Mobilities of a Spherical Particle Straddling the Interface of a Semi-Infinite Brinkman Flow

2021 ◽  
Author(s):  
M. S. Faltas ◽  
Hany H. Sherief ◽  
Allam Abdelaziz Allam ◽  
Baraa Ahmed
Keyword(s):  
Contact Angle ◽  
Reynolds Number ◽  
Spherical Particle ◽  
Capillary Number ◽  
Slip Parameter ◽  
Clear Fluid ◽  
Flat Interface ◽  
Permeability Parameter ◽  
Analytical Expressions ◽  
Resistance Coefficients

Abstract The motion of a spherical particle straddling the flat interface of a semi-infinite Brinkman flow is considered under conditions of low Reynolds number and low capillary number regime. The analysis is applied in the case of 90° contact angle and when the viscosity of the constituent fluid in the Brinkman region is much more than that of the adjacent fluid. Analytical expressions for the hydrodynamic scalar resistance coefficients are obtained and represented graphically as a function of the slip parameter at the surface of the particle and the permeability parameter of the porous region. The hydrodynamic mobilities are also obtained and represented in tables. The limiting cases of Stokes clear fluid and Darcy's flow are recovered.

scholarly journals Force distribution on a slender body close to an interface

1981 ◽  
Vol 24 (1) ◽  
pp. 27-36 ◽  
Author(s):  
J.R. Blake ◽  
G.R. Fulford
Keyword(s):  
Reynolds Numbers ◽  
Plane Wall ◽  
Slender Body ◽  
Force Distribution ◽  
Immiscible Liquids ◽  
Flat Interface ◽  
Small Reynolds Numbers ◽  
Rigid Plane ◽  
Limiting Case ◽  
Analytical Expressions

The motion of a slender body parallel and very close to a flat interface which separates two immiscible liquids of differing density and viscosity is considered for very small Reynolds numbers. Approximate analytical expressions are obtained for the distribution of forces acting on the slender body. The limiting case of a rigid plane wall yields results obtained previously.

Flow and Thermal Fields in a Pendant Droplet Moving on Lyophobic Surface

2010 ◽  
Author(s):  
Basant Singh Sikarwar ◽  
K. Muralidhar ◽  
Sameer Khandekar
Keyword(s):  
Heat Transfer ◽  
Contact Angle ◽  
Reynolds Number ◽  
Shear Stress ◽  
Heat Transfer Coefficient ◽  
Wall Shear Stress ◽  
Transfer Coefficient ◽  
Maximum Shear Stress ◽  
Computational Domain ◽  
Wall Shear

Clusters of liquid drops growing and moving on physically or chemically textured lyophobic surfaces are encountered in drop-wise mode of vapor condensation. As opposed to film-wise condensation, drops permit a large heat transfer coefficient and are hence attractive. However, the temporal sustainability of drop formation on a surface is a challenging task, primarily because the sliding drops eventually leach away the lyophobicity promoter layer. Assuming that there is no chemical reaction between the promoter and the condensing liquid, the wall shear stress (viscous resistance) is the prime parameter for controlling physical leaching. The dynamic shape of individual droplets, as they form and roll/slide on such surfaces, determines the effective shear interaction at the wall. Given a shear stress distribution of an individual droplet, the net effect of droplet ensemble can be determined using the time averaged population density during condensation. In this paper, we solve the Navier-Stokes and the energy equation in three-dimensions on an unstructured tetrahedral grid representing the computational domain corresponding to an isolated pendant droplet sliding on a lyophobic substrate. We correlate the droplet Reynolds number (Re = 10–500, based on droplet hydraulic diameter), contact angle and shape of droplet with wall shear stress and heat transfer coefficient. The simulations presented here are for Prandtl Number (Pr) = 5.8. We see that, both Poiseuille number (Po) and Nusselt number (Nu), increase with increasing the droplet Reynolds number. The maximum shear stress as well as heat transfer occurs at the droplet corners. For a given droplet volume, increasing contact angle decreases the transport coefficients.

