Effect of pulsations on the stability of a gas column

The effect of radial pulsations on the stability of a compressible cylindrical gas column surrounded by an ambient liquid is discussed. In the absence of pulsations, the stationary interface is susceptible to the Rayleigh capillary instability, which promotes the growth of longitudinal waves whose wave length is larger than 2 times the column radius, irrespective of the Reynolds number. A Floquet stability analysis for potential flow shows that the pulsations further destabilize the interface by extending the range of unstable wave numbers to a sequence of islands. A similar stability analysis for Stokes flow shows that the pulsations also have a destabilizing influence, though the presence of an insoluble surfactant has a competing stabilizing influence that may cause an overall reduction in the range of unstable wave numbers.     

Effects of shear-thinning/thickening nature on the stability of Couette-like flow with uniform crossflow

The linear stability of wall-injected pressure- driven Couette-like flow in power-law fluids is studied. Previous study on this kind of flow for Newtonian fluids by Nicoud and Angilella [Phys. Rev. E 56, 3000 （1997）] was extended to power-law fluids to understand the effects of shear-thinning/thickening nature on the flow stability. A related expression between the critical crossflow Reynolds number for Newtonian fluids and that for power-law fluids is obtained as the streamwise Reynolds number is large enough based on numerical computations, and verified theoretically in the case of a limiting condition with the power-law index.     

Effect of an insoluble surfactant film on the stability of the concentration-driven Marangoni flow

The stability and the structure of the concentration and capillary driven Marangoni flow from a localized source is experimentally investigated in the presence of an adsorbed layer of an insoluble surfactant. It is found that the presence of the surfactant on the interface leads to the instability of the main axisymmetric flow with the result that a secondary azimuthally-periodic flow with a multivortex structure is developed. The structure of the convective motion on the interface is studied as a function of the Marangoni flow intensity and the surface density of the surfactant. The azimuthal wavenumber is shown to increase with the Marangoni number and to decrease with increase in the surface density of the surfactant. It is established that there exists a threshold value of the surface density of the surfactant at which the surface flow does not occur.     

Interfacial instability of turbulent two-phase stratified flow: Pressure-driven flow and non-Newtonian layers

We derive a flat-interface model to describe the flow of two horizontal, stably stratified fluids, where the bottom layer exhibits non-Newtonian rheology. The model takes into account the yield stress and power-law nature of the bottom fluid. In the light of the large viscosity contrast assumed to exist across the fluid interface, and for large pressure drops in the streamwise direction, the possibility for the upper Newtonian layer to display fully developed turbulence must be considered, and is described in our model. We develop a linear-stability analysis to predict the conditions under which the flat-interface state becomes unstable, and pay particular attention to characterizing the influence of the non-Newtonian rheology on the instability. Increasing the yield stress (up to the point where unyielded regions form in the bottom layer) is destabilizing; increasing the flow index, while bringing a broader spectrum of modes into play, is stabilizing. In addition, a second mode of instability is found, which depends on conditions in the bottom layer. For shear-thinning fluids, this second mode becomes more unstable, and yet more bottom-layer modes can become unstable for a suitable reduction in the flow index. One further difference between the Newtonian and non-Newtonian cases is the development of unyielded regions in the bottom layer, as the linear wave on the interface grows in time. These unyielded regions form in the trough of the wave, and can be observed in the linear analysis for a suitable parameter choice.     

