Transient thermocapillary convection flows driven by the evenly heated lateral wall of a rectangular cavity for zero-gravity condition are investigated by scaling analysis and numerical simulation. Scaling analysis suggests a set of flow regimes in different dynamical evolutions of the surface flow, dependent on Marangoni and Prandtl numbers and aspect ratios. In the typical case, the surface flow may travel, for example, under flow regimes of unsteady inertial-thermocapillary balance, unsteady viscous-thermocapillary balance, and steady viscous-thermocapillary balance in different dynamical evolutions. Additionally, scaling laws of the thickness and velocity of transient thermocapillary convection flows under different flow regimes have been obtained. Furthermore, two-dimensional numerical simulation has been performed. The numerical results show good agreement with the corresponding scaling predictions.

Microstructured surfaces with pillar arrays are widely used to control the wetting morphology and spreading dynamics of droplets. In both simulations and experiments, it is shown that fabricating the surface with various microstructures is a very effective method for achieving the desired symmetry of the moving contact line. However, the method for characterizing miscellaneous pillar-arrayed microstructured surfaces is still insufficient. This paper presents the configurational entropy to characterize the microstructured surfaces with pillar arrays. By calculating the configurational entropy of pillar-arrayed microstructured surfaces, the relationship between the configurational entropy and the wetting morphology of droplets is obtained. For pillar-arrayed microstructured surfaces with the configurational entropy S > 0, the droplet wetting morphology may be much more complex than those with S = 0. The relationship is found to be consistent with the previous results. Furthermore, the wetting dynamics has been analysed. This study may be useful to understand the mechanism of droplet wetting on pillar-arrayed microstructured surfaces and provide insights for the design and manufacture of microstructured surfaces.

Transient thermocapillary convection under a surface of a linear temperature distribution in a top open cavity at a zero-gravity condition is investigated using scaling analysis and numerical simulation. Induced by the linear temperature distribution on a surface, a surface flow (SF) occurs. Then the pressure gradient near the sidewall drives a vertical flow (VF). The evolution in dynamics and heat transfer of the SF and the VF is argued, which is determined by Marangoni number (Ma), Prandtl number (Pr), and aspect ratio (A). Scaling analysis shows that there are four typical evolutions of the VF and two typical evolutions of the thermal boundary layer. Furthermore, velocity, boundary layer thickness, and Nusselt number of transient thermocapillary convection are scaled under different regimes in different evolutions, and a number of new scaling laws are proposed. Additionally, the flow structures under different regimes are characterized, and selected scaling laws obtained in scaling analysis are validated by numerical simulation results.

Transient thermocapillary convection flows near a suddenly heated vertical wire are widely present in nature and industrial systems. The current study investigates the dynamical evolution and heat transfer for these transient flows near a suddenly heated vertical wire, employing scaling analysis and axisymmetric numerical simulation methodologies. Scaling analysis indicates that there exist four possible scenarios of the dynamical evolution and heat transfer for these transient flows, dependent on the wire curvature, Marangoni number and Prandtl number. In a typical scenario of the dynamical evolution and heat transfer, heat is first conducted into the fluid after sudden heating, resulting in an annular vertical thermal boundary layer around the wire. The radial temperature gradient may generate a thermocapillary force on the liquid surface, dragging the liquid away from the wire. The pressure gradient also drives a vertical flow along the wire. Further, the current study analyses and derives the scaling laws of the velocity, thickness and Nusselt number for the surface and vertical flows in different scenarios. Additionally, a number of two-dimensional axisymmetric numerical simulations are performed. The flow structure around the suddenly heated vertical wire is characterised under different regimes and the validation for the proposed scaling laws in comparison with numerical results is presented.

Bénard–Marangoni convection in an open cavity has attracted much attention in the past century. In most of the previous works, liquids with Prandtl numbers larger than unity were used to study in this issue. However, the Bénard–Marangoni convection with liquids at Prandtl numbers lower than unity is still unclear. In this study, Bénard–Marangoni convection in an open cavity with liquids at Prandtl numbers lower than unity in zero-gravity conditions is investigated to reveal the bifurcations of the flow and quantify the heat and mass transfer. Three-dimensional direct numerical simulation is conducted by the finite-volume method with a SIMPLE scheme for the pressure–velocity coupling. The bottom boundary is nonslip and isothermal heated. The top boundary is assumed to be flat, cooled by air and opposed by the Marangoni stress. Numerical simulation is conducted for a wide range of Marangoni numbers (Ma) from 5.0 × 10¹ to 4.0 × 10⁴ and different Prandtl numbers (Pr) of 0.011, 0.029, and 0.063. Generally, for small Ma, the liquid metal in the cavity is dominated by conduction, and there is no convection. The critical Marangoni number for liquids with Prandtl numbers lower than unity equals those with Prandtl numbers larger than unity, but the cells are different. As Ma increases further, the cells pattern becomes irregular and the structure of the top surface of the cells becomes finer. The thermal boundary layer becomes thinner, and the column of velocity magnitudes in the middle slice of the fluid is denser, indicating a stronger convection with higher Marangoni numbers. A new scaling is found for the area-weighted mean velocity magnitude at the top boundary of u_m~Ma Pr^−2/3, which means the mass transfer may be enhanced by high Marangoni numbers and low Prandtl numbers. The Nusselt number is approximately constant for Ma ≤ 400 but increases slowly for Ma > 400, indicating that the heat transfer may be enhanced by increasing the Marangoni number.