A theoretical analysis is presented which brings steady laminar film flow of power-law fluids within the framework of classical boundary layer theory. The upper part of the film, which consists of a developing viscous boundary layer and an external inviscid freestream, is treated separately from the viscous dominated part of the flow, thereby taking advantage of the distinguishing features of each flow region. It is demonstrated that the film boundary layer developing along a vertical wall can be described by a generalized Falkner-Skan type equation originally developed for wedge flow. An exact similarity solution for the velocity field in the film boundary layer is thus made available. Downstream of the boundary layer flow regime the fluid flow is completely dominated by the action of viscous shear, and fairly accurate solutions are obtained by the Von Karman integral method approach. A new form of the velocity profile is assumed, which reduces to the exact analytic solution for the fully-developed film. By matching the downstream integral method solution to the upstream generalized Falkner-Skan similarity solution, accurate estimates for the hydrodynamic entrance length are obtained. It is also shown that the flow development in the upstream region predicted by the approximate integral method closely corresponds to the exact similarity solution for that flow regime. An analytical solution of the resulting integral equation for the Newtonian case is compared with previously published results.

Gravity-driven laminar film flow of power-law fluids along vertical walls

Hydrodynamic entrance lengths of laminar falling films

Developing laminar flow in a liquid film issuing from a full slot and descending along a vertical wall is analysed for the limiting cases of low flow rate and high surface tension. Neither limiting case is approached uniformly and the singular perturbation method with matched asymptotic expansions is employed. The location of a free boundary, the curved meniscus, is unknown a priori, and the limiting meniscus profiles are obtained. An interesting viscous boundary layer is found at low flow rates.

Developing flow on a vertical wall

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V.M.K. Sastri

Papers

Accelerating laminar liquid film along an inclined wall