The Effect of Film Thickness on EHD-Driven Instability of Interface Separating Two Liquids

2009 ◽  
Author(s):  
Payam Sharifi ◽  
Asghar Esmaeeli
Keyword(s):  
Stokes Equations ◽  
Thin Liquid Film ◽  
Front Tracking ◽  
Thin Layers ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Interface Instability ◽  
Navier Stokes Equations ◽  
Dielectric Model ◽  
Leaky Dielectric Model

Most of the studies conducted so far on EHD-driven instability of superimposed fluids have been concerned with liquid layers of modest depths. In many applications, however, the liquid layers can be very thin. Since the dynamics in thin films is generally governed by lubrication equations rather than full Navier-Stokes equations, it is expected that the interface dynamics will be quite different from that of the liquids with modest depths. The objective of this study is to explore the effect of initial liquid thickness on the dynamics of the phase boundary. To do this end, we perform Direct Numerical Simulations (DNS) using a front tracking/finite difference scheme, in conjunction with Taylor’s leaky dielectric model. For the physical parameters used here, it is shown that for sufficiently thick liquid layers, the interface instability leads to formation of liquid columns that merge together to form a big column. However, for thin layers, the interactions between the columns are weaker and lead to a short and a longer column that are connected by a thin liquid film.

scholarly journals Effects of surfactant on propagation and rupture of a liquid plug in a tube

2019 ◽  
Vol 872 ◽  
pp. 407-437 ◽  
Author(s):  
M. Muradoglu ◽  
F. Romanò ◽  
H. Fujioka ◽  
J. B. Grotberg
Keyword(s):  
Shear Stress ◽  
Evolution Equations ◽  
Stokes Equations ◽  
Thin Liquid Film ◽  
Front Tracking ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Liquid Plug ◽  
Front Tracking Method ◽  
Airway Walls

Surfactant-laden liquid plug propagation and rupture occurring in lower lung airways are studied computationally using a front-tracking method. The plug is driven by an applied constant pressure in a rigid axisymmetric tube whose inner surface is coated by a thin liquid film. The evolution equations of the interfacial and bulk surfactant concentrations coupled with the incompressible Navier–Stokes equations are solved in the front-tracking framework. The numerical method is first validated for a surfactant-free case and the results are found to be in good agreement with the earlier simulations of Fujioka et al. (Phys. Fluids, vol. 20, 2008, 062104) and Hassan et al. (Intl J. Numer. Meth. Fluids, vol. 67, 2011, pp. 1373–1392). Then extensive simulations are performed to investigate the effects of surfactant on the mechanical stresses that could be injurious to epithelial cells, such as pressure and shear stress. It is found that the liquid plug ruptures violently to induce large pressure and shear stress on airway walls and even a tiny amount of surfactant significantly reduces the pressure and shear stress and thus improves cell survivability. However, addition of surfactant also delays the plug rupture and thus airway reopening.

Evaporation of Thin Film of Polar Liquid in Presence of Soluble Surfactant

2015 ◽  
Vol 1105 ◽  
pp. 105-109 ◽  
Author(s):  
Varvara Yu. Gordeeva ◽  
Andrey V. Lyushnin
Keyword(s):  
Liquid Film ◽  
Stokes Equations ◽  
Thin Liquid Film ◽  
Specific Interaction ◽  
Surface Concentration ◽  
Double Electric Layer ◽  
Solid Substrate ◽  
Polar Liquid ◽  
Navier Stokes ◽  
Navier Stokes Equations

Evaporation of a thin layer of a polar liquid (water) having a free surface and located on a solid substrate is investigated. A surfactant is solved in the liquid film. The surface tension is a linear function of the surface concentration of the surfactant. The surface energy of the solid-liquid interface is a nonmonotonic function of the layer thickness and is the sum of the Van der Waals interaction and the specific interaction of the double electric layer on the interface. The effect of the solvable surfactant on the dynamics of the propagation of the evaporation front in the thin liquid film is analyzed in the long-wave approximation in the system of Navier-Stokes equations.

The Effect of Electrostatic Forces on the Distribution of Drops in a Channel

2002 ◽  
Author(s):  
Arturo Ferna´ndez ◽  
Jiacai Lu ◽  
Asghar Esmaeeli ◽  
Gre´tar Tryggvason
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Hydrodynamic Interaction ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Dielectric Fluids ◽  
Wide Range ◽  
Leaky Dielectric Model

Direct numerical simulations are used to examine the effect of electric fields on the behavior of suspension of drops in dielectric fluids. The effect of electric field is modeled using the “leaky dielectric” model, coupled with the full Navier-Stokes equations. The governing equations are solved using a front-tracking/finite volume technique. The interaction of the drops is strongly dependant on the conductivity and the permittivity ratio, but fibration, where drops line up into long columns, takes place over a wide range of these parameters. The hydrodynamic interaction due to fluid circulation induced by the electric field has a strong influence on the drop distribution and the rate of fibration.

