On the Various Wave Motions Observed at a Liquid Interface Due to Marangoni Stresses and Instability

With mass or heat transfer across a liquid surface and hence with Marangoni stresses (Ma-stress, in short) past an instability threshold patterned convection or wavy motions may be excited and sustained. Here we report on waves observed: waves with anomalous dispersion (dv/d(lambda) < 0; (lambda)= wavelength, v = wave velocity), dispersion-free waves, and waves with normal dispersion (dv/d(lambda) > 0), in an otherwise stably stratified liquid layer. Experimental data obtained using a variety of setups, playing with different mass- or heat-transfer systems, is gathered together in a comprehensive picture about these wave types. Using data obtained in unsteady and steady experiments, we show by means of the (v,(lambda))-plot the eventual change from one form of dispersion to another, and hence from one wave type to another as the level of Ma-stress (or driving force) changes with time and eventually decreases. In a typical sequence, for strong enough driving force, and hence at high values of the gradient of concentration or temperature, waves with anomalous dispersion are observed and, as the driving force decreases, yield to waves with normal dispersion. Transitions are also observed from dispersion-free waves decaying into waves with normal dispersion. The picture is purposely completed by comparing these experimental findings with the features nominally corresponding to capillary and internal gravity waves driven by mechanical vibration of the container using the same liquids with, however, no Ma-stress.