环形腔内双层薄液层热毛细对流的渐近解

为了解水平温度梯度作用下环形腔内双层薄液层热毛细对流的基本特性,采用渐近线方法获得了热毛细对流的近似解. 环形腔外壁被加热,内壁被冷却,上、下壁面绝热. 结果表明,当环形腔宽度与内半径比趋于零时,环形腔退化为矩形腔,所得到的主流区速度场和温度场的表达式演化为Nepomnyashchy 等得到的矩形腔内的结果;与数值模拟结果的比较发现,在主流区渐近解与数值解吻合较好.      

Occurrence of thermocapillary convection in a two-layer system in the presence of a soluble surfactant

The present study considers the effect of the solubility of a surfactant on monotonic oscillatory thermocapillary instability of equilibrium in a two-layer system. It is established that with increase in the parameter which characterizes the solubility of the surfactant a reduction takes place in the threshold of the monotonic instability; finally the monotonic perturbations become most dangerous.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 171–175, March–April, 1988.     

Onset of thermocapillary convection in a two-layer system with the release of heat at the interface

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 69–73, January–February, 1990.     

Convection in a two-layer system due to the combined action of the Rayleigh and thermocapillary instability mechanisms

In a two-layer system loss of stability may be monotonic or oscillatory in character. Increasing oscillatory perturbations have been detected in the case of both Rayleigh [1, 2] and thermocapillary convection [3–5]; however, for many systems the minimum of the neutral curve corresponds to monotonic perturbations. In [5] an example was given of a system for which oscillatory instability is most dangerous when the thermogravitational and thermocapillary instability mechanisms are simultaneously operative. In this paper the occurrence of convection in a two-layer system due to the combined action of the Rayleigh (volume) and thermocapillary (surface) instability mechanisms is systematically investigated. It is shown that when the Rayleigh mechanism operates primarily in the upper layer of fluid, in the presence of a thermocapillary effect oscillatory instability may be the more dangerous. If thermogravitational convection is excited in the lower layer of fluid, the instability will be monotonic.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 166–170, January–February, 1987.     

Flow-rate and thrust coefficients for two-layer flows in a convergent nozzle

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 187–189, January–February, 1990.     

Effect of fluid microstructure on stability of plane two-layer flows

The stability of plane two-layer Couette and Poiseuille flows, where the lower layer consists of a Grad-model fluid and the upper layer is a viscous Newtonian fluid, is investigated. The disturbances are assumed to be of the long-wave type, and the analysis involves expansion in wave numbers and is limited by two approximations. Numerical calculations are made for some values of the parameters. The calculations indicate that the rotational energy of the fluid in the lower layer has a destabilizing effect on the flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 125–127, July–August, 1978.     

Stability of two-layer fluid flows with evaporation at the interface

The problem of stability of two-layer (fluid-gas) flows with account of evaporation at the thermocapillary interface is studied under the condition of a fixed gas flow rate. In the upper gas-vapor layer, the Dufour effect is taken into account. A novel exact solution of the Navier–Stokes equations in the Boussinesq approximation is constructed. The effects of longitudinal temperature gradients, gravity, thicknesses of the gas and fluid layers, and the gas flow rate on the flow structure, the onset of recirculated flows near the interface, the evaporation rate, and the properties of characteristic disturbances are investigated.     

Onset of oscillatory thermocapillary convection in systems with a deformable interface

Oscillatory interfacial instability is investigated with allowance for the deformation of the interface. The possibility of two types of oscillations being excited is established. One of these is similar to the well-known type in systems with a plane interface, while the other is determined by the oscillations of the deformable surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 11–16, July–August, 1991.     

Longwave instability of two-layer dielectric fluid flows in a transverse electrostatic field

Some aspects of the problem of the stability and the nature of the secondary regimes of a plane two-layer Poiseuille flow of viscous dielectric fluids between horizontal electrodes with a constant potential difference are considered. A linear analysis shows that the electrostatic field can induce the growth of perturbations with an asymptotically small wavenumber when the dielectric permeabilities of the fluids are different. On the assumption that the perturbation wavelength is large as compared with the thickness of one of the layers and comparable with the thickness of the other in order of magnitude, one of the possible mechanisms of development of finite fluctuations is investigated. Within the framework of this mechanism the initial mathematical mdoel can be reduced to an integrodifferential evolutionary Kuramoto-Sivashinsky-type equation describing the behavior of the fluid interface. The periodic solutions of this equation, which are investigated numerically, are bounded and fairly diverse. Krasnoyarsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 45–55, March–April, 2000.     

FLOQUET STABILITY ANALYSIS OF TWO-LAYER FLOWS IN VERTICAL PIPE WITH PERIODIC FLUCTUATION

Based on linear stability theory, parametric resonance phenomenon of a liquid-gas cylindrical flow in a vertical pipe with periodic fluctuation was discussed with the help of Floquet theory and Chebyshev spectral collocation method. The effects of different physical parameters were investigated on the properties of parametric resonance and the stability characteristics of flow field.     

Combined action of anticonvective and thermocapillary mechanisms of instability in multilayer systems

The nonlinear regimes of convection in the system of three immiscible viscous fluids heated from above are investigated. The interfaces are assumed to be flat. The boundary value problem is solved by the finite-difference method. Transitions between convective motions with different spatial structures are investigated. The common diagram of instability regimes is constructed. The new phenomena caused by direct and indirect interaction of anticonvective and thermocapillary mechanisms of instability are considered. Specifically, different oscillatory configurations where anticonvection arises mainly near the upper interface and thermocapillary convection appears mainly near the lower interface have been found.     