Pressure, Frictional Resistance, and Flow Characteristics of the Partially Wetted Rotating Disk

1968 ◽  
Vol 90 (2) ◽  
pp. 395-404 ◽  
Author(s):  
H. N. Ketola ◽  
J. M. McGrew
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Flow Characteristics ◽  
Frictional Resistance ◽  
Rotating Disk ◽  
Practical Applications ◽  
Stationary Wall ◽  
Spacing Ratio ◽  
Analytical Expressions

A theory of the partially wetted rotating disk is described and experimental data presented which verify the application of this theory in practical applications. Four different flow regimes may be identified according to the value of the disk Reynolds number and the spacing ratio between the disk and stationary wall. The analytical expressions for prediction of the pressure gradient developed and the frictional resistance are uniquely determined by the disk Reynolds number, spacing ratio, and the degree of wetting of the disk.

An Experimental Study of the Viscous Resistance of a 0,564-CB Form

1979 ◽  
Vol 23 (02) ◽  
pp. 140-156
Author(s):  
P. N. Joubert ◽  
P. H. Hoffmann
Keyword(s):  
Experimental Study ◽  
Reynolds Number ◽  
Skin Friction ◽  
Resistance Coefficient ◽  
Viscous Resistance ◽  
Local Skin ◽  
Friction Resistance ◽  
Local Skin Friction ◽  
The University ◽  
Resistance Coefficients

Wind tunnel tests were performed to determine the viscous resistance and its components for a 0.564-CB model from the BSRA Trawler Series. It was found that the sum of the pressure and skin friction resistance coefficients agreed well with the viscous resistance coefficient determined from drag balance tests. The range of Reynolds number examined was from 1.15 × 106 to 5.17 × 106. The results for the viscous resistance and its components were fitted using least-squares methods to various equations. The results were also compared with the results of previous tests done at the University of Melbourne on models of Lucy Ash-. ton and a 0.80-CB tanker. It was found that the skin friction and viscous resistance coefficients had curves of quite different position and slope. Local skin friction distribution showed noteworthy differences, especially at the stern, with high values at the keel and low values approaching the waterline.

scholarly journals A spherical particle straddling a fluid/gas interface in an axisymmetric straining flow

1990 ◽  
Vol 217 ◽  
pp. 263-298 ◽  
Author(s):  
J. A. Stoos ◽  
L. G. Leal
Keyword(s):  
Contact Angle ◽  
Spherical Particle ◽  
Numerical Solutions ◽  
Contact Angles ◽  
Boundary Integral ◽  
Equilibrium Contact Angle ◽  
Equilibrium Configurations ◽  
Wide Range ◽  
The Stability ◽  
Neutrally Buoyant

Numerical solutions, obtained via the boundary-integral technique, are used to consider the effect of a linear axisymmetric straining flow on the existence of steady-state configurations in which a neutrally buoyant spherical particle straddles a gas–liquid interface. The problem is directly applicable to predictions of the stability of particle capture in flotation processes, and is also of interest in the context of contact angle and surface tension measurements. A primary goal of the present study is a determination of the critical capillary number, Cac, beyond which an initially captured particle is pulled from the interface by the flow, and the dependence of Cac on the equilibrium contact angle θc. We also present equilibrium configurations for a wide range of contact angles and subcritical capillary numbers.

The Effect of Surface Wettability on Viscous Film Deposition

2009 ◽  
Author(s):  
Alexandru Herescu ◽  
Jeffrey S. Allen
Keyword(s):  
Contact Angle ◽  
Film Thickness ◽  
Capillary Number ◽  
High Speed ◽  
Glass Tube ◽  
Contact Angles ◽  
Film Deposition ◽  
Surface Wettability ◽  
Working Fluid ◽  
Uniqueness Of The Solution

The viscous deposition of a liquid film on the inside of a capillary has been experimentally investigated with a focus on the relationship between the film thickness and surface wettability. With distilled water as a working fluid tests were run in a 622 microns diameter glass tube with contact angles of 30° and 105°, respectively. In the first set of experiments the tube was uncoated while in the second set a fluoropolymer coating was applied to increase the contact angle. A film thickness dependence with the contact angle θ (surface wettability) as well as the Capillary number in the form hR ∼ Ca2/3/cosθ is inferred from scaling arguments. For partial wetting it may explain the existence of a thicker film for nonzero contact angle. It was further found that the non-wetting case of 105° contact angle deviates significantly from the existing theories, the film thickness presenting a weak dependence with the Capillary number. This deviation as well as the apparent non-uniqueness of the solution is thought to be caused by the film instability (rupture) observed during the tests. The thickness of the deposited film as a function of the Capillary number was estimated from the liquid mass exiting the capillary and the gas-liquid interface (meniscus) velocity, and compared to Bretherton’s data and a correlation proposed by Quere. The film thickness measurements as well as the meniscus velocity were determined with the aid of a Photron high speed camera with 10000 frames per second sampling capability coupled with a Nikon TE-2000 inverted microscope and a Precisa electronic balance.

