FILM FLOW IN THE SPACE BETWEEN A CIRCULAR BUBBLE AND A SQUARE TUBE

The flow of a viscous fluid in the space defined between a bubble with circular cross section and a square tube is considered here. This problem is relevant to two-phase flows in porous media, the coating of tubes of square cross section, and more recently the design and operation of three-phase monolithic reactors. The formulation takes into account the action of gravity and the presence of a pressure field. The solution, developed as an infinite series of harmonic polynomials, satisfies the boundary conditions on the circle defined by the free-surface of the bubble and on the square defined by the wetted perimeter of the tube. The result demonstrates an efficient analytic technique for dealing with boundary conditions combining square and circular geometries. Liquid flow rates and velocity profiles measured experimentally and computed numerically agree very well with the theoretical results. © 1993 Academic Press, Inc.