Double diffusive effects on pressure-driven miscible displacement flows in a channel

2012 ◽  
Vol 712 ◽  
pp. 579-597 ◽  
Author(s):  
Manoranjan Mishra ◽  
A. De Wit ◽  
Kirti Chandra Sahu
Keyword(s):  
Stokes Equations ◽  
Miscible Displacement ◽  
Interfacial Instability ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Finite Volume Approach ◽  
Diffusive Effects ◽  
The Moment ◽  
Double Diffusive ◽  
Pressure Driven

AbstractThe pressure-driven miscible displacement of a less viscous fluid by a more viscous one in a horizontal channel is studied. This is a classically stable system if the more viscous solution is the displacing one. However, we show by numerical simulations based on the finite-volume approach that, in this system, double diffusive effects can be destabilizing. Such effects can appear if the fluid consists of a solvent containing two solutes both influencing the viscosity of the solution and diffusing at different rates. The continuity and Navier–Stokes equations coupled to two convection–diffusion equations for the evolution of the solute concentrations are solved. The viscosity is assumed to depend on the concentrations of both solutes, while density contrast is neglected. The results demonstrate the development of various instability patterns of the miscible ‘interface’ separating the fluids provided the two solutes diffuse at different rates. The intensity of the instability increases when increasing the diffusivity ratio between the faster-diffusing and the slower-diffusing solutes. This brings about fluid mixing and accelerates the displacement of the fluid originally filling the channel. The effects of varying dimensionless parameters, such as the Reynolds number and Schmidt number, on the development of the ‘interfacial’ instability pattern are also studied. The double diffusive instability appears after the moment when the invading fluid penetrates inside the channel. This is attributed to the presence of inertia in the problem.

Dynamics of the interface between miscible liquids subjected to horizontal vibration

2015 ◽  
Vol 784 ◽  
pp. 342-372 ◽  
Author(s):  
Y. A. Gaponenko ◽  
M. Torregrosa ◽  
V. Yasnou ◽  
A. Mialdun ◽  
V. Shevtsova
Keyword(s):  
Time Scales ◽  
Stokes Equations ◽  
Immiscible Fluids ◽  
Interfacial Instability ◽  
Navier Stokes ◽  
Layer System ◽  
Navier Stokes Equations ◽  
Horizontal Vibration ◽  
Natural Time ◽  
Miscible Liquids

We present experimental evidence of the existence of an interfacial instability between two miscible liquids of similar (but non-identical) viscosities and densities under horizontal vibration. A stably stratified two-layer system is composed of the same binary mixture with different concentrations placed in a confined cell (with length twice as large as the height). Unlike the case of immiscible fluids, here, the interface is a transient layer of small but non-zero thickness. In the experiments, the frequency and amplitude were varied within the ranges 2–24 Hz and 1.5–16 mm, respectively. When the value of the oscillatory forcing increases, the amplitudes of the interface perturbations grow continuously, forming a saw-tooth frozen structure. This evolution is also examined numerically. In addition to the solutions of full 3-D Navier–Stokes equations, an averaging approach with separation of time scales is used for situations in which the forcing period is very small compared to the natural time scales of the problem. The simulation of averaged equations provides the explanation of the instability development, the calculations of the full nonlinear equations shed light on the decay of a wavy pattern. The results of numerical modelling perfectly support the experimental observations.

Numerical Investigation of 3D Flow and Torque Transmission in Fluid Couplings Under Unsteady Working Condition

1995 ◽  
Author(s):  
T. Formanski ◽  
H. Huitenga ◽  
N. K. Mitra ◽  
M. Fiebig
Keyword(s):  
Turbulent Flows ◽  
Working Condition ◽  
Stokes Equations ◽  
Time History ◽  
Operating Conditions ◽  
Navier Stokes ◽  
3D Flow ◽  
Navier Stokes Equations ◽  
Torque Transmission ◽  
The Moment

Hydrodynamic couplings transmit torque by fluid circulation due to a speed differential between the impeller on the drive side and the runner on the driven side without mechanical contact. Detailed studies of the 3D flow in fluid couplings working at steady operating point were carried out in the last few years for laminar and turbulent flows. In this paper a study of fluid couplings working under unsteady operating conditions is reported for the first time. The unsteady Reynolds averaged Navier-Stokes equations together with the k-ϵ model have been solved by a finite-volume method. The calculations were done by using contour-fitted grids with non-staggered variable arrangement in a rotating frame of reference. The results give insight into the flow structure inside a coupling under unsteady working condition. An integration of the flow field for the considered operating points yields the transmitted torque. The time history of the change of the moment of momentum gives further insights into the behaviour of a fluid coupling under unsteady operating conditions.

Pressure-driven flow of a thin viscous sheet

1995 ◽  
Vol 292 ◽  
pp. 359-376 ◽  
Author(s):  
B. W. Van De Fliert ◽  
P. D. Howell ◽  
J. R. Ockenden
Keyword(s):  
Shell Theory ◽  
Stokes Equations ◽  
Thin Sheet ◽  
Theory Model ◽  
Navier Stokes ◽  
Coordinate Frame ◽  
Leading Order ◽  
Navier Stokes Equations ