A note on the mechanism of the instability at the interface between two shearing fluids

1984 ◽  
Vol 144 ◽  
pp. 463-465 ◽  
Author(s):  
E. J. Hinch
Keyword(s):  
Interfacial Tension ◽  
Couette Flow ◽  
Viscous Fluids ◽  
Physical Explanation ◽  
Two Fluids ◽  
Equal Density

In a recent paper Hooper & Boyd (1983) have shown that the unbounded stratified Couette flow of two viscous fluids of equal density and with no interfacial tension is always unstable. They found that the instability arises at the interface between the two fluids and occurs at short wavelengths where viscosity is more important than inertia. The purpose of this note is to provide a simple physical explanation of the mechanics of the instability.

Measurement of interfacial tension of immiscible liquids of equal density

AIChE Journal ◽  
1988 ◽  
Vol 34 (1) ◽  
pp. 155-157 ◽  
Author(s):  
S. B. Reddy Karri ◽  
V. K. Mathur
Keyword(s):  
Interfacial Tension ◽  
Immiscible Liquids ◽  
Equal Density

Vorticity generation and conservation for two-dimensional interfaces and boundaries

2014 ◽  
Vol 758 ◽  
pp. 63-93 ◽  
Author(s):  
M. Brøns ◽  
M. C. Thompson ◽  
T. Leweke ◽  
K. Hourigan
Keyword(s):  
Free Surface ◽  
Circular Cylinder ◽  
Couette Flow ◽  
Poiseuille Flow ◽  
Vortex Sheet ◽  
Newtonian Fluids ◽  
Two Dimensional ◽  
Two Fluids ◽  
Vorticity Generation ◽  
Planar Couette Flow

AbstractThe generation, redistribution and, importantly, conservation of vorticity and circulation is studied for incompressible Newtonian fluids in planar and axisymmetric geometries. A generalised formulation of the vorticity at the interface between two fluids for both no-slip and stress-free conditions is presented. Illustrative examples are provided for planar Couette flow, Poiseuille flow, the spin-up of a circular cylinder, and a cylinder below a free surface. For the last example, it is shown that, although large imbalances between positive and negative vorticity appear in the wake, the balance is found in the vortex sheet representing the stress-free surface.

Couette flow of two fluids between concentric cylinders

1985 ◽  
Vol 150 ◽  
pp. 381-394 ◽  
Author(s):  
Yuriko Renardy ◽  
Daniel D. Joseph
Keyword(s):  
Surface Tension ◽  
Viscous Fluid ◽  
Thin Layer ◽  
Couette Flow ◽  
Numerical Study ◽  
Outer Cylinder ◽  
Immiscible Fluids ◽  
Stable Configuration ◽  
Two Fluids ◽  
Concentric Cylinders

We consider the flow of two immiscible fluids lying between concentric cylinders when the outer cylinder is fixed and the inner one rotates. The interface is assumed to be concentric with the cylinders, and gravitational effects are neglected. We present a numerical study of the effect of different viscosities, different densities and surface tension on the linear stability of the Couette flow. Our results indicate that, with surface tension, a thin layer of the less-viscous fluid next to either cylinder is linearly stable and that it is possible to have stability with the less dense fluid lying outside. The stable configuration with the less-viscous fluid next to the inner cylinder is more stable than the one with the less-viscous fluid next to the outer cylinder. The onset of Taylor instability for one-fluid flow may be delayed by the addition of a thin layer of less-viscous fluid on the inner wall and promoted by a thin layer of more-viscous fluid on the inner wall.

scholarly journals Convective/absolute instability in miscible core-annular flow. Part 1: Experiments

2009 ◽  
Vol 618 ◽  
pp. 305-322 ◽  
Author(s):  
M. d'OLCE ◽  
J. MARTIN ◽  
N. RAKOTOMALALA ◽  
D. SALIN ◽  
L. TALON
Keyword(s):  
Annular Flow ◽  
Absolute Instability ◽  
Control Parameters ◽  
Core Radius ◽  
Two Fluids ◽  
Pipe Flows ◽  
The Core ◽  
Flow Part ◽  
Annular Pipe ◽  
Equal Density

