The lateral migration of spherical particles sedimenting in a stagnant bounded fluid

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Abstract
Singular perturbation techniques are used to calculate the migration velocity of a spherical particle sedimenting, at low Reynolds numbers, in a stagnant viscous fluid bounded by one or two infinite vertical plane walls. The method is then used to study the migration of a pair of spherical particles sedimenting either in unbounded fluid or in fluid bounded by a plane vertical wall. The migration phenomenon is studied experimentally by recording the trajectory of a spherical particle settling through a viscous fluid bounded by parallel vertical plane walls. Duct- to particle-diameter ratios in the range of 27 to 48 were used with the Reynolds number based on the particle radius being between 0·03 and 0·136.In all cases the particle is observed to migrate away from the walls until it reaches an equilibrium position at the axis of the duct. The experimentally determined migration velocities agree well with those predicted by the present theory.