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Self-rewetting fluids (SRFs) (e.g., aqueous solutions of long-chain alcohols) show anomalous nonlinear (quadratic) variations of surface tension with temperature involving a positive gradient, leading to different thermocapillary convection compared to normal fluids (NFs). Moreover, surface-active materials or surfactants can significantly alter interfacial dynamics by their adsorption on fluid interfaces. The coupled effects of temperature- and surfactant-induced Marangoni stresses on migration bubbles in SRFs remain unexplored. We use a robust lattice Boltzmann (LB) method based on central moments to simulate the two-fluid motions, capture interfaces, and compute the transport of energy and surfactant concentration fields, and systematically study the surfactant-laden bubble dynamics in SRFs. When compared to motion of bubbles in normal fluids, in which they continuously migrate without a stationary behavior, our results show that they exhibit dramatically different characteristics in SRFs. Not only is the bubble motion directed towards the minimum temperature location in SRFs, but, more importantly, the bubble attains an equilibrium position. In the absence of surfactants, such an equilibrium position arises at the minimum reference temperature occurring at the center of the domain. The addition of surfactants moves the equilibrium location further upstream, which is controlled by the magnitude of the Gibbs elasticity parameter that determines the magnitude of the surface tension variation with surfactants. The quadratic sensitivity coefficient of surface tension on temperature associated with the SRF modulates this behavior. The lower this quantity, the greater is the role of surfactants modifying the equilibrium position of the bubble in SRF. These findings provide new means to potentially manipulate the bubble dynamics, and especially to tune its equilibrium states., Comment: 57 pages, 30 figures

Cross-stream migration of a deformable bubble is investigated computationally in a pressure-driven channel flow of a viscoelastic fluid via interface-resolved simulations. The flow equations are solved fully coupled with the Giesekus model equations using the front-tracking method and extensive simulations are performed for a wide range of flow parameters to reveal the effects of bubble deformability, fluid elasticity, shear-thinning, and fluid inertia on the bubble migration dynamics. Migration rate of a bubble is found to be much higher than that of a solid particle under similar flow conditions mainly due to free-slip condition on its surface. It is observed that direction of bubble migration can be altered by varying shear-thinning of the ambient fluid. With a strong shear-thinning, the bubble migrates towards the wall while it migrates towards the center of the channel in a purely elastic fluid without shear-thinning. An onset of elastic flow instability is observed beyond a critical Weissenberg number, which in turn causes a path instability even for a nearly spherical bubble. An inertial path instability is also observed once bubble deformation exceeds a critical value. Shear-thinning is found to be suppressing the path instability in a viscoelastic fluid with a high polymer concentration whereas it reverses its role and promotes path instability in a dilute polymer solution. It is found that bubble migration towards wall induces a secondary flow with a velocity that is about an order of magnitude higher than the one induced by a solid particle under similar flow conditions.

A novel theoretical model for bubble dynamics is established that simultaneously accounts for the liquid compressibility, phase transition, oscillation, migration, ambient flow field, etc. The bubble dynamics equations are presented in a unified and concise mathematical form with clear physical meanings and extensibility. The bubble oscillation equation can be simplified to the Keller-Miksis equation by neglecting the effects of phase transition and bubble migration. The present theoretical model effectively captures the experimental results for bubbles generated in free fields, near free surfaces, adjacent to rigid walls, and in the vicinity of other bubbles. Based on the present theory, we explore the effect of the bubble content by changing the vapor proportion inside the cavitation bubble for an initial high-pressure bubble. It is found that the energy loss of the bubble shows a consistent increase with increasing Mach number and initial vapor proportion. However, the radiated pressure peak by the bubble at the collapse stage increases with the decreasing Mach number and increasing vapor proportion. The energy analyses of the bubble reveal that the presence of vapor inside the bubble not only directly contributes to the energy loss of the bubble through phase transition but also intensifies the bubble collapse, which leads to greater radiation of energy into the surrounding flow field due to the fluid compressibility.