We address the issue of the convective or absolute nature of the instability of core-annular pipe flows, in experiments using two miscible fluids of equal density but different viscosities, the core fluid being much less viscous than the wall one. We use a concentric co-current injection of the two fluids. An axisymmetric parallel base state is obtained downstream the injector. The core radiusRIand the Reynolds numberReof the so-obtained base state are varied independently due to the control of the flow rate of each fluid. However, a downstream destabilization of this base state was observed within the explored range of the two control parametersRIandRe. Moreover, the fixed location of this destabilization, observed for some particular parameters, suggests an absolute nature of the instability. We present a tentative delineation of the nature (convective or absolute) of the instability and discuss the accessible measurements to experimentally address this issue.

scholarly journals Connection between Classical Solutions of Stokes first Problem and those of Simple Couette Flow. Applications

2020 ◽  
Vol 2 (3) ◽  
pp. 1-3
Author(s):  
Constantin Fetecau ◽  
◽  
Marneni Narahari ◽  
Keyword(s):  
Shear Stress ◽  
Exact Solutions ◽  
Couette Flow ◽  
Direct Consequence ◽  
Viscous Fluids ◽  
Classical Solutions ◽  
New Exact Solutions ◽  
Constant Shear ◽  
Constant Shear Stress

The classical solutions of the first problem of Stokes for viscous fluids, as it was to be expected, are obtained as limiting cases of those of the simple Couette flow. Something similar is valid for the motions of the fluids induced by a constant shear stress on the boundary. As a direct consequence, new exact solutions are immediately obtained for other two classes of motions of the same fluids.

scholarly journals CERTAIN INTERFACIAL TENSION RELATIONS AND THE BEHAVIOR OF BACTERIA IN FILMS

1924 ◽  
Vol 40 (5) ◽  
pp. 647-660 ◽  
Author(s):  
Stuart Mudd ◽  
Emily B. H. Mudd
Keyword(s):  
Interfacial Tension ◽  
Solid Particle ◽  
Aqueous Phase ◽  
Organic Phase ◽  
Good Evidence ◽  
Liquid Interface ◽  
Organic Liquids ◽  
Unequal Distribution ◽  
Interfacial Tensions ◽  
Two Fluids

To account for the behavior of a solid particle in the interface between two fluids it is necessary to consider, as indicated by Clark Maxwell, three surface tensions: Tso, the tension in the interface between the solid particle and the organic phase; Tsw, the tension in the interface between solid particle and aqueous phase; and Tow, the organic phase-water interfacial tension. If Tso > Tsw + Tow, (2), the stronger solid-organic phase tension should pull the line of intersection of the three phases around the periphery of the solid particle until the particle is completely enveloped in the water phase. If Tsw > Tow + Tow (3), the solid-water tension should pull the line of meeting of the phases about the particle until it is enveloped in the organic phase. If See PDF for Equation the particle should be stable in the interface, only leaving it when mechanical work overcomes the equilibrium due to the balance of interfacial tensions. The ordinary bacteria used have been stable in the interfaces between water or aqueous solutions and all organic liquids tested; i.e., condition (4) obtains. In preparations in which Tow is large, stability has been found by experiment to be greater than when Tow is small, as follows from condition (4). The force, dependent upon condition (4), which holds bacteria in the liquid-liquid interface, and the force, dependent upon unequal distribution of tension in the liquid-liquid interface, which causes bacteria to glide along the interface, prove to be of the same order of magnitude as the force due to bacterial flagella. Interfacial tensions or its own motility may dominate the movement of the bacterium, according to circumstances. When bacteria thresh their way out of the interface, escape is into the aqueous phase. Acid-fast bacteria possess very low or, in some cases, no stability in the interface, passing easily or even spontaneously into the organic phase. Good evidence has been advanced by other workers to indicate that the surfaces of ordinary bacteria contain many polar radicals; on the other hand, the acid-fast microorganisms are coated with predominantly non-polar substances. It follows from known principles, therefore, that Tsw should be greater than Tsw with ordinary bacteria, and Tsw should be greater than Tso with acid-fast bacteria. Consideration of relations (2) and (3) above will show that these conditions should result in the differences in behavior of acid-fast and ordinary bacteria actually found by experiment. The theoretical and experimental data here developed contradict the theoretical formulations of the surface tension factor in phagocytosis advanced by Rhumbler and by Tait and substantiate those of Fenn.