Effects of surfactant on liquid film thickness in the Bretherton problem

The effects of insoluble and soluble surfactant on the motion of a long bubble propagating through a capillary tube are investigated computationally using a finite-difference/front-tracking method. Emphasis is placed on the effects of surfactant on the liquid film thickness between the bubble and the tube wall. The numerical method is designed to solve the evolution equations of the interfacial and bulk surfactant concentrations coupled with the incompressible Navier–Stokes equations. A non-linear equation of state is used to relate surface tension coefficient to surfactant concentration at the interface. Computations are first performed for soluble cases and then repeated for the corresponding clean and insoluble cases for a wide range of governing non-dimensional parameters in order to investigate the effects of surfactant and surfactant solubility. The computed film thickness for the clean case is found to be in a good agreement with Taylor’s law indicating the accuracy of the numerical method. We found that both the insoluble and soluble surfactant generally have a thickening effect on the film thickness, which is especially pronounced at low capillary numbers. This thickening effect strengthens with increasing sensitivity of surface tension to interfacial surfactant coverage mainly due to the enhanced Marangoni stresses along the liquid film. It is also observed that film thickening shows a non-monotonic behavior for variations in Peclet number. The validity of insoluble surfactant assumption is assessed for various non-dimensional numbers and it is demonstrated that insoluble assumption is valid only when capillary number is very low, i.e., Ca ≪ 1 and when surface tension is highly sensitive to interfacial surfactant coverage, i.e., the elasticity number is large.     

双自由面溶质?热毛细液层的不稳定性

溶质?热毛细对流是流体界面的浓度和温度分布不均导致的表面张力梯度驱动的流动, 它主要存在于空间微重力环境、小尺度流动等表面张力占主导的情况中, 例如晶体生长、微流控、合金浇筑凝固、有机薄液膜生长等. 对其流动进行稳定性分析具有重要意义. 本文采用线性稳定性理论研究了双自由面溶质?热毛细液层对流的不稳定性, 得到了两种负毛细力比(η)下的临界Marangoni数与Prandtl数(Pr)的函数关系, 并分析了临界模态的流场和能量机制. 研究发现: 溶质?热毛细对流和纯热毛细对流的临界模态有较大的差别, 前者是同向流向波、逆向流向波、展向稳态模态和逆向斜波, 后者是逆向斜波和逆向流向波. 在Pr较大时, Pr增加会降低流动稳定性; 在其他参数下, Pr增加会增强流动稳定性. 在中低Pr, 溶质毛细力使流动更加不稳定; 在大Pr时, 溶质毛细力的出现可能使流动更加稳定; 在其他参数下, 溶质毛细力会减弱流动稳定性. 流动稳定性不随η单调变化. 在多数情况下, 扰动浓度场与扰动温度场都是相似的. 能量分析表明: 扰动动能的主要能量来源是表面张力做功, 但其中溶质毛细力和热毛细力做功的正负性与参数有关.      

STABILITY OF ULTRATHIN LIQUID FILM EVOLUTION WITH SURFACTANT

针对固体基底上厚度小于100 nm的含活性剂超薄液膜演化过程, 基于润滑理论推导出包含分离压影响的液膜厚度和活性剂浓度的演化方程, 采用正则模态法导出了描述液膜线性稳定性的特征方程, 分析了多个特征参数对线性稳定性的影响, 数值模拟了液膜厚度和活性剂浓度演化历程, 对比了模拟所得非线性结果与线性分析预测结果的一致性.结果表明:范德华力具有促进扰动增长的作用, 较强的玻恩斥力促使扰动衰减, 使液膜趋于稳定;较小的毛细力数易使液膜凹陷处发生二次失稳, 并最终导致去润湿现象发生;液膜厚度和溶于液膜内部的活性剂浓度初值越大, 液膜稳定性越强, 液膜表面活性剂浓度影响则相反;增大吸附系数不利于液膜稳定性.     

Anomalous motion of viscous fingers in surfactant solutions in a Hele–Shaw cell

Viscous fingering in surfactant solutions in a rectangular Hele–Shaw cell was investigated. Test fluids were aqueous solutions of cetyltrimethylammonium bromide (CTAB) with sodium salicylate (NaSal) as a counter ion, and the ratio of mole concentration of CTAB and that of NaSal was 1–7.7. Two fluids that had a mole concentration different from that of CTAB were used. Air was injected into the cell and the growth of the interface between air and a CTAB/NaSal solution was observed. The fingertip grew similar to the finger growth in shear-thinning fluids at low pressure gradients. It took a cuspidate shape at the intermediate pressure gradient, and a sudden protrusion at a critical shear rate occurred. In high shear rate regions, the finger behaved as in a less shear-thinning fluid. These phenomena relate to rheological properties of the test fluids. Comparison with flow curves for CTAB/NaSal systems showed that the critical shear rate related to the shear rate at which a bending point appeared in the flow curve.     

