Theoretical considerations of laser induced liquid-liquid interface deformation

In the increasingly active field of optofluidics, a series of experiments involving near-critical two-fluid interfaces have shown a number of interesting non-linear effects. We here offer, for the first time to our knowledge, an explanation for one such feature, observed in experiments by Casner and Delville [Phys. Rev. Lett. {\bf 90}, 144503 (2003)], namely the sudden formation of "shoulder"-like shapes in a laser-induced deformation of the liquid-liquid interface at high laser power. Two candidate explanations are the following: firstly, that the shape can be explained by balancing forces of buoyancy, laser pull and surface tension only, and that the observed change of deformation shape is the sudden jump from one solution of the strongly nonlinear governing differential equation to another. Secondly, it might be that the nontrivial shape observed could be the result of temperature gradients due to local absorptive heating of the liquid. We report that a systematic search for solutions of the governing equation in the first case yields no trace of solutions containing such features. By contrast, an investigation of the second option shows that the narrow shape of the tip of the deformation can be explained by a slight {\it heating} of the liquids. The local heating amounts to a few kelvins, with the parameters given, although there are uncertainties here. Our investigations suggest that local temperature variations are the crucial element behind the instability and the shoulder-like deformation.