scholarly journals Stability of lubricated viscous gravity currents. Part 2. Global analysis and stabilisation by buoyancy forces

2019 ◽  
Vol 871 ◽  
pp. 1007-1027 ◽  
Author(s):  
Katarzyna N. Kowal ◽  
M. Grae Worster
Keyword(s):  
Global Analysis ◽  
Companion Paper ◽  
Density Difference ◽  
Local Analysis ◽  
Instability Criterion ◽  
The Novel ◽  
Two Fluids ◽  
Buoyancy Forces ◽  
Equal Density ◽  
Time Dependent Analysis

The novel viscous fingering instability recently found in the experiments of Kowal & Worster (J. Fluid Mech., vol. 766, 2015, pp. 626–655), involving two superposed currents of viscous fluid, has been shown to originate at the lubrication front when the fluids are of equal density. However, when the densities are unequal, additional buoyancy forces associated with the underlying layer act to suppress this instability and are largest at the lubrication front, which is where the instability originates. In this paper, we investigate the interaction between the mechanism of the instability and the stabilising influence of these buoyancy forces by performing a global and fully time-dependent analysis, which does not use the frozen-time approximation. We determine a critical condition for instability in terms of the viscosity ratio and the density difference between the two layers. Consistently with the local analysis of the companion paper, instabilities occur when the jump in hydrostatic pressure gradient across the lubrication front is negative, or, equivalently, when the intruding fluid is less viscous than the overlying fluid, provided the two fluids are of equal densities. Once there is a non-zero density difference, these driving buoyancy forces suppress the instability for large wavelengths, giving rise to wavelength selection. As the density difference increases, the instability criterion requires higher viscosity ratios for any instability to occur, and the band of unstable wavenumbers becomes bounded. Large enough density differences suppress the instability completely.

Shock formation in two-layer equal-density viscous gravity currents

2019 ◽  
Vol 863 ◽  
pp. 730-756
Author(s):  
Tim-Frederik Dauck ◽  
Finn Box ◽  
Laura Gell ◽  
Jerome A. Neufeld ◽  
John R. Lister
Keyword(s):  
Similarity Solution ◽  
Viscosity Ratio ◽  
Gravity Current ◽  
Travelling Wave ◽  
Similarity Solutions ◽  
Shock Formation ◽  
Late Time ◽  
Influx Rate ◽  
Two Fluids ◽  
Equal Density

The flow of a viscous gravity current over a lubricating layer of fluid is modelled using lubrication theory. We study the case of an axisymmetric current with constant influx which allows for a similarity solution, which depends on three parameters: a non-dimensional influx rate ${\mathcal{Q}}$; a viscosity ratio $m$ between the lower and upper layer fluid; and a relative density difference $\unicode[STIX]{x1D700}$. The limit of equal densities $\unicode[STIX]{x1D700}=0$ is singular, as the interfacial evolution equation changes nature from parabolic to hyperbolic. Theoretical analysis of this limit reveals that a discontinuity, or shock, in the interfacial height forms above a critical viscosity ratio $m_{crit}=3/2$, i.e. for a sufficiently less viscous upper-layer fluid. The physical mechanism for shock formation is described, which is based on advective steepening of the interface between the two fluids and relies on the lack of a contribution to the pressure gradient from the interfacial slope for equal-density fluids. In the limit of small but non-zero density differences, local travelling-wave solutions are found which regularise the singular structure of a potential shock and lead to a constraint on the possible shock heights in the form of an Oleinik entropy condition. Calculation of a simplified time-dependent system reveals the appropriate boundary conditions for the late-time similarity solution, which includes a shock at the nose of the current for $m>3/2$. The numerically calculated similarity solutions compare well to experimental measurements with respect to the predictions of self-similarity, the radial extent and the self-similar top-surface shapes of the current.

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