Simulations of 2D and 3D thermocapillary flows by a least-squares finite element method

Numerical results for time-dependent 2D and 3D thermocapillary flows are presented in this work. The numerical algorithm is based on the Crank–Nicolson scheme for time integration, Newton's method for linearization, and a least-squares finite element method, together with a matrix-free Jacobi conjugate gradient technique. The main objective in this work is to demonstrate how the least-squares finite element method, together with an iterative procedure, deals with the capillary-traction boundary conditions at the free surface, which involves the coupling of velocity and temperature gradients. Mesh refinement studies were also carried out to validate the numerical results. © 1998 John Wiley & Sons, Ltd.     

Validation of the S‐CLSVOF method with the density‐scaled balanced continuum surface force model in multiphase systems coupled with thermocapillary flows

Three numerical methods, namely, volume of fluid (VOF), simple coupled volume of fluid with level set (S‐CLSVOF), and S‐CLSVOF with the density‐scaled balanced continuum surface force (CSF) model, have been incorporated into OpenFOAM source code and were validated for their accuracy for three cases: (i) an isothermal static case, (ii) isothermal dynamic cases, and (iii) non‐isothermal dynamic cases with thermocapillary flow including dynamic interface deformation. Results have shown that the S‐CLSVOF method gives accurate results in the test cases with mild computation conditions, and the S‐CLSVOF technique with the density‐scaled balanced CSF model leads to accurate results in the cases of large interface deformations and large density and viscosity ratios. These show that these high accuracy methods would be appropriate to obtain accurate predictions in multiphase flow systems with thermocapillary flows. Copyright © 2016 John Wiley & Sons, Ltd.     

Instability of the interface in two-layer flows with large viscosity contrast at small Reynolds numbers

The Kelvin–Helmholtz instability is believed to be the dominant instability mechanism for free shear flows at large Reynolds numbers. At small Reynolds numbers, a new instability mode is identified when the temporal instability of parallel viscous two fluid mixing layers is extended to current-fluid mud systems by considering a composite error function velocity profile. The new mode is caused by the large viscosity difference between the two fluids. This interfacial mode exists when the fluid mud boundary layer is sufficiently thin. Its performance is different from that of the Kelvin–Helmholtz mode. This mode has not yet been reported for interface instability problems with large viscosity contrasts.These results are essential for further stability analysis of flows relevant to the breaking up of this type of interface.     

Transient electro-osmotic and pressure driven flows of two-layer fluids through a slit microchannel

By method of the Laplace transform, this article presents semi-analytical solutions for transient electroosmotic and pressure-driven flows (EOF/PDF) of two-layer fluids between microparallel plates. The linearized Poisson-Boltzmann equation and the Cauchy momentum equation have been solved in this article. At the interface, the Maxwell stress is included as the boundary condition. By numerical computations of the inverse Laplace transform, the effects of dielectric constant ratio ε , density ratio ρ , pressure ratio p, viscosity ratio μ of layer II to layer I, interface zeta potential difference △ψ, interface charge density jump Q, the ratios of maximum electro-osmotic velocity to pressure velocity α , and the normalized pressure gradient B on transient velocity amplitude are presented.We find the velocity amplitude becomes large with the interface zeta potential difference and becomes small with the increase of the viscosity. The velocity will be large with the increases of dielectric constant ratio; the density ratio almost does not influence the EOF velocity. Larger interface charge density jump leads to a strong jump of velocity at the interface. Additionally, the effects of the thickness of fluid layers (h1 and h2 ) and pressure gradient on the velocity are also investigated.     

Stability of two-layer systems with respect to convective mixing

The occurrence and development of convection in a two-layer system heated below has been investigated [1–5] under the assumption that the interface of the fluids is horizontal and is not subject to deformations. However, this assumption may not be satisfied if the surface tension on the interface is small and the fluids have either nearly equal densities or the heavier fluid is situated at the top. In the present paper, an attempt is made to study the convection regimes in a two-layer system with deformation of the interface when there is heating from below or above. The simultaneous influence of the convective and Rayleigh-Taylor instability mechanisms is taken into account; the surface tension on the interface is assumed to be infinitesimally small, and thermocapillary effects are ignored. A two-fluid variant of the method of markers and cells [6–9] is used for the numerical solution of the convection equations. A diagram of the regimes is constructed. It is shown that depending on the values of the parameters the system either preserves its two-layer structure, or the development of the conveetive motion leads to the breakup of the interface and complete mixing of the fluids.     

Stable two-layer flows at all Re; visco-plastic lubrication of shear-thinning and viscoelastic fluids

Multi-fluid flows are frequently thought of as being less stable than single phase flows. Consideration of different non-Newtonian models can give rise to different types of hydrodynamic instability. Here we show that with careful choice of fluid rheologies and flow paradigm, one can achieve multi-layer flows that are linearly stable for Re = ∞. The basic methodology consists of two steps. First we eliminate interfacial instabilities by using a yield stress fluid in one fluid layer and ensuring that for the base flow configurations studied we maintain an unyielded plug region at the interface. Secondly we eliminate linear shear instabilities by ensuring a strong enough Couette component in the second fluid layer, imposed via the moving interface. We show that this technique can be applied to both shear-thinning and visco-elastic fluids.