scholarly journals Diffusiophoresis of a Colloidal Cylinder at Small Finite Péclet Numbers

2019 ◽  
Vol 3 (2) ◽  
pp. 44
Author(s):  
Chang ◽  
Keh
Keyword(s):  
Particle Velocity ◽  
Asymptotic Expansions ◽  
Concentration Gradient ◽  
Interfacial Layer ◽  
Fluid Velocity ◽  
Solute Concentration ◽  
Cylindrical Particle ◽  
Governing Equations ◽  
Nonelectrolyte Solution ◽  
Solute Convection

The diffusiophoretic migration of a circular cylindrical particle in a nonelectrolyte solution with a solute concentration gradient normal to its axis is analytically studied for a small but finite Péclet number . The interfacial layer of interaction between the solute molecules and the particle is taken to be thin, but the polarization of its mobile molecules is allowed. Using a method of matched asymptotic expansions, we solve the governing equations of conservation of the system and obtain an explicit formula for the diffusiophoretic velocity of the cylinder correct to the order . It is found that the perturbed solute concentration and fluid velocity distributions have the order , but the leading correction to the particle velocity has the higher order . The correction to the particle velocity to the order can be either positive or negative depending on the polarization parameter of the thin interfacial layer, establishing that the solute convection effect is complicated and can enhance or retard the diffusiophoretic motion. The particle velocity at can be about 17% smaller or 0.2% greater than that at . Under practical conditions, the solute convection effect on the diffusiophoretic velocity is much greater for a cylindrical particle than for a spherical particle, whose leading correction has the order .

Viscoelectric Effect on the Electroosmotic Flow in Nanochannels With Heterogeneous Zeta Potentials

2018 ◽  
Author(s):  
Edson M. Jimenez ◽  
Federico Méndez ◽  
Juan P. Escandón
Keyword(s):  
Electroosmotic Flow ◽  
Fluid Velocity ◽  
Volumetric Flow Rate ◽  
Mass Conservation ◽  
Double Layers ◽  
Fluid Viscosity ◽  
Governing Equations ◽  
Flat Plates ◽  
Zeta Potentials ◽  
Poisson Boltzmann

In the present work, we realize a study about the influence of viscoelectric effect on the electroosmotic flow of Newtonian fluids in nanochannels formed by two parallel flat plates. In the problem, the channel walls have heterogeneous zeta potentials which follow a sinusoidal distribution; moreover, viscoelectric effects appear into the electric double layers when high zeta potentials are considered at the channel walls, modifying the fluid viscosity and the fluid velocity. To find the solution of flow field, the modified Poisson-Boltzmann, mass conservation and momentum governing equations, are solved numerically. In the results, combined effects from the zeta potential heterogeneities and viscosity changes yields different kind of flow recirculations controlled by the dephasing angle, amplitude and number of waves of the heterogeneities at the walls. The viscoelectric effect produces a decrease in the magnitude of velocity profiles and volumetric flow rate when the high zeta potentials are magnified. Additionally, the heterogeneous zeta potentials at the walls generate an induced pressure on the flow. This investigation extend the knowledge of electroosmotic flows under field effects for future mixing applications.

scholarly journals What can asymptotic expansions tell us about large-scale quasi-geostrophic anticyclonic vortices?

1995 ◽  
Vol 2 (3/4) ◽  
pp. 186-193 ◽  
Author(s):  
A. Stegner ◽  
V. Zeitlin
Keyword(s):  
Asymptotic Expansions ◽  
Large Scale ◽  
Characteristic Size ◽  
Governing Equations ◽  
Free Surface Elevation ◽  
Circular Profile ◽  
Frontal Dynamics ◽  
Rotating Shallow Water ◽  
Steady Solutions ◽  
Rotating Shallow Water Equations

Abstract. The problem of the large-scale quasi-geostrophic anticyclonic vortices is studied in the framework of the baratropic rotating shallow- water equations on the β-plane. A systematic approach based on the multiplescale asymptotic expansions is used leading to a hierarchy of governing equations for the large-scale vortices depending on their characteristic size, velocity and a free surface elevation. Among them are the Charney-Obukhov equation, the intermediate geostrophic model equation, the frontal dynamics equation and some new nonlinear quasi-geostrophic equation. We are looking for steady-drifting axisymmetric anticyclonic solutions and find them in a consistent way only in this last equation. These solutions are soliton-like in the sense that the effects of weak non-linearity and dispersion balance each other. The same regimes on the paraboloidal β-plane are studied, all giving a negative result in what concerns the axisymmetric steady solutions, except for a strong elevation case where any circular profile is found to be steadily propagating within the accuracy of the approximation.