Asymmetry in transitional pipe flow of drag-reducing polymer solutions

New experimental data are presented and discussed for fully developed pipe flow of shear-thinning, viscoelastic polymer solutions in the transitional regime between laminar and turbulent flow. The data confirm that such transitional flows exhibit significant departures from axisymmetry in contrast to the fully developed pipe flow of Newtonian fluids or both laminar and turbulent flows of such drag-reducing liquids. The azimuthal structure of the asymmetry is investigated together with its axial development and also the velocity fluctuation levels. These data do not lead to an explanation for the asymmetry but do suggest that the influence of the flow geometry both upstream and downstream can be ruled out.     

Stability of a liquid jet into incompressible gases and liquids: Part 2. Effects of the irrotational viscous pressure

In this paper we investigate the effects of an irrotational, viscous pressure on the stability of a liquid jet into gases and liquids. The analysis extends our earlier work (part 1) in which the stability of the viscous jet was studied assuming that the motion and pressure are irrotational and the viscosity enters through the jump in the viscous normal stress in the normal stress balance at the interface. The liquid jet is always unstable; at high Weber numbers the instability is dominated by capillary instability; at low W the instability is dominated by Kelvin–Helmholtz (KH) waves generated by pressures driven by the discontinuous velocity. In the irrotational analysis the viscosity is important but the effects of shear are neglected. In fact a discontinuous velocity is not compatible with the continuity of the tangential components of velocity and shear stress so that KH instability is not properly posed for exact study using the no-slip condition but some of the effects of viscosity can be ascertained using viscous potential flow. The theory is called viscous potential flow (VPF). Here we develop another irrotational theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance by selecting viscous contributions to the irrotational pressure. These pressures generate a hierarchy of potential flows in powers of the viscosity, but only the first one, linear in viscosity, in the irrotational viscous stress, is thought to have physical significance. The tangential velocity and shear stress in an irrotational study cannot be made continuous, but the effects of the discontinuous velocity and stress in the mechanical energy balance can be removed “in the mean.” This theory with the additional viscous pressure is called VCVPF, viscous correction of VPF. VCVPF is VPF with the additional pressures. The theory here cannot be compared with an exact solution, which would not allow the discontinuous velocity and stress. In other problems, like capillary instability, in which VCVPF can be compared with an exact solution, the agreements are uniformly excellent in the wave number when one of the fluids is gas and in good but not uniform, agreement when both fluids are liquids.     

Linear instability of the electrified free interface between two cylindrical shells of viscoelastic fluids through porous media

In this paper, we have discussed the linear stability analysis of the electrified surface separating two coaxial Oldroyd-B fluid layers confined between two impermeable rigid cylinders in the presence of both interfacial insoluble surfactant and surface charge through porous media. The case of long waves interfacial stability has been studied. The dispersion relation is solved numerically and hence the effects of various parameters are illustrated graphically. Our results reveal that the influence of the physicochemical parameter β is to shrink the instability region of the surface and reduce the growth rate of the unstable normal modes. Such important effects of the surfactant on the shape of interfacial structures are more sensitive to the variation of the β corresponding to non-Newtonian fluids-model compared with the Newtonian fluids model. In the case of long wave limit, it is demonstrated that increasing β, has a dual role in-fluence (de-stabilizing effects) depending on the viscosity of the core fluid. It has a destabilizing effect at the large values of the core fluid viscosity coefficient, while this role is exchanged to a regularly stabilizing influence at small values of such coefficient.     