scholarly journals Application of Recursive Theory of Slow Viscoelastic Flow to the Hydrodynamics of Second-Order Fluid Flowing through a Uniformly Porous Circular Tube

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1170 ◽  
Author(s):  
Kaleemullah Bhatti ◽  
Abdul Majeed Siddiqui ◽  
Zarqa Bano
Keyword(s):  
Reynolds Number ◽  
Stream Function ◽  
Stokes Equations ◽  
Circular Tube ◽  
Volume Flow Rate ◽  
Small Diameter ◽  
Second Order ◽  
Navier Stokes ◽  
Flow Variables ◽  
Analytical Expressions

Slow velocity fluid flow problems in small diameter channels have many important applications in science and industry. Many researchers have modeled the flow through renal tubule, hollow fiber dialyzer and flat plate dialyzer using Navier Stokes equations with suitable simplifying assumptions and boundary conditions. The aim of this article is to investigate the hydrodynamical aspects of steady, axisymmetric and slow flow of a general second-order Rivlin-Ericksen fluid in a porous-walled circular tube with constant wall permeability. The governing compatibility equation have been derived and solved analytically for the stream function by applying Langlois recursive approach for slow viscoelastic flows. Analytical expressions for velocity components, pressure, volume flow rate, fractional reabsorption, wall shear stress and stream function have been obtained correct to third order. The effects of wall Reynolds number and certain non-Newtonian parameters have been studied and presented graphically. The obtained analytical expressions are in agreement with the existing solutions in literature if non-Newtonian parameters approach to zero. The solutions obtained in this article may be considered as a generalization to the existing work. The results indicate that there is a significant dependence of the flow variables on the wall Reynolds number and non-Newtonian parameters.

Simulations of Droplet Collisions in Shear Flow

2012 ◽  
Author(s):  
Orest Shardt ◽  
J. J. Derksen ◽  
Sushanta K. Mitra
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Capillary Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Simple Shear Flow ◽  
Number Range ◽  
Droplet Collisions ◽  
Critical Capillary Number ◽  
Boltzmann Method

When droplets collide in a shear flow, they may coalesce or remain separate after the collision. At low Reynolds numbers, droplets coalesce when the capillary number does not exceed a critical value. We present three-dimensional simulations of droplet coalescence in a simple shear flow. We use a free-energy lattice Boltzmann method (LBM) and study the collision outcome as a function of the Reynolds and capillary numbers. We study the Reynolds number range from 0.2 to 1.4 and capillary numbers between 0.1 and 0.5. We determine the critical capillary number for the simulations (0.19) and find that it is does not depend on the Reynolds number. The simulations are compared with experiments on collisions between confined droplets in shear flow. The critical capillary number in the simulations is about a factor of 25 higher than the experimental value.

Analysis of a porous inclined slider bearing lubricated with a magnetic fluid considering slip velocity

2007 ◽  
Vol 221 (3) ◽  
pp. 81-85 ◽  
Author(s):  
N Ahmad ◽  
J P Singh
Keyword(s):  
Theoretical Model ◽  
Magnetic Fluid ◽  
Slip Velocity ◽  
Magnetic Parameter ◽  
Load Capacity ◽  
Slip Parameter ◽  
Slider Bearing ◽  
Permeability Parameter ◽  
Velocity Effect

A theoretical model of a magnetic-fluid-based porous inclined slider bearing has been considered to study the slip velocity effect on the load capacity of the bearing. The expression for load capacity has been obtained in terms of the slip parameter and the permeability parameter. The dependence of load on the magnetic parameter, the permeability parameter, and the slip parameter has been studied graphically. Minimization of the slip parameter and the permeability parameter have been discussed for the possible increase in load capacity.

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