On thermocapillary instability of a liquid column with a co-axial gas flow (original) (raw)

Thermocapillary instabilities in liquid columns under co – and counter-current gas flows

International Journal of Heat and Mass Transfer

The thermocapillary flows in an infinite liquid column surrounded by an annular channel of gas with the axial temperature gradient are investigated. The gas is pumped through the channel parallel to the interface with a given flow rate. The solution for stationary motion is derived and possible flow regimes are analyzed depending on the Marangoni number and dimensionless gas flow rate. Linear stability analysis of these regimes is performed. It is shown that gas pumping in the same direction with respect to the thermocapillary motion on the interface has a destabilizing effect on the system. Gas pumping in the opposite direction can be stabilizing or destabilizing depending on the gas flow rate. It is shown that the motion of liquid can be completely vanished by the gas flow with a specified flow rate. The obtained results demonstrate the possibility of controlling thermocapillary flows and their stability in liquid columns (liquid bridges) by gas flows.

Thermocapillary Flow in an Annular Two-Layer Liquid System

Journal of Advanced Thermal Science Research, 2016

By means of a hybrid lattice Boltzmann method, thermocapillary flow, driven by the surface tension owing to a horizontal temperature gradient along the interface in immiscible two-layer liquid system, is simulated numerically. The dynamic behavior of the interface is captured by using phase-field theory. The dependence of flow and interface deformation on the density ratio, Capillary number and aspect ratio, is investigated.

Thermocapillary instability of a liquid layer under heat flux modulation

The parametric excitation of the Marangoni instability in a horizontal liquid layer is analyzed in the case of a heat flux periodically varying at the deformable interface. Two response modes of the convective system to an external periodic stimulation, synchronous and subharmonic ones, have been found. The cellular and long-wave instability thresholds are compared. The neutral stability curves are presented for a variety of external conditions. It is shown that contrary to the classical parametric resonance, the synchronous disturbances may become most dangerous for the stability of the base state, and the long-wave mode may cause the instability prior to the cellular mode within a definite range of parameters.

Thermosolutal instability in a horizontal fluid layer affected by rotation

Thermal Science, 2019

Thermosolutal convective instability in a horizontal layer affected by rotation is studied. Stationary convection and over-stability cases are considered for different boundary conditions. Analytical solutions were obtained when both boundaries are free and numerical results were obtained for the cases of free and rigid boundaries. The numerical computations of this problem were performed using the method of expansion of Chebyshev polynomials. This method is better suited to the solution of hydrodynamic stability problems than expansions in other sets of orthogonal polynomials. This method not only has high accuracy but also allows stationary and over-stable modes to be treated simultaneously, which is important if perchance the critical eigenvalue flits between the different modes in response to changing parameter values. The results obtained show that the effect of both solute concentration and rotation is to stabilize the system for stationary convection case and for the over-stability case when both boundaries are free. However, when both boundaries are rigid some unexpected behavior are obtained in the case of over-stability.

Study of Thermocapillary Effects in Two Fluid Systems Using a Single Phase Model

Thermocapillary flow (subsequently also named Marangoni convection) is of considerable technological importance in material processing applications particularly under microgravity conditions. For the first time, the current study accounts for the effects of the driving forces developed in both normal and tangential directions of an interface located between two immiscible fluids within a differentially heated rectangular cavity. A 2-D numerical procedure on the basis of the single phase level set method for unsteady viscous free surface flows is developed. The time dependent Navier-Stokes equations and the level set equation are solved by means of the control volume approach on a staggered rectangular grid system. The numerical model interprets the tangential and the normal stresses by the single-phase model using the heavy side function. The topological changes of the interface between the two immiscible fluids are described by the level set method. Two different cases have been st...

Thermocapillary flows in two-fluids liquid bridges

Acta Astronautica, 2003

In this paper we consider the ow and interfaces deformation in non-isothermal two-liquids bridges, i.e. in liquid bridges held between two parallel planar disks, posed at di erent temperature, which are composed by two coaxial immiscible liquid columns, an inner column of liquid (a) forming an axisymmetric interface with an outer annular column of liquid (b) bounded by a free surface from the external still gas. The motion in the two bulk phases arises due to surface gradients of the interface tensions, induced by the imposed temperature di erence, both at the liquid-liquid interface and at the external free surface; for the interface tensions it is assumed a linear dependence on the temperature. Under the hypothesis of Reynolds, Peclet and capillary numbers very small, the ÿeld equations are expanded in a series of successive linear approximations; the zeroth-order approximation is the Stokes problem, that is analytically solved via separation of variables in terms of inÿnite series of modiÿed ÿrst-order Bessel functions of ÿrst and second kind and Papkovitch-Fadle bi-orthogonal eigenfunctions. To improve convergence of the series, Cesaro sums are used. The solution is given for the zeroth order temperature, velocity and pressure ÿelds and for the ÿrst-order deviation of the interfaces from the hydrostatic shape. Streamlines, velocity proÿles and interface shapes are presented and discussed in terms of Marangoni numbers, viscosity ratio of the two bulk phases and aspect ratios of the two liquid columns.

The axisymmetric thermocapillary motion of a fluid particle in a tube

Journal of Fluid Mechanics, 1991

The thermocapillary migration of a fluid particle in a tube, owing to an imposed axial temperature gradient, is studied theoretically for the case of steady, axisymmetric, creeping, translation in the absence of thermal convection and fluid particle distortion from sphericity, and for an insulated tube. Formulated with these assumptions, the migration is a linear Stokes flow which is separable into two fixed-fluid particle flow idealizations. One is the fluid motion in a quiescent continuous phase, owing only to the thermocapillary surface stress. This stress causes fluid streaming which exerts a lift force on the fluid particle in the direction of the warmer fluid described by a lift coefficient. The second idealization is uniform flow in the absence of thermocapillary forces. The force on the fluid particle owing to this flow represents the hydrodynamic resistance to the forward motion of the fluid particle in the presence of the tube wall, and is described in terms of a drag coef...

Experiments on the multi-roll-structure of thermocapillary flow in side-heated thin liquid layers

Advances in Space Research, 1999

The multi-roll-structure (MRS) with convection rolls, all with the same sense of rotation and axes perpendicular to the applied temperature gradient appears in thin layers driven by thermocapillarity prior to time dependent states. Detailed experimental and numerical results are reported. The MRS in large Prandtl-number fluids is dominated by thermocapillarity and separates from the buoyancy driven bulk flow for deep layers. We prepare a microgravity experiment MAGIA to study thermocapillary flow structures without coupling to buoyancy in a 20.0 mm wide annular layer with free surface of variable depth heated by the outer wall and cooled at the inside.