Hydrodynamics of rivulet flow

Abstract

A theoretical analysis of the hydrodynamics of liquid rivulets flowing down an inclined surface is presented. Steady state solutions are developed for the laminar flow cose which relate the flow rate to the rivulet width, the physical properties of the liquid, and the contact angle. Excellent verification of the theoretical predictions was obtained in a number of experiments with various liquids on an inclined glass plate. All constants in the equations were derived from theory. These results will be useful in obtaining a better understanding and correlation of such phenomena as liquid flow over packings and catalysts and flow along walls and tube surfaces, as in condensation and evaporotion.

CFD Study on Liquid Flow Behavior on Inclined Flat Plate Focusing on Effect of Flow Rate

“…Fig. 6b illustrates that rivulet flows over the plate width keep semi-circular interfaces, which are in agreement with the theorectical studies by Towell and Rothfeld (1966). Furthermore, the width and the height of the rivulet with a higher Re-number are greater than those with a lower Re-number.…”

Fully developed magnetohydrodynamic flow in a rivulet.

“…Suppose that the location of the free surface is given by the equation z = h(y). At the free surface the jump in pressure is balanced by the surface tension [9], [10]. This gives:…”

Rivulet flow of generalized Newtonian fluids

“…Despite the fact that in practice many of the fluids involved demonstrate significant non-Newtonian behavior, most of the previous work has focused on the simplest case of rivulet flow of a Newtonian fluid. Notable among the limited number of previous studies of non-Newtonian rivulet flow are those by Rosenblat [3], who extended the pioneering work of Towell and Rothfeld [1] to study uniform rivulet flow of a viscoelastic fluid, Wilson et al [13], who extended the pioneering work of Smith [2] and Duffy and Moffatt [9] to study nonuniform rivulet flow of a power-law fluid, Balmforth et al [12] and Wilson et al [14], who studied rivulet flow of a viscoplastic material, Yatim et al [25], who studied unsteady nonuniform rivulet flow of a power-law fluid, and Al Mukahal et al [33,34], who studied locally uniform rivulet flow of a power-law fluid. However, despite a growing body of work on free surface flow of fluids with various non-Newtonian rheologies (see, for example, the recent work by Jossic et al [38] on thin-film flow of an Ellis fluid, Tshehla [39] on thin-film flow of a Carreau fluid, Kheyfets and Kieweg [40] on thin-film flow of an Ellis fluid, Pritchard et al [41] on thin-film flow of a generalized Newtonian fluid, Fomin et al [42] on non-Newtonian rimming flow, and Peralta et al [43] on thin-film flow of a Carreau-Yasuda fluid) there is very little work on rivulet flow of fluids with other than the theoretically convenient but highly idealised power-law rheology.…”