Stability of liquid film falling down a vertical non-uniformly heated wall

The main object in this paper is to study the stability of a viscous film flowing down a vertical non-uniformly heated wall under gravity. The wall temperature is assumed linearly distributed along the wall and the free surface is taken to be adiabatic. A long wave perturbation method is used to derive the nonlinear evolution equation for the falling film. Using the method of multiple scale, the nonlinear stability analysis is studied for travelling wave solution of the evolution equation. The complex Ginzburg-Landau equation is determined to discuss the bifurcation analysis of the evolution equation. The results indicate that the supercritical unstable region increases and the subcritical stable region decreases with the increase of Peclet number. It has been also shown that the spatial uniform solution corresponding to the sideband disturbance may be stable in the unstable region.     

Stability of inertialess liquid film flowing down a heated inclined plane

This paper investigates the stability of inertialess falling film down an uniformly heated inclined plane. Normal mode analysis is performed to study the linear stability of the falling film.     

About the effect of microtexture on liquid film formation on a vertical surface

Formation of a liquid film on the surface of a cylinder with microtexture was studied visually. The effect of microtexture on evolution of waves on the surface of viscous liquid falling over the outer surface of a vertical cylinder under the action of gravity depending on Reynolds number is shown. The phenomenon of microwave formation on the film surface was determined; the size of these waves is comparable with the microtexture pitch.     

Numerical study of a thin liquid film flowing down an inclined wavy plane

We investigate the stability of a thin liquid film flowing down an inclined wavy plane using a direct numerical solver based on a finite element/arbitrary Lagrangian Eulerian approximation of the free-surface Navier-Stokes equations. We study the dependence of the critical Reynolds number for the onset of surface wave instabilities on the inclination angle, the waviness parameter, and the wavelength parameter, focusing in particular on mild inclinations and relatively large waviness so that the bottom does not fall monotonously. In the present parameter range, shorter wavelengths and higher amplitude for the bottom undulation stabilize the flow. The dependence of the critical Reynolds number evaluated with the Nusselt flow rate on the inclination angle is more complex than the classical relation (5/6 times the cotangent of the inclination angle), but this dependence can be recovered if the actual flow rate at critical conditions is used instead.     

Spreading of a viscous liquid film over the corrugated surface and the heat and mass transfer calculations

There are a lot of industrial applications of structured packing. Distillation columns are one of the examples where the liquid flows over the corrugated surface as a thin film to provide a good mass-transfer surface between the liquid and vapor phase. The purpose of the present paper is to study the hydrodynamics and the heat-mass transfer of the liquid film spreading down the corrugated surfaces when the corrugation amplitude is comparable with Nusselt’s film thickness (the amplitude corresponds to a small texture of the structured packing). As a result, a nonlinear type diffusion equation is obtained to describe the evolution of the film thickness profile. The nonlinear diffusion coefficient is obtained for three cases: a smooth inclined plate, a corrugated plate with large ribs, and an inclined corrugated plate with small ribs. The equations are solved numerically. As a result, it has been obtained that the small texture significantly increases the rate of the film thickness evolution in comparison with a smooth plate. To obtain the nonlinear diffusion coefficient in the case of a small texture, the hydrodynamics of the film flow over an inclined corrugated surface are studied. The viscosity, inertia, and surface tension forces are taken into account. The calculations were carried out on the basis of the Navier-Stokes equations. The influence of the microcorrugations on both the heat transfer from the wall and the mass transfer through the free surface was investigated.     

Stability of a dry patch in a viscous flowing film

We investigate the dewetting of liquid films flowing down an incline. At low flow rate we observe the formation of stationary dry patches edged with a liquid rim. Their shape can be predicted by a simple model in which the rim weight is balanced by surface tension. Above a critical flow rate per unit length Γ_c of typical scale U_cl_c (U_c capillary velocity, l_c capillary length), these dry patches cannot remain stationary and are swept away. An improved model taking into account capillary effects linked to contact line curvature, hydrostatic pressure in the film and inertial effects predicts this loss of stability in good agreement with experiments for sufficiently high viscosity values.     

Stability of the heated liquid film in the presence of the thermocapillary effect

Stability of the flow of the heated liquid film is studied in the presence of the thermocapillary effect. To describe the waves in the film, the integral model is used. According to results of linear analysis of stability, the thermocapillary effect expands the area of instability only at low values of Peclet number Pe, and at high values of Pe, the instability area narrows. Wave evolution in the film on a substrate with the fixed temperature was simulated numerically. Results of numerical simulations agree with the linear theory of stability.     

Experimental study of the instability of a film flowing down a vertical fiber

The wavy dynamics of a viscous film flowing axisymmetrically on a vertical fiber is characterized experimentally. The study of the initial response of the flow to natural noise shows a well-defined transition between a convective and an absolute instability [1]. In the convective case, disturbances of controlled frequencies have been applied at inlet. The flow responds to inlet excitation at frequencies lower than a well-defined cut-off frequency. A good agreement has been found with the linear stability analysis and with the solution to a two-equation model [2] in the nonlinear regime.     

