Stokes flow past bubbles and drops partially coated with thin films. Part 2. Thin films with internal circulation – a perturbation solution

1983 ◽  
Vol 132 ◽  
pp. 295-318 ◽  
Author(s):  
Robert E. Johnson ◽  
S. S. Sadhal
Keyword(s):  
Thin Films ◽  
Fluid Layer ◽  
Cell Structure ◽  
Creeping Flow ◽  
Immiscible Fluid ◽  
Fluid Viscosity ◽  
Perturbation Scheme ◽  
Bulk Fluid ◽  
Viscous Forces ◽  
Surface Tension Forces

In the present study we examine the steady axisymmetric creeping flow due to the motion of a liquid drop or a bubble which is partially covered by a thin immiscible fluid layer or film. The analysis is based on the assumption that surface-tension forces are large compared with viscous forces which deform the drop, and that the circulation in the film is weak. The latter assumption is satisfied provided that the film-fluid viscosity is not too small. A perturbation scheme based on the thinness of the fluid layer is used to construct the solution.One of the principal results is an expression for the drag force on the complex drop. We also find that the extent to which the drop or bubble is covered the film has a maximum value depending on the magnitude of the driving force on the film. In addition, we find the rather interesting result that when the ratio of the primary drop viscosity and bulk fluid viscosity is greater than ½, the circulation within the film may have a double-cell structure.

Effects of surface tension and viscosity on airway reopening

1990 ◽  
Vol 69 (1) ◽  
pp. 74-85 ◽  
Author(s):  
D. P. Gaver ◽  
R. W. Samsel ◽  
J. Solway
Keyword(s):  
Surface Tension ◽  
Fluid Viscosity ◽  
Opening Pressure ◽  
Viscous Forces ◽  
Considerable Portion ◽  
Airway Opening ◽  
Wall Compliance ◽  
Large Opening ◽  
Surface Tension Forces ◽  
The Relationship

We studied airway opening in a benchtop model intended to mimic bronchial walls held in apposition by airway lining fluid. We measured the relationship between the airway opening velocity (U) and the applied airway opening pressure in thin-walled polyethylene tubes of different radii (R) using lining fluids of different surface tensions (gamma) and viscosities (mu). Axial wall tension (T) was applied to modify the apparent wall compliance characteristics, and the lining film thickness (H) was varied. Increasing mu or gamma or decreasing R or T led to an increase in the airway opening pressures. The effect of H depended on T: when T was small, opening pressures increased slightly as H was decreased; when T was large, opening pressure was independent of H. Using dimensional analysis, we found that the relative importance of viscous and surface tension forces depends on the capillary number (Ca = microU/gamma). When Ca is small, the opening pressure is approximately 8 gamma/R and acts as an apparent “yield pressure” that must be exceeded before airway opening can begin. When Ca is large (Ca greater than 0.5), viscous forces add appreciably to the overall opening pressures. Based on these results, predictions of airway opening times suggest that airway closure can persist through a considerable portion of inspiration when lining fluid viscosity or surface tension are elevated.

scholarly journals Axial creeping flow in the gap between a rigid cylinder and a concentric elastic tube

2016 ◽  
Vol 806 ◽  
pp. 580-602 ◽  
Author(s):  
S. B. Elbaz ◽  
A. D. Gat
Keyword(s):  
Fluid Layer ◽  
Elastic Shell ◽  
Gravity Current ◽  
Travelling Wave ◽  
Elastic Tube ◽  
Creeping Flow ◽  
Shear Stresses ◽  
Length Scales ◽  
Rigid Cylinder ◽  
Viscous Forces

We examine transient axial creeping flow in the annular gap between a rigid cylinder and a concentric elastic tube. The gap is initially filled with a thin fluid layer. We employ an elastic shell model and the lubrication approximation to obtain governing equations for the elastohydrodynamic interaction. At long axial length scales viscous forces are balanced by elastic tension, while at shorter length scales the viscous–elastic balance is achieved by means of an interplay between elastic bending, tension and shear stresses. Based on a viscous gravity current analogy in the tensile–viscous regime, we devise propagation laws for displacement flows which are induced by a variety of boundary conditions and examine different limits of the prewetting thickness. Next we focus on the moving elastohydrodynamic contact line at the edge of a penetrating film. A uniform matched asymptotic solution connecting the interior tension-based region with a boundary layer region near the propagation front is presented. Finally, a constructive example is shown in which isolated moving deformation patterns are created and superimposed to form a travelling wave displacement field. The presented interaction between viscosity and elasticity may be applied to fields such as soft robotics and micro-scale or larger swimmers by allowing for the time-dependent control of an axisymmetric compliant boundary.