Modeling and computation of the cavitating flow in injection nozzle holes

2015 ◽  
Vol 06 (01) ◽  
pp. 1550003 ◽  
Author(s):  
Hatem Kanfoudi ◽  
Ridha Zgolli
Keyword(s):  
Transport Equation ◽  
Source Term ◽  
Stokes Equations ◽  
Volume Fraction ◽  
Variable Density ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Cavitating Flows ◽  
Navier Stokes Equations ◽  
Injection Nozzle

Cavitating flows inside a diesel injection nozzle hole were simulated using a mixture model. A two-dimensional (2D) numerical model is proposed in this paper to simulate steady cavitating flows. The Reynolds-averaged Navier–Stokes equations are solved for the liquid and vapor mixture, which is considered as a single fluid with variable density and expressed as a function of the vapor volume fraction. The closure of this variable is provided by the transport equation with a source term Transport-equation based methods (TEM). The processes of evaporation and condensation are governed by changes in pressure within the flow. The source term is implanted in the CFD code ANSYS CFX. The influence of numerical and physical parameters is presented in detail. The numerical simulations are in good agreement with the experimental data for steady flow.

scholarly journals Inertial dynamics of air bubbles crossing a horizontal fluid–fluid interface

2012 ◽  
Vol 707 ◽  
pp. 405-443 ◽  
Author(s):  
Romain Bonhomme ◽  
Jacques Magnaudet ◽  
Fabien Duval ◽  
Bruno Piar
Keyword(s):  
High Speed ◽  
Stokes Equations ◽  
Complex Dynamics ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Air Bubbles ◽  
Fluid Interface ◽  
Navier Stokes Equations ◽  
Film Drainage ◽  
Two Fluids

AbstractThe dynamics of isolated air bubbles crossing the horizontal interface separating two Newtonian immiscible liquids initially at rest are studied both experimentally and computationally. High-speed video imaging is used to obtain a detailed evolution of the various interfaces involved in the system. The size of the bubbles and the viscosity contrast between the two liquids are varied by more than one and four orders of magnitude, respectively, making it possible to obtain bubble shapes ranging from spherical to toroidal. A variety of flow regimes is observed, including that of small bubbles remaining trapped at the fluid–fluid interface in a film-drainage configuration. In most cases, the bubble succeeds in crossing the interface without being stopped near its undisturbed position and, during a certain period of time, tows a significant column of lower fluid which sometimes exhibits a complex dynamics as it lengthens in the upper fluid. Direct numerical simulations of several selected experimental situations are performed with a code employing a volume-of-fluid type formulation of the incompressible Navier–Stokes equations. Comparisons between experimental and numerical results confirm the reliability of the computational approach in most situations but also points out the need for improvements to capture some subtle but important physical processes, most notably those related to film drainage. Influence of the physical parameters highlighted by experiments and computations, especially that of the density and viscosity contrasts between the two fluids and of the various interfacial tensions, is discussed and analysed in the light of simple models and available theories.

Numerical Simulations of Three-Dimensional Flows in a Cubic Cavity With an Oscillating Lid

1993 ◽  
Vol 115 (4) ◽  
pp. 680-686 ◽  
Author(s):  
Reima Iwatsu ◽  
Jae Min Hyun ◽  
Kunio Kuwahara
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Time Dependent ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Navier Stokes Equations ◽  
Sinusoidal Oscillations ◽  
Dependent Flow

Numerical studies are made of three-dimensional flow of a viscous fluid in a cubical container. The flow is driven by the top sliding wall, which executes sinusoidal oscillations. Numerical solutions are acquired by solving the time-dependent, three-dimensional incompressible Navier-Stokes equations by employing very fine meshes. Results are presented for wide ranges of two principal physical parameters, i.e., the Reynolds number, Re ≤ 2000 and the frequency parameter of the lid oscillation, ω′ ≤ 10.0. Comprehensive details of the flow structure are analyzed. Attention is focused on the three-dimensionality of the flow field. Extensive numerical flow visualizations have been performed. These yield sequential plots of the main flows as well as the secondary flow patterns. It is found that the previous two-dimensional computational results are adequate in describing the main flow characteristics in the bulk of interior when ω′ is reasonably high. For the cases of high-Re flows, however, the three-dimensional motions exhibit additional complexities especially when ω′ is low. It is asserted that, thanks to the recent development of the supercomputers, calculation of three-dimensional, time-dependent flow problems appears to be feasible at least over limited ranges of Re.

scholarly journals Thin Liquid Film Dynamics on a Spinning Spheroid

Fluids ◽  
2021 ◽  
Vol 6 (9) ◽  
pp. 318
Author(s):  
Selin Duruk ◽  
Edouard Boujo ◽  
Mathieu Sellier
Keyword(s):  
Stokes Equations ◽  
Thin Liquid Film ◽  
Vertical Axis ◽  
Approximate Model ◽  
Navier Stokes ◽  
Lubrication Approximation ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Order Of Magnitude ◽  
The Impact

