On driving a viscous fluid out of a tube

1962 ◽  
Vol 14 (1) ◽  
pp. 81-96 ◽  
Author(s):  
B. G. Cox
Keyword(s):  
Surface Tension ◽  
Viscous Fluid ◽  
Equations Of Motion ◽  
Horizontal Tube ◽  
Tube Diameter ◽  
Experimental Results ◽  
Inviscid Fluid ◽  
Asymptotic Value ◽  
Two Fluids ◽  
Interfacial Surface

Two problems are considered. First, it is shown experimentally that the amount of viscous fluid left on the walls of a horizontal tube, when it is expelled by an inviscid fluid, reaches an asymptotic value of 0.60 of the amount required to fill the tube, when the parameter μU/T is increased, μ and T being the coefficients of viscosity and interfacial surface tension respectively, and U the velocity of the interface between the two fluids. Secondly, by neglecting the inertia terms in the equations of motion and the effect of gravity, a theory for the passage of this type of bubble is presented, together with experimental results in support of the theory. It is shown that such a solution is only valid under certain other restrictions, and then only to within half a tube diameter of the nose of the bubble.

Numerical simulations of sink flow in the Hele-Shaw cell with small surface tension

1997 ◽  
Vol 8 (6) ◽  
pp. 533-550 ◽  
Author(s):  
E. D. KELLY ◽  
E. J. HINCH
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Viscous Fluid ◽  
Numerical Simulations ◽  
Boundary Integral Equation ◽  
Numerical Algorithm ◽  
Boundary Integral ◽  
Inviscid Fluid ◽  
Small Surface ◽  
Hele Shaw Cell

The motion of an initially circular drop of viscous fluid surrounded by inviscid fluid in a Hele-Shaw cell withdrawn from an eccentric point sink is considered. Using a numerical algorithm based on a boundary integral equation, the solution for small, finite surface tension is observed. It is found that the zero-surface-tension formation of a cusp is avoided, and instead a narrow finger of inviscid fluid forms, which then rapidly propagates towards the sink. The scaling of the finger in the sink vicinity is determined.

The toroidal bubble

1968 ◽  
Vol 32 (1) ◽  
pp. 97-112 ◽  
Author(s):  
T. J. Pedley
Keyword(s):  
Surface Tension ◽  
Viscous Fluid ◽  
Energy Equation ◽  
Bubble Surface ◽  
Inviscid Fluid ◽  
Initial Instant ◽  
Bubble Volume ◽  
Toroidal Bubble ◽  
History Of ◽  
Impulse Equation

It has been observed by Walters & Davidson (1963) that release of a mass of gas in water sometimes produces a rising toroidal bubble. This paper is concerned with the history of such a bubble, given that at the initial instant the motion is irrotational everywhere in the water. The variation of its overall radius a with time may be predicted from the vertical impulse equation, and it should be possible to make the same prediction by equating the rate of loss of combined kinetic and potential energy to the rate of viscous dissipation. This is indeed seen to be the case, but not before it is recognized that in a viscous fluid vorticity will continually diffuse out from the bubble surface, destroying the irrotationality of the motion, and necessitating an examination of the distribution of vorticity. The impulse equation takes the same form as in an inviscid fluid, but the energy equation is severely modified. Other results include an evaluation of the effect of a hydrostatic variation in bubble volume, and a prediction of the time which will have elapsed before the bubble becomes unstable under the action of surface tension.

Turbulent drag reduction by compliant lubricating layer

2019 ◽  
Vol 863 ◽  
Author(s):  
Alessio Roccon ◽  
Francesco Zonta ◽  
Alfredo Soldati
Keyword(s):  
Surface Tension ◽  
Viscous Fluid ◽  
Drag Reduction ◽  
Fluid Viscosity ◽  
Two Phase ◽  
Main Layer ◽  
Two Fluids ◽  
Lubricating Layer ◽  
Light Oil ◽  
Set Up

We propose a physically sound explanation for the drag reduction mechanism in a lubricated channel, a flow configuration in which an interface separates a thin layer of less-viscous fluid (viscosity $\unicode[STIX]{x1D702}_{1}$) from a main layer of a more-viscous fluid (viscosity $\unicode[STIX]{x1D702}_{2}$). To single out the effect of surface tension, we focus initially on two fluids having the same density and the same viscosity ($\unicode[STIX]{x1D706}=\unicode[STIX]{x1D702}_{1}/\unicode[STIX]{x1D702}_{2}=1$), and we lower the viscosity of the lubricating layer down to $\unicode[STIX]{x1D706}=\unicode[STIX]{x1D702}_{1}/\unicode[STIX]{x1D702}_{2}=0.25$, which corresponds to a physically realizable experimental set-up consisting of light oil and water. A database comprising original direct numerical simulations of two-phase flow channel turbulence is used to study the physical mechanisms driving drag reduction, which we report between 20 and 30 percent. The maximum drag reduction occurs when the two fluids have the same viscosity ($\unicode[STIX]{x1D706}=1$), and corresponds to the relaminarization of the lubricating layer. Decreasing the viscosity of the lubricating layer ($\unicode[STIX]{x1D706}<1$) induces a marginally decreased drag reduction, but also helps sustaining strong turbulence in the lubricating layer. This led us to infer two different mechanisms for the two drag-reduced systems, each of which is ultimately controlled by the outcome of the competition between viscous, inertial and surface tension forces.

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.

