Film depth and concentration banding in free-surface Couette flow of a suspension.

The film depth of a free-surface suspension flowing in a partially filled horizontal concentric-cylinder, or Couette, device has been studied in order to assess its role in the axial concentration banding observed in this flow. The flow is driven by rotation of the inner cylinder. The banding phenomenon is characterized by particle-rich bands which under flow appear as elevated regions at the free surface separated axially by regions dilute relative to the mean concentration. The concentric cylinders studied had outer radius R(o) = 2.22 cm and inner radii R(i) = 0.64, 0.95 and 1.27 cm; the suspension, of bulk particle volume fraction phi = 0.2 in all experiments described, was composed of particles of either 250-300 microm diameter or less than 106 microm diameter, with the suspending fluid an equal density liquid of viscosity 160 P. The ratio of the maximum to the minimum particle volume fraction along the axis in the segregated condition varies from O(1) to infinite. The latter case implies complete segregation, with bands of clear fluid separating the concentrated bands. The film depth has been varied through variation of the filled fraction, f, of the annular gap between the cylinders and through the rotation rate. Film depth was analysed by edge detection of video images of the free surface under flow, and the time required for band formation was determined for all conditions at which film depth was studied. The film depth increases roughly as the square root of rotation speed for f = 0.5. Band formation is more rapid for thicker films associated with more rapid rotation rates at f = 0.5, whereas slower formation rates are observed with thicker films caused by large f, f > 0.65. It is observed that the film depth over the inner cylinder grows prior to onset of banding, for as yet unknown reasons. A mechanism for segregation of particles and liquid in film flows based upon 'differential drainage' of the particle and liquid phase in the gravity-driven flow within the film over the inner cylinder is formulated to describe the onset of concentration fluctuations. This model predicts that suspension drainage flows lead to growth of fluctuations in phi under regions of negative surface curvature.