scholarly journals Numerical Investigation of Entropy Generation in Unsteady MHD Generalized Couette Flow with Variable Electrical Conductivity

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
T. Chinyoka ◽  
O. D. Makinde
Keyword(s):  
Electrical Conductivity ◽  
Couette Flow ◽  
Entropy Generation ◽  
Fluid Velocity ◽  
Bejan Number ◽  
Governing Equations ◽  
Entropy Generation Number ◽  
Thermophysical Parameters ◽  
Second Law Analysis ◽  
Finite Difference Techniques

The thermodynamic second law analysis is utilized to investigate the inherent irreversibility in an unsteady hydromagnetic generalized Couette flow with variable electrical conductivity in the presence of induced electric field. Based on some simplified assumption, the model nonlinear governing equations are obtained and solved numerically using semidiscretization finite difference techniques. Effects of various thermophysical parameters on the fluid velocity, temperature, current density, skin friction, the Nusselt number, entropy generation number, and the Bejan number are presented graphically and discussed quantitatively.

Magnetohydrodynamic Free Convective Flow of Nanofluids Past an Oscillating Porous Flat Plate in A Rotating System with Thermal Radiation and Hall Effects

2015 ◽  
Vol 32 (2) ◽  
pp. 197-210 ◽  
Author(s):  
S. Das ◽  
R.N. Jana ◽  
O.D. Makinde
Keyword(s):  
Thermal Radiation ◽  
Flat Plate ◽  
Convective Flow ◽  
Fluid Velocity ◽  
Governing Equations ◽  
Rotating System ◽  
Free Convective Flow ◽  
Hall Effects ◽  
Porous Flat Plate ◽  
Perturbation Approximation

ABSTRACTThe unsteady magnetohydrodynamic free convective flow due to an oscillating porous flat plate in a rotating frame of reference are studied when thermal radiation and Hall currents are taken into consideration. The entire system rotates with a uniform angular velocity about an axis normal to the plate. A uniform magnetic field is applied along the normal to the plate directed into the fluid region. Copper, alumina and titania water nanofluids are considered. The governing equations are solved analytically by employing the small perturbation approximation. The numerical results for fluid velocity and temperature are presented graphically for the pertinent parameters and discussed in details.

CFD Application of the Diffusion-Inertia Model to Bubble Flows and Boiling Water Problems

2009 ◽  
Author(s):  
Alexander S. Filippov ◽  
Vladimir M. Alipchenkov ◽  
Nickolay I. Drobyshevsky ◽  
Roman V. Mukin ◽  
Valeri Th. Strizhov ◽  
...  
Keyword(s):  
Mass Transfer ◽  
Kinetic Equation ◽  
Probability Density Function ◽  
Turbulent Flows ◽  
Particle Velocity ◽  
Boiling Water ◽  
Extended Version ◽  
Governing Equations ◽  
Inertia Model ◽  
Water Problems

The paper is aimed at the application of a model for simulating the dispersed turbulent flows. The model presented proceeds from a kinetic equation for the probability density function of the particle velocity distribution in turbulent flow. This approach is called the diffusion-inertia model (DIM). Applications of the model to droplet and bubble flows are presented. In the case of vaporized liquid, the interphase heat and mass transfer is introduced by adding the corresponding governing equations. This extended version of the DIM was applied to simulating the boiling water flow in a heated pipe.

