Velocity of suspended fluid particles in a low Reynolds number converging flow

Abstract

We studied a pressure-driven, low Reynolds number fluid flow through a planar channel whose spanwise width along the flow varied inversely as the streamwise coordinate such that the extensional rate on the centerline was near constant. The effect of the near constant extensional rate on an immiscible droplet of silicone oil was studied by tracking its deformation. The droplet rapidly deformed into an ellipsoid and displayed a consistent lag velocity compared to the single phase background flow at the same point. The observations were attributed to the flow induced deformation of the immiscible droplet, which was a function of the magnitude of the initial capillary number. The streamwise component of the single phase velocity along the centerline of the converging flow was also estimated as leading order using lubrication theory. The estimated velocity is compared favorably with numerical simulations; validation with experimental measurement of the flow of castor oil through the channel by tracking tracer particles is performed. The accuracy of the determination of the velocity field by the lubrication theory allowed for the careful measurement of the velocity difference between the drop and suspended fluid velocities. This research validated lubrication theory predictions of the flow velocity through a converging channel and provided an experimental insight into the behavior of a suspended phase.