Linear Stability Analysis of Thermocapillary Flow in Rotating Shallow PoolsHeated from Inner Wall

Thermocapillary flow of silicon melt(Pr=0.011)in shallow annular pool heated from inner wall was simulated at the dimensionless rotation ratewranging from 0 to 7000.The effect of pool rotation on the stability of the thermocapillary flow was investigated.The steady axisymmetric basic state was solved by using the spectral element method;the critical stability parameters were determined by linear stability analysis;the mechanism of the flow instability was explored by the analysis of energy balance.A stability diagram,exhibiting the variation of the critical Marangoni number versus the dimensionless rotation ratewwas presented.The results reveal that only one Hopf bifurcation point appeared in the intervals ofω<3020 andω>3965,and the corresponding instability was caused by the shear energy,which was provided by the thermocapillary force and pool rotation,respectively.In addition,the competition between thermocapillary force and pool rotation leads to three Hopf bifurcation points in the range of 3020<ω<3965 with the increase of Marangoni number.

Analytical Solution of Thermocapillary Flow in Cylindrical Annuli with Curved Free Surface

In this paper we consider thermocapillary flow with interface deformation in cylindrical annuli subjected to lateral temperature gradient.Based on the assumption that Reynolds,Marangoni and capillary numbers are very small,we expanded the governing equations in terms of a small parameter,and the zeroth-order one is the Stokes problem,which can be analytically solved by use of separation of variables formulation.Solutions are obtained for the zeroth-order fluid and thermal fields as well as the first-order interfacial shapes.Streamlines,temperature distributions and interface shapes are presented and the influence of aspect ratios is investigated.

Lattice Boltzmann Method for Thermocapillary Flows

In this paper,we apply a recently proposed thermal axisymmetric lattice Boltzmann model to the thermocapillary driven flow in a cylindrical container.The temperature profiles and isothermal lines at the free surface with Prandtl(Pr)number fixed at 0.01 and Marangoni(Ma)number varying from 10 to 500 are measured and compared with the previous numerical results.In addition,we also give the numerical results for different Ma numbers at Pr=1.0.It is shown that present results greed well with those reported in previous studies.

A Review on the Evaporation Dynamics of Sessile Drops of Binary Mixtures:Challenges and Opportunities

The wetting and evaporation dynamics of sessile droplets have gained considerable attention over the last few years due to their relevance to many practical applications,ranging from a variety of industrial problems to several biological systems.Droplets made of binary mixtures typically undergo complex dynamics due to the differential volatility of the considered components and the ensuing presence of thermocapillary effects.For these reasons,many research groups have focused on the evaporation of binary droplets using a variegated set of experimental,numerical,and purely theoretical approaches.Apart from reviewing the state-of-the-art about the existing experimental,analytical,and computational techniques used to study the evaporation dynamics of binary sessile droplets,we also provide some indications about possible future research directions in this specific area.