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Thermocapillary flow of a thin liquid film in a confined two-layer system under a hydrophobic plate

Valeri Frumkin and Alexander Oron

  • Department of Mechanical Engineering, Technion–Israel Institute of Technology, Haifa 32000, Israel

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Phys. Rev. Fluids 2, 104002 – Published 26 October, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.104002

Abstract

We investigate flow in a thin liquid film over a heated solid surface in a bilayer two-dimensional gas-liquid system bounded on the gas side by an isothermal hydrophobic plate. The flow is driven by the Marangoni instability induced, in one case, by a thermal wave propagating along a flat solid substrate on the liquid side and in the other case by a left-right asymmetric topography of the thick solid substrate adjacent to the liquid phase uniformly heated at its outer surface. Using a long-wave approximation, we derive a nonlinear evolution equation governing the spatiotemporal dynamics of the liquid-gas interface and derive a closed-form expression indicating a nonzero value for a liquid flow rate in a steady state of the system, if attained. Numerical investigation is carried out to study the nonlinear dynamics of the gas-liquid interface and the resulting flow for various values of the system parameters. A linear stability analysis of the two-dimensional steady states of the system with a two-dimensional corrugated substrate on the liquid side is carried out with respect to three-dimensional out-of-plane disturbances. We demonstrate that the presence of a hydrophobic substrate enables a continuous flow for narrow systems associated with low values of the ratio between the mean thickness of the gas layer to that of the liquid, which would be impossible in its absence. This represents an extension of the conceptual methods discussed in our previous studies for the control and amplification of the average flow rate through the system for narrow systems, thus allowing for efficient thermocapillary transport in extremely small microfluidic devices.

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Phys. Rev. Fluids 2, 104002– Published 26 October, 2017
  • Received 13 June 2017

©2017 American Physical Society

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