Interfacial Instabilities in Stratified Shear Flows Involving Multiple Viscous and Viscoelastic Fluids

1995 ◽  
Vol 48 (11) ◽  
pp. 763-776 ◽  
Author(s):  
Kang Ping Chen
Keyword(s):  
Couette Flow ◽  
Poiseuille Flow ◽  
Shear Flows ◽  
Film Flow ◽  
Viscoelastic Fluids ◽  
Interfacial Instabilities ◽  
Inclined Plane ◽  
Recent Developments ◽  
Gravity Driven ◽  
Further Development

This article reviews recent developments in the analysis of interfacial instabilities in systems involving multiple viscous and viscoelastic fluids. The scope of the review is limited to three basic problems in stratified shear flows: plane Poiseuille-Couette flow, circular Poiseuille flow, and gravity-driven film flow down an inclined plane. Important advances in this field of study are summarized and areas deserving further development are discussed.

scholarly journals Patterns in Wall-Bounded Shear Flows

2020 ◽  
Vol 52 (1) ◽  
pp. 343-367 ◽  
Author(s):  
Laurette S. Tuckerman ◽  
Matthew Chantry ◽  
Dwight Barkley
Keyword(s):  
Numerical Simulations ◽  
Couette Flow ◽  
Poiseuille Flow ◽  
Pipe Flow ◽  
Shear Flows ◽  
Plane Couette Flow ◽  
Plane Poiseuille Flow ◽  
Flow Focusing ◽  
Annular Pipe ◽  
Flow Plane

Experiments and numerical simulations have shown that turbulence in transitional wall-bounded shear flows frequently takes the form of long oblique bands if the domains are sufficiently large to accommodate them. These turbulent bands have been observed in plane Couette flow, plane Poiseuille flow, counter-rotating Taylor–Couette flow, torsional Couette flow, and annular pipe flow. At their upper Reynolds number threshold, laminar regions carve out gaps in otherwise uniform turbulence, ultimately forming regular turbulent–laminar patterns with a large spatial wavelength. At the lower threshold, isolated turbulent bands sparsely populate otherwise laminar domains, and complete laminarization takes place via their disappearance. We review results for plane Couette flow, plane Poiseuille flow, and free-slip Waleffe flow, focusing on thresholds, wavelengths, and mean flows, with many of the results coming from numerical simulations in tilted rectangular domains that form the minimal flow unit for the turbulent–laminar bands.

Developing Laminar Gravity-Driven Thin Liquid Film Flow Down an Inclined Plane

2010 ◽  
Vol 132 (8) ◽  
Author(s):  
H. Lan ◽  
J. L. Wegener ◽  
B. F. Armaly ◽  
J. A. Drallmeier
Keyword(s):  
Surface Tension ◽  
Film Thickness ◽  
Liquid Film ◽  
Flow Rate ◽  
Film Flow ◽  
Thin Liquid Film ◽  
Inclined Plane ◽  
Liquid Film Flow ◽  
Gravity Driven ◽  
Surface Inclination

Three-dimensional (3D)—steady-developing-laminar-isothermal—and gravity-driven thin liquid film flow adjacent to an inclined plane is examined and the effects of film flow rate, surface tension, and surface inclination angle on the film thickness and film width are presented. The film flow was numerically simulated using the volume of fluid model and experimental verification was conducted by measuring film thickness and width using a laser focus displacement instrument. The steady film flow that is considered in this study does not have a leading contact line, however, it has two steady side contact lines with the substrate surface at the outer edge of its width. Results reveal that the film width decreases and the average film thickness increases as the film flows down the inclined plane. The film thickness and width decrease but its streamwise velocity increases as surface inclination angle (as measured from the horizontal plane) increases. A higher film flow rate is associated with a higher film thickness, a higher film width, and a higher average film velocity. Films with higher surface tension are associated with a smaller width and a higher average thickness. A ripple develops near the side contact line, i.e., the spanwise distribution of the film thickness exhibits peaks at the outer edges of the film width and the height of this ripple increases as the surface tension or the film flow rate increases. The width of the film decreases at a faster rate along the streamwise direction if liquid film has higher surface tension. Measurements of the film thickness and the film width compare favorably with the numerically simulated results.

‘Phase diagram’ of interfacial instabilities in a two-layer Couette flow and mechanism of the long-wave instability

2000 ◽  
Vol 414 ◽  
pp. 195-223 ◽  
Author(s):  
FRANÇOIS CHARRU ◽  
E. JOHN HINCH
Keyword(s):  
Phase Diagram ◽  
Growth Rate ◽  
Couette Flow ◽  
Flow Regimes ◽  
Interfacial Instabilities ◽  
Rate Versus ◽  
Layer Effect ◽  
Unified View ◽  
Gravity Driven ◽  
Layer Flow

