Dynamics and stability of evaporating and condensing liquid layers - Wei, Tao (2018)
Interfacial stability and pattern formation of evaporating or condensing liquid layers have attracted immense research interests. The prediction and control of interfacial instabilities are crucial in vapor-liquid systems, such as rupture of thin films in heat exchangers of electric devices. The present work concerns the nonlinear dynamics and stability of evaporating and condensing layers over a horizontal substrate, focusing on the effects of various interrelated physics on the gas-liquid interface. The evaporating layers are probed from two broad categories, non- and quasi-equilibrium. The non-equilibrium evaporating layers, covering a heated solid substrate and subjected to vapor recoil, capillarity, thermocapillarity, ambient cooling, viscosity, and negative or positive gravity combined with buoyancy effect, have been investigated in the framework of the long-wave (LW) theory. Linear stability analyses (LSA) identify the mechanisms of finite-time rupture, independent of thermocapillary effect and direction of gravity, and predict the effective growth rate of an infinitesimal interfacial perturbation which reveals competition among the mechanisms. A stability diagram is predicted for the onset of LW evaporative convection. In the (1+1)-dimensional [(1+1)D] simulation, well-defined capillary ridges can be observed on both sides of the valley under positive gravity (G > 0) and main and secondary droplets are expected to be seen under negative gravity (G < 0), while a ridge can be trapped in a large-scale drained region in both cases. Neglecting the other non-Boussinesq effects, buoyancy does not have a significant influence on interfacial evolution and rupture time (tr) but makes contributions to the evaporation-driven convection and heat transfer. The average Nusselt number is found to increase with a stronger buoyancy effect. The flow field and interface profile jointly manifest the LW Marangoni–Rayleigh–B´enard convection under positive gravity and the LW Marangoni convection under negative gravity. Then the more realistic (2 + 1)D simulation of moderate evaporation has been carried out with a random perturbation. The rupture patterns are characterized by irregular ridge networks with distinct height scales for sessile and pendent configurations. A variety of interfacial and internal dynamics are demonstrated, depending on evaporation conditions, gravity, Marangoni effect, and ambient cooling. Reasonable agreement is found between the present results and the reported experiments and simulations. The concept of dissipative compacton also brings to light the properties of interfacial fractalization. When quasi-equilibrium evaporation is considered with a simplified model, the interface instability is found to be enhanced by vapor recoil using the effective growth rate in LSA. The destabilizing mechanism of vapor thrust competes with the stabilizing surface tension which is not asymptotically negligible near rupture. Nonlinear evolution in (1+1)D shows that for weak mass loss and strong vapor recoil, the capillary ridges emerge around a deepening narrow valley with increasing wavelength in sessile layers, while, for Rayleigh–Taylor layers the main and secondary droplets are either partially coalesced or completely separated by a sharp dry-out point on the basis of initial condition (IC). The rupture location strongly depends on the characteristics of ICs except for the random perturbation. For both the quasi-equilibrium cases of G < 0 and G > 0, an increase in the modified evaporation number tends to reduce tr and droplet thicknesses. It is further investigated the (2 + 1)D nonlinear dynamics of a condensing layer, suspended from a cooled substrate and in contact with a vapor-inert gas mixture from below. A vapor boundary layer (VBL) is introduced, to which the changes in gaseous composition and temperature are assumed to be confined. An interfacial transport equation has been derived, which incorporates the effects of convection and diffusion of vapor within the VBL and couples with a LW interfacial evolution equation. The coupled nonlinear system is referred to as a 1.5-sided model, which can be reduced to a conventional one-sided model. An extended basic-state is also obtained, whose stability has been investigated with pseudo-steady LSA and time-dependent nonlinear simulation. With the 1.5-sided model, a regular non-rupture stable pattern is found in the Rayleigh–Taylor unstable layer due to local evaporation and condensation in the diffusion-limited regime. This is in sharp contrast to the prediction of the one-sided model without the convective and diffusive effects of vapor, where local rupture always occurs in finite time. Finally, conclusions are drawn, and perspectives of future study based on these works have been proposed, including to model the dynamics of thin evaporating droplets with moving contact lines resulting from the successive touchdown of an evaporating layer and to investigate the relation between short-wave convection and long-wave deformation instabilities in the presence of phase change.