Stokes flow past a sphere coated with a thin fluid film

1981 ◽  
Vol 110 ◽  
pp. 217-238 ◽  
Author(s):  
Robert Edward Johnson
Keyword(s):  
Surface Tension ◽  
Contact Angle ◽  
Stokes Flow ◽  
Fluid Layer ◽  
Fluid Film ◽  
Fluid Viscosity ◽  
Flow Past ◽  
Surface Tension Forces ◽  
Force Equilibrium ◽  
Flow Past A Sphere

The present study examines the steady, axisymmetric Stokes flow past a sphere coated with a thin, immiscible fluid layer. Inertial effects are neglected for both the outer fluid and the fluid film, and surface tension forces are assumed large compared with the viscous forces which deform the fluid film. Furthermore, the present analysis assumes that the mechanism driving the fluid circulation within the film is not too large. From force equilibrium on the film we find that a steady fluid film can only partially cover the sphere, i.e. the film must be held to the sphere by surface tension forces at the contact line. The extent of the sphere covered by the film is specified, in terms of the solid–fluid contact angle, by the condition of global force equilibrium on the fluid film.Using a perturbation scheme based on the thinness of the fluid layer the solution to the flow field is obtained analytically, except for the fluid-film profile (i.e. the fluid–fluid interface) which requires numerical calculations. One of the principal results is an expression for the drag force on the fluid-coated particle. In particular, we find that the drag on a sphere is reduced by the presence of a fluid coating when the ratio of the film fluid viscosity to the surrounding fluid viscosity is less than ¼. Detailed numerical computations are conducted for a few typical cases. The calculations show that a film of prescribed areal extent, i.e. specified contact angle, is only possible when the magnitude of the driving force on the film is below some maximum value. A simple experiment was also performed, and photographs, which qualitatively illustrate the fundamental fluid-film configurations predicted by the theory, are presented.

scholarly journals The role of soluble surfactants in the linear stability of two-layer flow in a channel

2019 ◽  
Vol 873 ◽  
pp. 18-48 ◽  
Author(s):  
A. Kalogirou ◽  
M. G. Blyth
Keyword(s):  
Critical Micelle Concentration ◽  
Linear Stability ◽  
Stokes Equations ◽  
Fluid Layer ◽  
Sorption Kinetics ◽  
Navier Stokes ◽  
Fluid Viscosity ◽  
Navier Stokes Equations ◽  
Bulk Fluid ◽  
Layer Flow

The linear stability of Couette–Poiseuille flow of two superposed fluid layers in a horizontal channel is considered. The lower fluid layer is populated with surfactants that appear either in the form of monomers or micelles and can also get adsorbed at the interface between the fluids. A mathematical model is formulated which combines the Navier–Stokes equations in each fluid layer, convection–diffusion equations for the concentration of monomers (at the interface and in the bulk fluid) and micelles (in the bulk), together with appropriate coupling conditions at the interface. The primary aim of this study is to investigate when the system is unstable to arbitrary wavelength perturbations, and in particular, to determine the influence of surfactant solubility and/or sorption kinetics on the instability. A linear stability analysis is performed and the growth rates are obtained by solving an eigenvalue problem for Stokes flow, both numerically for disturbances of arbitrary wavelength and analytically using long-wave approximations. It is found that the system is stable when the surfactant is sufficiently soluble in the bulk and if the fluid viscosity ratio $m$ and thickness ratio $n$ satisfy the condition $m<n^{2}$. On the other hand, the effect of surfactant solubility is found to be destabilising if $m\geqslant n^{2}$. Both of the aforementioned results are manifested for low bulk concentrations below the critical micelle concentration; however, when the equilibrium bulk concentration is sufficiently high (and above the critical micelle concentration) so that micelles are formed in the bulk fluid, the system is stable if $m<n^{2}$ in all cases examined.

