Head-on collision between solitary waves and thermocapillary instabilities in Maxwell fluid using Rayleigh-Bénard-Marangoni system

Abstract

Purpose This work aims to present an analytical study of the head-on collision of bidirectional solitary waves in a Rayleigh–Bénard–Marangoni system consisting of a viscoelastic Maxwell fluid. The fluid is bounded by a rigid, nonpermeable lower surface and a deformable free surface at the top, where a constant heat flux is applied. Design/methodology/approach An extended Poincaré–Lighthill–Kuo method is used, incorporating stretched coordinates and phase functions, with an asymptotic expansion carried out consistently at successive orders. This approach yields coupled Korteweg–de Vries-type evolution equations governing the right- and left-propagating waves. The solutions are derived up to the second-order approximation, and the expressions for phase shift, distortion profile, maximum run-up amplitude and Nusselt number are presented explicitly. Findings The effect of wave interaction on heat transfer is quantified through the Nusselt number, showing that viscoelastic memory induces persistent changes in the vertical temperature gradient. Explicit expressions for phase shifts show that, unlike Newtonian fluids, viscoelastic relaxation leads to persistent trajectory corrections, resulting in intrinsically inelastic collisions, lasting waveform asymmetry and nonlinear peak broadening. A feasibility analysis based on representative physical parameters indicates that these nonlinear and depression-type solitary waves are most likely observable in the Bénard–Marangoni regime under experimentally accessible conditions. Originality/value To the best of the authors’ knowledge, the head-on collisions between solitary waves in a thermally driven Maxwell Rayleigh–Bénard–Marangoni system are studied using a perturbation approach for the first time in this paper. In contrast to earlier studies, this work has been restricted to unidirectional wave propagation. Therefore, the present results reveal intriguing facts that could be useful for experimental purposes.