Absolute instability induced by Marangoni effect in thin liquid film flows on vertical cylindrical surfaces

Experiments on liquid film thickness around Taylor finger

Taylor finger is characterized by a single elongated air bubble that grows upward during the drainage of liquid from closed top vertical tubes. The characteristic of the Taylor finger is similar to the Taylor bubble commonly observed in gas–liquid two-phase flow. During the upward growth of the Taylor finger, liquid from the tube drains as a thin film around it. The exact prediction of film thickness is important in several engineering designs and process calculations such as the design of contacting devices, two-phase flow through porous media, boiling in tubes, and monolith reactors. The present study proposes an experimental technique to estimate the thickness of the draining liquid film. Based on experiments an empirical model has been proposed for non-dimensional film thickness in the inviscid region. The proposed model agrees well with the experimental data and equation proposed in published literatures (Davies, R. M., and G. Taylor. 1950. “The Mechanics of Large Bubbles Rising Through Extended Liquids and Through Liquids in Tubes.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 200, 375–90; Dukler, A. E., and J. Fabre. 1994. “Gas-Liquid Slug Flow.” Multiphase Science and Technology 8: 1–4; Fabre, J., and A. Liné. 1992. “Modeling of Two-Phase Slug Flow.” Annual Review of Fluid Mechanics 24: 21–46).

Role of suction pressure in the stability of a gravity-driven thermoviscous liquid film flow down the interior surface of a cylinder

This study aims to analyze the stability of a gravity-driven thin film flow in the heated/cooled interior surface of a vertical hollow cylinder. The model development involves simplifying the flow and energy equations using the usual thin-film approximation, where the average film thickness is considered to be much smaller than the radius of cylinder. A dispersion relation is then derived to study the temporal stability of the system in order to quantify the effect of various non-dimensional parameters present in the model, such as the thermoviscous number, Marangoni number, Biot number, and Bond number. Another non-dimensional parameter is introduced by considering an opposing suction pressure in the annulus region. The thermocapillary stress and the thermoviscous effect are shown to strongly affect the temporal stability of the flow. It is shown that although the suction pressure affects the velocity profile of the flow, it does not affect the temporal stability results. The suction pressure is then shown to have some effect on the spatiotemporal stability. Critical condition is presented for the transition between absolutely and convectively unstable systems, and parameter regimes are presented to quantify the effect of the above-mentioned parameters.

Effect of slip on the contact-line instability of a thin liquid film flowing down a cylinder

Liquid coating films on solid surfaces exist widely in a plethora of industrial processes. In this study, we focus on the falling of a liquid film on the side surface of a vertical cylinder, where the surface is viewed as slippery, such as a liquid-infused surface. The evolution profiles and flow instability of the advancing contact line are comprehensively analyzed. The governing equation of the thin film flow is derived according to the lubrication model, and the traveling-wave solutions are numerically obtained. The results show that the wave speed increases with the increase of a larger slippery length. A linear stability analysis (LSA) is carried out to verify the traveling solutions and time responses. Although previous studies tell us that the wall slippage always promotes the surface flow instability of the thin film flow, the linear stability analysis, numerical simulations, and nonlinear traveling-wave solutions in the current study present a different conclusion. The analysis show that for a thin film flow with a dynamic contact line the wall slippage in different directions plays much more complex roles. The streamwise slippery effect always impedes the instability of the flow and suppresses the wave height of traveling wave, while the transverse slippery effect has a dual effect on the surface instability. The transverse slippery effect significantly improves the instability while the wave number of the perturbation is small, and simultaneously it reduces the cutoff wave number. The transverse slippery effect will change its role if the wave number of the perturbation exceeds a critical value, which can stabilize the contact line.