scholarly journals Influence of Eccentricity and Angular Velocity on Force Effects on Rotor of Magnetorheological Damper

2018 ◽  
Vol 180 ◽  
pp. 02091
Author(s):  
Dominik Šedivý ◽  
Petr Ferfecki ◽  
Simona Fialová
Keyword(s):  
Magnetic Induction ◽  
Magnetorheological Damper ◽  
Squeeze Film ◽  
Fluid Viscosity ◽  
Squeeze Film Damper ◽  
Viscous Forces ◽  
Angular Velocities ◽  
Volume Method ◽  
Gap Width ◽  
Made In

This article presents the evaluation of force effects on squeeze film damper rotor. The rotor is placed eccentrically and its motion is translate-circular. The amplitude of rotor motion is smaller than its initial eccentricity. The force effects are calculated from pressure and viscous forces which were measured by using computational modeling. Damper was filled with magnetorheological fluid. Viscosity of this non-Newtonian fluid is given using Bingham rheology model. Yield stress is not constant and it is a function of magnetic induction which is described by many variables. The most important variables of magnetic induction are electric current and gap width between rotor and stator. The simulations were made in finite volume method based solver. The motion of the inner ring of squeeze film damper was carried out by dynamic mesh. Numerical solution was solved for five different initial eccentricities and angular velocities of rotor motion.

Spin-coating of vertically stratified thin liquid films

2010 ◽  
Vol 647 ◽  
pp. 265-285 ◽  
Author(s):  
A. McINTYRE ◽  
L. N. BRUSH
Keyword(s):  
Thin Films ◽  
Spin Coating ◽  
Lower Layer ◽  
Liquid Films ◽  
Thin Liquid Films ◽  
Uniform Thickness ◽  
Viscous Forces ◽  
Liquid Free Surface ◽  
Device Applications ◽  
Lower Liquid

Spin-coating is a process used to fabricate thin films for device applications. In this paper, lubrication theory is used to derive an axisymmetric model for the spin-coating of two immiscible vertically stratified Newtonian thin films. The model includes gravitational, van der Waals, capillary and viscous forces, differences in liquid layer properties and evaporation/condensation effects. Thinning calculations focus on the effects of viscosity and condensation/evaporation. In this case, for layers of uniform thickness, the lower layer thins monotonically yet never reaches zero thickness. With evaporation mass loss the upper layer disappears in finite time, whereas with condensation effects the upper layer approaches a steady-state thickness. Fully nonlinear calculations are carried out for films with non-uniform thickness and the deviation of the interfaces from the flat state is monitored. In general, disturbances to the lower layer have a greater effect on the upper layer than those of disturbances of the upper layer on the lower layer. Disturbances along the upper gas–liquid free surface propagate outward more rapidly than those along the lower liquid–liquid interface and disturbances that decrease the film thickness tend to dissipate more slowly.

scholarly journals From the Phan–Thien–Tanner/Oldroyd-B Non-Newtonian Model to the Double Shear Thining Rabinowisch Thin Film Model

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Guy Bayada ◽  
Laurent Chupin ◽  
Sébastien Martin
Keyword(s):  
Thin Film ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Solvent Mixture ◽  
Deborah Number ◽  
Fluid Viscosity ◽  
Three Dimensional Model ◽  
Bulk Fluid ◽  
Double Shear ◽  
Viscoelastic Effects

In this paper, an asymptotic expansion is used to derive a description of Phan–Tien– Tanner (PTT)/Oldroyd-B flows in the thin film situation without the classical “upper convective maxwell”(UCM) assumption. We begin with a short presentation of the Phan–Thien–Tanner/Oldroyd-B models, which introduce viscoelastic effects in a solute–solvent mixture. The three-dimensional flow is described using five parameters, namely the Deborah number (De) (or the relaxation parameter λ), the viscosity ratio r, the bulk fluid viscosity η, the material slip parameter a related to the “convected derivative” and an elongation number κ. Then we focus on the thin film assumption and the related asymptotic analysis that allows us to derive a reduced model. A perturbation procedure for “not too small” values of κ allows us to obtain further results such as an asymptotic “effective viscosity/ shear rate” law, which appears to be a perturbation of the double Rabinowisch model, whose parameters are completely defined by those of the original three-dimensional model. And last a numerical procedure is proposed based on a penalized Uzawa method, to compute the corresponding solution. This algorithm can also be used for any generalized double Newtonian shear thinning Carreau law.