Experimental studies of interfacial instabilities in multilayer pressure-driven flow of polymeric melts

The interfacial deformation and stability of two-(A-B) as well as three-layer symmetric (A-B-A) and asymmetric (A-B-C) pressure-driven flow of viscoelastic fluids has been investigated. Flow visualization in conjunction with digital image processing has been used to observe and measure the rate of encapsulation and interfacial stability/instability of the flow. Specifically, the encapsulation behavior as well as stability/instability of the interface and the corresponding growth or decay rate of disturbances as a function of various important parameters, namely, number of layers and their arrangement, layer depth ratio, viscosity and elasticity ratio as well as disturbance frequency, have been investigated. Based on these experiments, we have shown that the encapsulation phenomena occurs irrespective of the stability/instability of the interface and in cases when both encapsulation and instability occur simultaneously their coupling leads to highly complex and three-dimensional interfacial wave patterns. Moreover, it has been shown that the simple notion that less viscous fluids encapsulate more viscous fluids is incorrect and depending on the wetting properties of the fluid as well as their first and second normal stresses the reverse could occur. Additionally, in two- and three-layer flows it has been shown that by placing a thin, less viscous layer adjacent to the wall longwave disturbances can be stabilized while short and intermediate wavelength disturbances are stabilized when the more elastic fluid is the majority component. Furthermore, in three-layer flows it has been demonstrated that in the linear instability regime no dynamic interaction between the two interfaces is possible for short and intermediate wavenumber disturbances. However, in the nonlinear stability regime dynamic interactions between interfaces have been observed in this range of disturbance wavenumbers leading to highly chaotic flows. Finally, in the parameter space of this study no subcritical bifurcations were observed while supercritical bifurcations resulting in waves with a pointed front and a gradual tail were observed.     

The characteristics of spiral waves in an axially rotating pipe

An experimental study of the instability of a flow in an axially rotating pipe is performed by means of LDV and flow visualization technique. It is found that the axial velocity of the rotating pipe flow fluctuates like a sine wave at first, then its fluctuating pattern assumes a somewhat sawtooth wave form as a spiral wave appears, which is predicted by means of linear and nonlinear stability analysis. At a certain rotation rate, the amplitude of the velocity fluctuations amounts to 30% of the axial velocity. At the down-stream section, another fluctuating component appears in the velocity, which interferes with the initially appearing component, then the fluctuation becomes one with broad-band spectral components. There is a close analogy between this spectral evolution and that of a Taylor-Couette flow. Deformation of the velocity distribution is obtained from the velocity fluctuating pattern and its phase, and the structure of the spiral wave is considered. The strength, azimuthal wavenumber and angular velocity of the spiral wave obtained from the velocity data are confirmed by flow visualization. The change of pressure loss in the rotating pipe is compared with the case without rotation.     

Study of shear-thinning/thickening effects on plane Couette-Poiseuille flow with uniform crossflow

The shear-thinning/thickening effects on the plane Couette-Poiseuille flow with a uniform crossflow are studied. The detailed solution procedures for both theo- retical and numerical purposes are given. In order to clarify the difference between the Newtonian flow and the power-law flow, all cases of the plane Couette-Poiseuille flows with uniform crossflows for different power indexes are assigned to the phase diagram in the parameter plane corresponding to the Couette number and the crossflow Reynolds number. The effects of shear-thinning/thickening on the phase diagram are discussed. An important feature of the shear-thinning circumstance distinguished from the shear- thickening circumstance is discovered.     

Evolution Equations for the Surface Concentration of an Insoluble Surfactant; Applications to the Stability of an Elongating Thread and a Stretched Interface

The general form of the convection–diffusion equation governing the evolution of the surface concentration of an insoluble surfactant over an evolving interface is reviewed and discussed for three-dimensional, axisymmetric, and two-dimensional configurations. The linearized form of the evolution equation is then derived around cylindrical and planar shapes in a framework that is suitable for carrying out a linear stability analysis for axisymmetric or two-dimensional perturbations. Particular attention is paid to the cases of quiescent unperturbed fluids, unidirectional shear flow, and elongational flow. By way of application, the linearized transport equations are combined with Stokes-flow hydrodynamics to investigate the stability of an elongating cylindrical viscous thread suspended in an ambient viscous fluid or in a vacuum, and the stability of a two-dimensional interface separating two semi-infinite fluids and stretched under the action of an orthogonal stagnation-point flow. The results illustrate the possibly important role of the surfactant on the linear growth of periodic waves on the cylindrical interface, and reveal that the surfactant has no effect on the stability of the planar interface.     