Interfacial friction and mass transfer at gas flow into vacuum through a nozzle with a near-wall liquid film

The cycle of experiments on interaction between the co-current gas flow and the near-wall liquid film were carried out at high gas flow velocities, including the supersonic ones. The local parameters of the near-wall film were measured by the capacitance probes. It is shown that the co-current gas flow affects the near-wall film significantly, causing intensive wave formation, droplet detachment from the film surface, and their entrainment by the gas flow. It is determined that a relative amount of liquid entrained by the co-current flow is generalized by the Weber number of this gas flow.     

Nonstationary periodic spatial waves on the surface of a viscous liquid film falling down a vertical cylinder

The flows of viscous liquid film over the outer surface of a vertical cylinder are examined. Investigation of wave regimes in the case of low flow rates and large cylinder radii is reduced to the analysis of solutions to a nonlinear evolution equation for the film thickness. There are countable numbers of steady-state traveling solution families in the considered model. In turn, most of them are unstable to 2D and 3D perturbations. Thus, evolution of initial perturbations in different ranges of parameter values differs significantly. Some typical scenarios of perturbation development are presented in this work. Initial perturbations with some symmetries, kept in the process of evolution, are of a particular interest. In these cases, solutions are drawn up to the steady-state traveling solutions with similar symmetry.     

Destabilization of a viscous film flowing down in the form of a vertical cylindrical curtain

In this Letter, we study experimentally a viscous liquid curtain in an annular geometry. Gap and median radius can be varied in such a way that the base of the initially stationary cylindrical curtain is led to oscillate by decreasing the flow rate. Standing and traveling waves in the plane of the annulus are observed and a nontrivial expression linking pulsation to flow rate per surface unit and viscosity can be defined.     

倾斜波动壁面上液膜表面波演化特性的影响

对倾斜波动壁面上流体表面波的演化规律进行了研究. 考虑壁面形状为正弦波动壁面的情况, 分析液膜流动的线性稳定性, 并研究不同倾斜角度下扰动波波形随时间的演化情况及流经不同壁面形状时扰动波的波形变化. 对整体的波形结构分析可知, 随着时间的演化, 扰动波的演化过程呈现为更大波长的近周期变化规律, 与平板上的流动结构对比发现波动情况变得更加复杂; 当液膜流经波动壁面时, 扰动波在空间上不再呈现规律性变化, 且随着壁面倾斜角度的增加, 扰动波的振幅逐渐增加; 在相同的壁面倾角下, 波动壁面上的扰动波振幅大于平板壁面的扰动情况, 且波形扭曲程度更明显; 随着Re的增加, 扰动波振幅逐渐增加, 其对应波形的扭曲程度加深, 且随着壁面振幅的增加, 静态波振幅及扰动波振幅均随之增加, 对应的行进波周期不变. 最后, 分析了壁面倾斜角度对流动稳定性的影响.     

Absolute and convective instabilities of a viscous film flowing down a vertical fiber

The stability of a viscous film flowing down a vertical fiber under the action of gravity is analyzed both experimentally and theoretically. At large or small film thicknesses, the instability is convective, whereas an absolute instability mode is observed in an intermediate range of film thicknesses for fibers of small enough radius. The onset of the experimental irregular wavy regime corresponds precisely to the theoretical prediction of the threshold of the convective instability.     

Heat and mass transfer on MFD flow through porous media over an accelerating surface in the presence of suction and blowing

The heat and mass transfer of electrically conducting fluid through porous media over an accelerating surface subject both to power law surface temperature and power law heat flux variations with a temperature-dependent heat source in the presence of a transverse uniform magnetic field is studied. A series solution to the energy and species concentration equation in terms of Kummer’s function is studied. The effect of Prandtl number and Schmidt number is studied with the help of graphs.     

表面弹性对含可溶性活性剂垂直液膜排液的影响

针对含可溶性活性剂的垂直液膜排液过程,在考虑表面弹性作用的基础上,采用润滑理论建立了液膜厚度、表面速度、表面和内部活性剂浓度的演化方程组,通过数值计算分析了表面弹性和活性剂溶解度耦合作用下的液膜演化特征.结果表明：表面弹性是影响可溶性活性剂垂直液膜排液过程中必不可少的因素.排液初期,随表面弹性增加,液膜初始厚度增大,表面更趋于刚性化.随排液进行,弹性不同的液膜呈现不同的典型排液特征：当弹性较小时,液膜上部表面张力高,下部表面张力低,产生正向的马兰戈尼效应,与重力作用相抗衡.当弹性较大时,膜上部表面张力低,下部表面张力高,产生逆向的马兰戈尼效应,促使液膜排液加速,更易发生失稳.活性剂溶解度通过控制液膜表面的活性剂分子吸附量,进而影响表面弹性：当活性剂溶解度较大时,液膜厚度较小,很快发生破断;随溶解度降低,液膜稳定性增加,初始表面弹性也随之增大,并随液膜变薄逐渐接近极限膨胀弹性值.