A unified view is given of the instabilities that may develop in two-layer Couette flows, as a ‘phase diagram’ in the parameter space. This view is obtained from a preliminary study of the single-fluid Couette flow over a wavy bottom, which reveals three flow regimes for the disturbances created at the bottom, each regime being characterized by a typical penetration depth of the vorticity disturbances and an effective Reynolds number. It appears that the two-layer flow exhibits the same flow regimes for the disturbances induced by the perturbed interface, and that each type of instability can be associated with a flow regime. Typical curves giving the growth rate versus wavenumber are deduced from this analysis, and favourably compared with the existing literature. In the second part of this study, we propose a mechanism for the long wavelength instability, and provide simple estimates of the wave velocity and growth rate, for channel flows and for semi-bounded flows. In particular, an explanation is given for the ‘thin-layer effect’, which is typical of multi-layer flows such as pressure driven flows or gravity driven flows, and according to which the flow is stable if the thinner layer is the less viscous, and unstable otherwise.

Gravity-driven creeping flow of two adjacent layers through a channel and down a plane wall

1998 ◽  
Vol 371 ◽  
pp. 345-376 ◽  
Author(s):  
C. POZRIKIDIS
Keyword(s):  
Free Surface ◽  
Numerical Simulations ◽  
Channel Flow ◽  
Film Flow ◽  
Finite Amplitude ◽  
Creeping Flow ◽  
Plane Wall ◽  
Surface Velocity ◽  
Inclined Plane ◽  
Gravity Driven

We study the stability of the interface between (a) two adjacent viscous layers flowing due to gravity through an inclined or vertical channel that is confined between two parallel plane walls, and (b) two superimposed liquid films flowing down an inclined or vertical plane wall, in the limit of Stokes flow. In the case of channel flow, linear stability analysis predicts that, when the fluids are stably stratified, the flow is neutrally stable when the surface tension vanishes and the channel is vertical, and stable otherwise. This behaviour contrasts with that of the gravity-driven flow of two superimposed films flowing down an inclined plane, where an instability has been identified when the viscosity of the fluid next to the plane is less than that of the top fluid, even in the absence of fluid inertia. We investigate the nonlinear stages of the motion subject to finite-amplitude two-dimensional perturbations by numerical simulations based on boundary-integral methods. In both cases of channel and film flow, the mathematical formulation results in integral equations for the unknown interface and free-surface velocity. The properties of the integral equation for multi-film flow are investigated with reference to the feasibility of computing a solution by the method of successive substitutions, and a deflation strategy that allows an iterative procedure is developed. In the case of channel flow, the numerical simulations show that disturbances of sufficiently large amplitude may cause permanent deformation in which the interface folds or develops elongated fingers. The ratio of the viscosities and densities of the two fluids plays an important role in determining the morphology of the emerging interfacial patterns. Comparing the numerical results with the predictions of a model based on the lubrication approximation shows that the simplified approach can only describe a limited range of motions. In the case of film flow down an inclined plane, we develop a method for extracting the properties of the normal modes, including the ratio of the amplitudes of the free-surface and interfacial waves and their relative phase lag, from the results of a numerical simulation for small deformations. The numerical procedure employs an adaptation of Prony's method for fitting a signal described by a time series to a sum of complex exponentials; in the present case, the signal is identified with the cosine or sine Fourier coefficients of the interface and free-surface waves. Numerical simulations of the nonlinear motion confirm that the deformability of the free surface is necessary for the growth of small-amplitude perturbations, and show that the morphology of the interfacial patterns developing subject to finite-amplitude perturbations is qualitatively similar to that for channel flow.

scholarly journals Recent Developments of Antimony-Based Anodes for Sodium- and Potassium-Ion Batteries

2021 ◽  
Author(s):  
Bochao Chen ◽  
Ming Liang ◽  
Qingzhao Wu ◽  
Shan Zhu ◽  
Naiqin Zhao ◽  
...  
Keyword(s):  
Structural Characteristics ◽  
Low Cost ◽  
Potassium Ion ◽  
Research Progress ◽  
Research Directions ◽  
Weak Charge ◽  
Recent Developments ◽  
High Theoretical Capacity ◽  
Further Development ◽  
Sodium And Potassium

AbstractThe development of sodium-ion (SIBs) and potassium-ion batteries (PIBs) has increased rapidly because of the abundant resources and cost-effectiveness of Na and K. Antimony (Sb) plays an important role in SIBs and PIBs because of its high theoretical capacity, proper working voltage, and low cost. However, Sb-based anodes have the drawbacks of large volume changes and weak charge transfer during the charge and discharge processes, thus leading to poor cycling and rapid capacity decay. To address such drawbacks, many strategies and a variety of Sb-based materials have been developed in recent years. This review systematically introduces the recent research progress of a variety of Sb-based anodes for SIBs and PIBs from the perspective of composition selection, preparation technologies, structural characteristics, and energy storage behaviors. Moreover, corresponding examples are presented to illustrate the advantages or disadvantages of these anodes. Finally, we summarize the challenges of the development of Sb-based materials for Na/K-ion batteries and propose potential research directions for their further development.

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