Characterisation of hydraulic jumps/falls with surface tension variations in thin film flows

The effects of surface tension gradients in flowing thin films are studied. Thermodynamic viability of inverted hydraulic jump-like waves is character ised through a dimensionless parameter beta arising from the control volume analysis of hydraulic jumps. The factor beta is the ratio of effective gra vity forces upstream to downstream when the upstream and downstream surface tensions differ. Further, the linear stability theory is numerically solve d to determine critical stability due to the surface tension gradients alon g the free surface. The surface tension is assumed to be changing on a long er scale than the depth. This assumption allows the treatment of the spatia l dependency of surface tension parametrically. Approximate analytical solu tions to the perturbation system of first order in wave number give a relat ionship between the parameters which determines the bifurcating value of Re ynolds number, Reb. This bifurcation Reynolds number explicitly depends on the initial pressure gradient imposed along the flow direction. Surface ten sion gradients tend to destabilise the flow. For a surface tension gradient of 1%, Re-b drops about 33% from its value in the absence of surface tensi on gradients. The numerical results are in accordance with analytical resul ts for limiting cases of long waves and small inertia, respectively. (C) 20 01 Elsevier Science B.V. All rights reserved.