The hydrodynamic stability of helium ll between rotating cylinders. I

1957 ◽  
Vol 241 (1224) ◽  
pp. 9-28 ◽  
Keyword(s):  
Viscous Fluid ◽  
Hydrodynamic Instability ◽  
Present Theory ◽  
Inviscid Fluid ◽  
Rotating Cylinders ◽  
Two Fluids ◽  
Constant Vorticity ◽  
A Value ◽  
Good Accord ◽  
The Difference

The hydrodynamic instability of helium ll between rotating cylinders is investigated on two assumptions regarding the mutual friction force, F, between the normal and the super­fluid components of the liquid. On both assumptions F is proportional to the constant vorticity which prevails in the stationary state and to the difference in the velocities between the two fluids; however, on one assumption the effect of F is confined entirely to the transverse plane, while on the other it is allowed to be isotropic (with respect to the difference in the velocities). The hydrodynamic problem is solved for the case when the two cylinders (of radii R 1 and R 2 ) are rotated in the same direction and ( R 2 — R 1 ) ≪ ½ ( R 2 + R 1 ). It follows from the theory that when ∂( r 2 Ω)/∂ r < 0 (where Ω denotes the angular velocity and r the distance from the axis) the flow becomes (eventually) unstable along two branches: the first of these is the normal (Taylor) instability of a viscous fluid inhibited by its coupling with an inviscid fluid, and the second is the (Rayleigh) instability of the superfluid inhibited, in turn, by its coupling with a viscous fluid. Further, in all cases the critical Taylor number of instability (suitably defined) becomes asymptotic to a relation which is equivalent to Γ 2 = ½ ( R 2 2 — R 2 1 )R 2 1 , where Γ is the coupling constant. From an experiment of Kolm & Herlin’s (1956), to which the present theory appears applicable, a value of Γ = 0·52 is deduced; this is in very good accord with the value Γ = 0·55 which Hall & Vinen (1956 α ) have deduced from an unrelated experiment.

On a sphere performing linear and torsional oscillations in a viscous fluid

1988 ◽  
Vol 66 (7) ◽  
pp. 576-579
Author(s):  
G. T. Karahalios ◽  
C. Sfetsos
Keyword(s):  
Boundary Layer ◽  
Viscous Fluid ◽  
Secondary Flow ◽  
Small Amplitude ◽  
Equations Of Motion ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Time Varying ◽  
Torsional Oscillations

A sphere executes small-amplitude linear and torsional oscillations in a fluid at rest. The equations of motion of the fluid are solved by the method of successive approximations. Outside the boundary layer, a steady secondary flow is induced in addition to the time-varying motion.

scholarly journals Steady rimming flows with surface tension

2008 ◽  
Vol 597 ◽  
pp. 91-118 ◽  
Author(s):  
E. S. BENILOV ◽  
M. S. BENILOV ◽  
N. KOPTEVA
Keyword(s):  
Thin Film ◽  
Surface Tension ◽  
Viscous Fluid ◽  
Small Parameter ◽  
Outer Region ◽  
Lubrication Approximation ◽  
Steady Flows ◽  
Matched Asymptotics ◽  
Weak Surface ◽  
Rimming Flows

We examine steady flows of a thin film of viscous fluid on the inside of a cylinder with horizontal axis, rotating about this axis. If the amount of fluid in the cylinder is sufficiently small, all of it is entrained by rotation and the film is distributed more or less evenly. For medium amounts, the fluid accumulates on the ‘rising’ side of the cylinder and, for large ones, pools at the cylinder's bottom. The paper examines rimming flows with a pool affected by weak surface tension. Using the lubrication approximation and the method of matched asymptotics, we find a solution describing the pool, the ‘outer’ region, and two transitional regions, one of which includes a variable (depending on the small parameter) number of asymptotic zones.

Ferrohydrodynamic Capillary Convection

2018 ◽  
Vol 11 (2) ◽  
Author(s):  
Francisco J. Arias ◽  
Salvador A. De Las Heras
Keyword(s):  
Magnetic Field ◽  
Surface Tension ◽  
Concentration Gradient ◽  
Deductive Reasoning ◽  
Marangoni Convection ◽  
Marangoni Effect ◽  
Magnetic Fluids ◽  
Homogeneous Magnetic Field ◽  
Gradient Field ◽  
Two Fluids

Abstract In this work, consideration is given to capillary convection on ferrofluids from the concentration gradient induced when a nonhomogeneous magnetic field is applied. It is known that mass transfer along an interface between two fluids can appear due to a gradient of the surface tension in the so-called Marangoni effect (or Gibbs–Marangoni effect). Because the surface tension is both thermal and concentration dependent, Marangoni convection can be induced by either a thermal or a concentration gradient, where in the former case, it is generally referred as thermocapillary convection. Now, it has been theoretically and experimentally demonstrated that a ferrofluid under the action of a non-homogeneous magnetic field can induce a concentration gradient of suspended magnetic nanoparticles, and also the effect of Fe3O4 nanoparticles on the surface tension has been measured. Therefore, by deductive reasoning and taking into account the above mentioned facts, it is permissible to infer ferrohydrodynamic capillary convection on magnetic fluids under the presence of a magnetic gradient field. Utilizing a simplified physical model, the phenomenon was investigated and it was found that ferrohydrodynamic-Marangoni convection could be induced with particle size in the range up to 10 nm, which is the range of magnetic fluids to escape magnetic agglomeration.

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