TY - JOUR
T1 - Particle grouping in oscillating flows
AU - Sazhin, Sergei
AU - Shakked, Tal
AU - Sobolev, Vladimir
AU - Katoshevski, David
N1 - Funding Information:
The authors are grateful to EPSRC (Grant EP/D002044/1), UK, for their financial support.
PY - 2008/3/1
Y1 - 2008/3/1
N2 - An equation describing the dynamics of spherical particles in an oscillating Stokesian flow in the frame of reference moving with the phase velocity of the wave, and only taking into account the contribution of the drag force, is simplified in two limiting cases. Firstly, the case when Stokes numbers are small is considered. Secondly, the analysis focuses on the case when the initial location of the particles is close to the location where the particles are grouped (their velocities and accelerations in the wave frame of reference are equal to zero), xlim. This is followed by an analysis of the dynamics of non-Stokesian particles. In all cases, the analytical results are validated against the results of numerical solution of the equation of particle motion. Three types of trajectories are predicted when particles approach xlim: the trajectories describing the monotonic approach to xlim, the trajectories describing the approach to xlim with oscillations and trajectories repelled from xlim. These are identified with stable nodes, stable foci and saddles. The trajectories in the zone between stable nodes and foci are identified as stable stars. Using Dulac's criterion, it is pointed out that none of the particle trajectories in the position-velocity plane can be closed. This result is illustrated by the trajectories calculated using the numerical solution of the equation for particle dynamics for various parameter values.
AB - An equation describing the dynamics of spherical particles in an oscillating Stokesian flow in the frame of reference moving with the phase velocity of the wave, and only taking into account the contribution of the drag force, is simplified in two limiting cases. Firstly, the case when Stokes numbers are small is considered. Secondly, the analysis focuses on the case when the initial location of the particles is close to the location where the particles are grouped (their velocities and accelerations in the wave frame of reference are equal to zero), xlim. This is followed by an analysis of the dynamics of non-Stokesian particles. In all cases, the analytical results are validated against the results of numerical solution of the equation of particle motion. Three types of trajectories are predicted when particles approach xlim: the trajectories describing the monotonic approach to xlim, the trajectories describing the approach to xlim with oscillations and trajectories repelled from xlim. These are identified with stable nodes, stable foci and saddles. The trajectories in the zone between stable nodes and foci are identified as stable stars. Using Dulac's criterion, it is pointed out that none of the particle trajectories in the position-velocity plane can be closed. This result is illustrated by the trajectories calculated using the numerical solution of the equation for particle dynamics for various parameter values.
KW - Clustering
KW - Spray
KW - Stokesian flow
UR - http://www.scopus.com/inward/record.url?scp=38849125015&partnerID=8YFLogxK
U2 - 10.1016/j.euromechflu.2007.04.003
DO - 10.1016/j.euromechflu.2007.04.003
M3 - Article
AN - SCOPUS:38849125015
SN - 0997-7546
VL - 27
SP - 131
EP - 149
JO - European Journal of Mechanics, B/Fluids
JF - European Journal of Mechanics, B/Fluids
IS - 2
ER -