The present work explores the impact of rotation on the dynamics of a thin liquid layer deposited on a spheroid (bi-axial ellipsoid) rotating around its vertical axis. An evolution equation based on the lubrication approximation was derived, which takes into account the combined effects of the non-uniform curvature, capillarity, gravity, and rotation. This approximate model was solved numerically, and the results were compared favorably with solutions of the full Navier–Stokes equations. A key advantage of the lubrication approximation is the solution time, which was shown to be at least one order of magnitude shorter than for the full Navier–Stokes equations, revealing the prospect of controlling film dynamics for coating applications. The thin film dynamics were investigated for a wide range of geometric, kinematic, and material parameters. The model showed that, in contrast to the purely gravity-driven case, in which the fluid drains downwards and accumulates at the south pole, rotation leads to a migration of the maximum film thickness towards the equator, where the centrifugal force is the strongest.

scholarly journals The Effect of Varying Magnetic Number, Reynolds Number and Pressure Gradient on Velocity Profiles in an MHD Flow

2020 ◽  
Vol 5 (7) ◽  
pp. 387-394
Author(s):  
LIHAVI ANNET ◽  
Dr. Virginia Kitetu ◽  
Dr. Mary wainaina
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Hartmann Number ◽  
Stokes Equations ◽  
Mhd Flow ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Parallel Plates ◽  
Navier Stokes Equations ◽  
Electrically Conducting

Magnetohydrodynamic ow of a hot viscous electrically conducting incompressible uid through parallel plates is studied. In the study, the e ect of Hartmann number (M), pressure gradient and Reynolds number (Re) on the velocity eld is investigated. The Navier-stokes equations were coupled with Ohms law and then solved using nite di erence method (FDM). The velocity eld was computed for various values of the physical parameters and shown graphically. It was found that as the Hartmann number M increases, the velocity pro les decreased due to increased Lorents force while an increase in Reynolds number causes an increase in the velocity of the uid. All these analysis was done using MATLAB program and the results were presented in tables and graphs.

scholarly journals Numerical investigation of an unsteady nanofluid flow with magnetic and suction effects to the moving upper plate

2020 ◽  
Vol 12 (2) ◽  
pp. 168781402090358 ◽  
Author(s):  
Muhammad Shuaib ◽  
Abbas Ali ◽  
Muhammad Altaf Khan ◽  
Aatif Ali
Keyword(s):  
Numerical Investigation ◽  
Stokes Equations ◽  
Volume Fraction ◽  
Nonlinear Partial Differential Equations ◽  
Variable Magnetic Field ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Nanofluid Flow ◽  
Navier Stokes Equations ◽  
Nicolson Scheme

The recent work provides the numerical investigation of an unsteady viscous nanofluid flow between two porous plates under the effect of variable magnetic field and suction/injection. Navier Stokes equations are modeled to study the hydrothermal properties of four different nanoparticles copper [Formula: see text], silver [Formula: see text], aluminum oxide [Formula: see text], and titanium oxide [Formula: see text]. The resultant nonlinear partial differential equations, governing the viscous fluid flow, are solved numerically using Crank–Nicolson scheme. The effect of important physical parameters such as volume fraction, magnetic strength, and porosity parameter are shown both graphically and in tabular form. It is found that due to the greatest thermal diffusivity for nanofluid [Formula: see text], comparatively the velocity increases more rapidly with the increasing value of volume fraction. Due to this effect, it is preferred to use nanofluid [Formula: see text] for transportation purposes.

scholarly journals Growth and spectra of gravity–capillary waves in countercurrent air/water turbulent flow

2015 ◽  
Vol 777 ◽  
pp. 245-259 ◽  
Author(s):  
Francesco Zonta ◽  
Alfredo Soldati ◽  
Miguel Onorato
Keyword(s):  
Stokes Equations ◽  
Capillary Waves ◽  
Turbulence Theory ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Generation Process ◽  
Navier Stokes Equations ◽  
Interface Waves ◽  
Two Phases ◽  
Wave Induced

Using direct numerical simulation of the Navier–Stokes equations, we analyse the dynamics of the interface between air and water when the two phases are driven by opposite pressure gradients (countercurrent configuration). The Reynolds number ($\mathit{Re}_{{\it\tau}}$), the Weber number ($\mathit{We}$) and the Froude number ($\mathit{Fr}$) fully describe the physical problem. We examine the problem of the transient growth of interface waves for different combinations of physical parameters. Keeping$\mathit{Re}_{{\it\tau}}$constant and varying$\mathit{We}$and$\mathit{Fr}$, we show that, in the initial stages of the wave generation process, the amplitude of the interface elevation${\it\eta}$grows in time as${\it\eta}\propto t^{2/5}$. The wavenumber spectra,$E(k_{x})$, of the surface elevation in the capillary range are in good agreement with the predictions of wave turbulence theory. Finally, the wave-induced modification of the average wind and current velocity profiles is addressed.

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