Polymer “threads” and drag reduction

A number of different polymer fluids were ejected on the centerline of a water pipe-flow facility. Two distinct flow regions were identified: Reynolds numbers above 25000, where centerline injection acted as a rather efficient mixing device for water-soluble polymer — and no drag-reduction resulted from non water-soluble materials; and Reynolds numbers from 10000 to 25000, where strong evidence exists that under certain conditions, a viscoelastic fluid thread can interact with turbulence eddies and reduce the overall flow friction in the pipe.On Sabbatical leave from San Diego State University.     

Transient mixed convection flow instabilities in a vertical pipe

The present paper investigates a numerical study of flow instabilities in transient mixed convection in a vertical pipe. At the entrance of the pipe, the flow is suddenly submitted to a temperature step. The convection heat transfer on the outer surface of the pipe is taken into account. The governing equations are solved using a finite difference explicit scheme. The numerical results show that the time development of streamlines and isotherms is strongly dependent on the inlet temperature steps. For positive temperature steps, the unsteady vortex is significant in the vicinity of the wall and the reversal flow appears below the wave instability. In the case of negative temperature steps and especially for the low Reynolds number, the reversal flow appears on top of the wave instability. During the transient, the apparition of the vortical structures along the wall leads to the wall boundary layer instability. This phenomenon is due to the transient mixed convection flows. The temperature step effects on the heat transfer of the flow are presented in our paper.     

3D particle image velocimetry of the flow field around a sphere sedimenting near a wall: Part 1. Effects of Weissenberg number

The flow fields surrounding a sphere sedimenting through a liquid near a vertical wall are characterized using 3D stereoscopic particle-image velocimetry (PIV) experiments. Three different fluids, a Newtonian reference fluid, a constant (shear) viscosity Boger fluid, and a shear-thinning elastic fluid, are used to determine the effects of both elasticity and shear-thinning on the flow field. All three fluids have similar zero shear viscosities. The Weissenberg number is manipulated by varying the diameter and the composition of the ball. Significant differences are found for the different types of fluid, demonstrating both the influence of elasticity and shear-thinning on the velocity fields. In addition, the impact of the wall on the flow field is qualitatively different for each fluid. We find that the flow behind the sphere is strongly dependent on the fluid properties as well as the elasticity. Also, the presence of a negative wake is found for the shear-thinning fluid at high Weissenberg number (Wi > 1).     

Two-dimensional unsteady laminar flow of a power law fluid across a square cylinder

The two-dimensional and unsteady free stream flow of power law fluids past a long square cylinder has been investigated numerically in the range of conditions 60≤Re≤160 and 0.5≤n≤2.0. Over this range of Reynolds numbers, the flow is periodic in time. A semi-explicit finite volume method has been used on a non-uniform collocated grid arrangement to solve the governing equations. The global quantities such as drag coefficients, Strouhal number and the detailed kinematic variables like stream function, vorticity and so on, have been obtained for the above range of conditions. While, over this range of Reynolds number, the flow is known to be periodic in time for Newtonian fluids, a pseudo-periodic flow regime displaying more than one dominant frequency in the lift is observed for shear-thinning fluids. This seems to occur at Reynolds numbers of 120 and 140 for n=0.5 and 0.6, respectively. Broadly speaking, the smaller the value of the power law index, lower is the Reynolds number of the onset of the pseudo-periodic regime. This work is concerned only with the fully periodic regime and, therefore, the range of Reynolds numbers studied varies with the value of the power law index. Not withstanding this aspect, in particular here, the effects of Reynolds number and of the power law index have been elucidated in the unsteady laminar flow regime. The leading edge separation in shear-thinning fluids produces an increase in drag values with the increasing Reynolds number, while shear-thickening fluid behaviour delays this separation and shows the lowering of the drag coefficient with the Reynolds number. Also, the preliminary results suggest the transition from the steady to unsteady flow conditions to occur at lower Reynolds numbers in shear-thinning fluids than that in Newtonian fluids.