2.

Sign in / Sign up

Export Citation Format

Share Document