Analytical Study of MHD Thermoconvective Waves through its Propagation

2017 ◽  
Vol 3 (01) ◽  
Author(s):  
Madan Lal
Keyword(s):  
Magnetic Field ◽  
Viscous Fluid ◽  
Concentration Gradient ◽  
Analytical Study ◽  
Solute Concentration ◽  
Horizontal Magnetic Field ◽  
Electrically Conducting ◽  
Specific Order ◽  
Waves Propagation ◽  
Propagation Of Waves

Following is the analytical study on the propagation of undamped thermoconvective waves, an electrically conducting viscous fluid is hypothesized which has the property of uniform horizontal magnetic field in heating the uniform vertical concentration gradient for a solute. It has seen that undamped thermoconvective waves propagation in a specific order, whereas the heating of fluid, is based on the solute concentration, this decreased vertically or show vertical pattern. If the heating of fluid takes place in upward manner the propagation of waves is highly effected, the above aspect proves hypothetically and has shown that its laboratory demonstration is also possible.

Evaluation of a coupled mass transport-biofilm process model using dissolved oxygen microsensors

1995 ◽  
Vol 32 (8) ◽  
pp. 107-114 ◽  
Author(s):  
A. B. Cunningham ◽  
E. Visser ◽  
Z. Lewandowski ◽  
M. Abrahamson
Keyword(s):  
Dissolved Oxygen ◽  
Process Model ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Solute Concentration ◽  
Diffusion Reaction ◽  
Navier Stokes ◽  
Biofilm Thickness ◽  
Artificial Biofilm ◽  
Biofilm Process

A 2-dimensional model has been developed which couples hydrodynamics, solute transport and reaction in a steady state biofilm system of irregular geometry under laminar flow. Biofilm thickness is initially specified over the domain and remains constant during the simulations. The Navier-Stokes equations are coupled with advection-diffusion-reaction equations describing oxygen transport and solved using finite differences. This model facilitates computational investigation of fluid velocity and solute concentration distributions in proximity to the fluid-biofilm interface. Model evaluation has been carried out using dissolved oxygen profiles measured by microsensors in a rectangular open channel with a 300 μm (approximate) artificial biofilm composed of alginate gel with an 8×1010 cells/ml concentration of Ps. aeruginosa cells. Significant variability in dissolved oxygen profile shape was observed at three locations on the artificial biofilm. Model simulations of these experiments facilitated a direct comparison between observed and computed values of dissolved oxygen concentration in the vicinity of the fluid-biofilm interface. Simulated profiles agreed closely with measured profiles at all three locations.

Drag Coefficient and Settling Velocity of Particles in Non-Newtonian Suspensions

1987 ◽  
Vol 109 (3) ◽  
pp. 319-323 ◽  
Author(s):  
M. Y. Dedegil
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Drag Coefficient ◽  
Yield Stress ◽  
Particle Velocity ◽  
Settling Velocity ◽  
Fluid Velocity ◽  
Newtonian Fluids ◽  
Drag Forces ◽  
Physical Composition

Drag forces on bodies in non-Newtonian fluids which are to be described by using the Reynolds number should only contain forces which are associated with the fluid velocity or particle velocity. Forces due to the yield stress τ0 must be considered separately. According to its physical composition, the Reynolds number must be calculated by means of the fully representative shear stress including the yield stress τ0. Then the drag coefficient cD as a function of the Reynolds number can be traced back to that of Newtonian fluids.

Effect of Solute Concentration Gradients on the Onset of Convection: Uniform and Nonuniform Initial Gradients

1986 ◽  
Vol 108 (4) ◽  
pp. 776-782 ◽  
Author(s):  
M. Kaviany ◽  
M. Vogel
Keyword(s):  
Temperature Gradient ◽  
Concentration Gradient ◽  
Fluid Layer ◽  
Onset Time ◽  
Solute Concentration ◽  
Concentration Gradients ◽  
Linear Amplification ◽  
Onset Of Convection ◽  
Gradient Layer ◽  
Good Agreement

The time of the onset of convection in a fluid layer, which is initially stably stratified and then heated from below in a transient manner, is determined experimentally and analytically. The initial stratification is due to the presence of a solute concentration gradient. In addition to initial linear solute concentration distributions two other specific initial solute concentration distributions are considered. In Case 1, a zero gradient layer is located underneath a nonzero and uniform gradient layer. In Case 2, the zero gradient layer is on the top. The linear amplification theory is applied to the prediction of the onset time. Interferometry is used as a means of determining the onset time experimentally. It is shown that since the adverse temperature gradient is concentrated near the bottom, any nonuniformity in the solute concentration gradient in this region reduces the effectiveness of the gradient in delaying the onset. Experimental and predicted results are in good agreement.

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