Instability and Transition of a Plane Bubble Plume

2002 ◽  
Author(s):  
Ophe´lie Caballina ◽  
Eric Climent ◽  
Jan Dusˇek
Keyword(s):  
Stokes Equations ◽  
Fluid Layer ◽  
Fluid Velocity ◽  
Continuous Phase ◽  
Collective Effects ◽  
Recent Experimental Data ◽  
Fluid Viscosity ◽  
Bubble Plume ◽  
Carrier Fluid ◽  
Bubble Cloud

When bubbles are continuously released from a located source at the bottom of a fluid layer initially at rest, a plume is produced. The motion of the carrier fluid is initiated and driven by buoyancy of the bubble cloud. In the present study, a detailed analysis of the bubble plume transition is investigated. The continuous phase flow is obtained by direct numerical resolution of Navier-Stokes equations forced by the presence of bubbles. Collective effects induced by the presence of bubbles are modelled by a spatio-temporal distribution of momentum. Time evolution of the dispersed phase is solved by lagrangian tracking of all the bubbles. Focused on the description of plume transition, several configurations (plume widths, fluid viscosity, injection rate) are investigated. During the laminar ascension of the plume, fluid velocity profiles can be non-dimensionalised on a single auto-similar evolution. Dimensional analysis provides a prediction of the limit rising velocity of the plume top. This prediction has been confirmed by our numerical simulations. Furthermore, our first results point out the symmetry breaking induced by plume instability which appears beyond a critical transition height. Various data show that the Grashof number based on injection conditions is the key parameter to predict the transition of the plume. Our results agree very well with recent experimental data. Comparison with experiments on thermal plumes in air shows that the bubble plume is more unstable. This feature should be related to the lack of diffusion in the lagrangian transport of density gradient by the bubble cloud and to the slip velocity between the two phases.

Effects of capillary number, Bond number, and gas solubility on water saturation of sand specimens

2013 ◽  
Vol 50 (2) ◽  
pp. 133-144 ◽  
Author(s):  
Bruce L. Kutter
Keyword(s):  
Capillary Number ◽  
Water Saturation ◽  
Fluid Pressure ◽  
Infiltration Rate ◽  
Capillary Forces ◽  
Bond Number ◽  
Pore Fluid ◽  
Degree Of Saturation ◽  
Fluid Viscosity ◽  
Viscous Forces

To better understand how to prepare completely water-saturated specimens or centrifuge models from dry sand, the mechanisms of the infiltration and filling of pores in sand are studied. Complete saturation has been shown by others to be especially important in studies involving the triggering of liquefaction. This paper discusses how the degree of saturation obtained during infiltration increases with the “Bond number”, Bo (ratio of body forces and capillary forces), and the “capillary number”, Ca (ratio of viscous forces and capillary forces), as well as the solubility of gas bubbles in the pore fluid. Bo is varied by changing the particle size, fluid density, and centrifugal acceleration. Ca is varied by changing the fluid viscosity and infiltration rate. The dissolution of gas is encouraged by replacing pore air by CO2 (56 times more soluble in water than N2), by de-airing the liquid prior to infiltration or by increasing the pore fluid pressure after infiltration. Infiltration experiments performed at 1g and in a centrifuge are presented. A new technique for measuring the degree of saturation is also presented. Quantitative pressure–saturation relations are presented for different gasses, illustrating the importance of replacement of air by CO2. Spinning a specimen in a centrifuge during infiltration is also useful for speeding up the saturation process and for achieving higher degrees of saturation.

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