Mathematical modelling of thermocapillary patterning in thin liquid film: an equilibrium study

Yang, Qingzhen; Li, Ben Q.; Lv, Xuemeng; Song, Fenhong; Liu, Yankui; Feng, Xiuli

doi:10.1017/jfm.2021.407

Cited by 9 publications

(3 citation statements)

References 40 publications

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“…In heat transfer systems with a free surface experiencing surface-tension variations, the fluid motion driven by the temperature-induced surface tension gradient, which has been called thermocapillary flow, is often encountered. Since thermocapillary flow plays important roles in crystal growth [1], surface patterning [2], melting [3] and coating [4], much research has been conducted theoretically and experimentally.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulations on Thermocapillary Flow on Heated Sinusoidal Topography

Kim

2024

Korean J. Chem. Eng.

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The interaction between thermocapillary flow and substrate geometry is analyzed numerically.Taking surface tension into account, the momentum equation is derived and solved using a commercial FEM solver, Comsol Multiphysics where the effects of surface tension and surface deflection can be easily incorporated into the momentum equation. In the case of Ma ≈ Ma 𝑐 , the strong symmetric thermocapillary flow is observed when the wavelength of topography, 𝜆 𝑇 , and the wavelength of instability motion, 𝜆, are nearly the same. This interesting phenomenon has been called flow-structure resonance. Through the numerical simulations, various flow modes, such as symmetric two-cell and four-cell modes, asymmetric two-cell mode, and oscillatory asymmetric two-cell mode are identified by changing the Marangoni number and wavelength of topography. It is clearly shown that for a certain 𝜆 𝑇 -system, the transition from oscillatory mode to steady one is possible by relaxing the previous nondeformable surface condition due to high surface tension, i.e., Cr → 0. The present study reveals that the preferred flow mode is the complex function of the various parameters such as the Marangoni number, the Biot number, the wavelength of topography, and the capillary number.

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Section: Introductionmentioning

confidence: 99%

Numerical Simulations on Thermocapillary Flow on Heated Sinusoidal Topography

Kim

2024

Korean J. Chem. Eng.

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“…[2]. Liquid film thickness is a very important parameter in the gas-liquid two-phase flow [3][4][5]. However, the complexity and irregularity of annular flow pose a challenge for the liquid film parameters' measurement.…”

Section: Introductionmentioning

confidence: 99%

Liquid film parameter measurement based on thermal distribution sensor in horizontal annular flow

Zhao,

Sun,

Zhang

et al. 2023

Meas. Sci. Technol.

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Liquid film is an important carrier of mass and heat transfer in annular flow, and the parameter detection of which plays an important role in the energy metering of natural gas production processes and the safe and reliable operation of cooling and heating systems. In this paper, a liquid film velocity equation is derived based on the analysis of the heat balance equation between the liquid film and tube wall. According to the constant power principle, the thermal distributed flow measurement sensor is designed by using the multi-physical field coupling simulation technique According to the momentum balance equation of the Laurinat model, considering the pump mechanism of the disturbance wave and using magnitude comparison and stress balance, a liquid film thickness circumferential distribution model in the horizontal annular flow is proposed. Utilizing the model and designed sensor, the liquid film thickness of four locations (0°, 90°, 180°, 270°) measurements are obtained for 64 horizontal annular flow conditions. Laboratory results indicate that the mean absolute percent error of the model is 32.66% and the 82.81% relative error is within the ±30% error band.

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“…The study was later experimentally consolidated by the same group. 41 Yang et al 42 theoretically and numerically investigated the equilibrium state of a deformed interface for a polymer−air system under a transverse thermal gradient. Furthermore, Yang et al 19 and Song et al 43 numerically studied the dynamic evolution of a liquid film interface (polymer−air system).…”

Section: ■ Introductionmentioning

confidence: 99%

Marangoni Flows in a Bilayer Liquid Microfilm Interface on Wave-Contoured Hot Substrates

Agrawal,

Das,

Dhar

2023

Langmuir

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This study explores the thermal Marangoni hydrodynamics in an immiscible, binary-liquid thin-film system, which is open to the gas phase at the top and rests on a heated substrate with wavy topology. The sinusoidal contour of the heated (constant-temperature) substrate results in temperature gradients along the liquid–liquid and liquid–gas interfaces, causing fluctuations in the interfacial tension, ultimately leading to Marangoni hydrodynamics in the liquid–liquid films. This type of flow is notable in liquid film coatings on patterned surfaces, which are widely used in MEMS/NEMS applications (Weinstein, S. J.; Palmer, H. J. Liquid Film Coating: Scientific Principles and Their Technological Implications; 1997, pp 19–62; Palacio, M.; Bhushan, B. Adv. Mater. 2008, 20, 1194–1198) and biological cell sorting operations (Witek, M. A.; Freed, I. M.; Soper, S. A. Anal. Chem. 2019, 92, 105–131). We solve the coupled Navier–Stokes and energy equations by the perturbation technique to obtain approximate analytical solutions and an understanding of the thermal and hydrodynamic transport in the system domain. Our study explores the parametric influence of the relative thermal conductivity of the liquid layers (k), film thickness ratio (r), and the system’s Biot number (Bi) on these transport phenomena. While the strength of the thermal Marangoni effect that is generated reduces with an increase in the relative thermal conductivity (k), the impact of r depends on the k value. We observe that for k > 1 the intensity of Marangoni flow increases with r; however, the opposite holds for k < 1. Furthermore, larger values of Bi induce higher resistance to the vertical conduction from the wavy substrate compared to the convection resistance offered at the top surface, destructively interfering with the ability of the patterned substrate to generate interfacial temperature fluctuations and hence weakening the Marangoni flow.

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Mathematical modelling of thermocapillary patterning in thin liquid film: an equilibrium study

Abstract: Abstract

Cited by 9 publications

References 40 publications

Numerical Simulations on Thermocapillary Flow on Heated Sinusoidal Topography

Numerical Simulations on Thermocapillary Flow on Heated Sinusoidal Topography

Liquid film parameter measurement based on thermal distribution sensor in horizontal annular flow

Marangoni Flows in a Bilayer Liquid Microfilm Interface on Wave-Contoured Hot Substrates

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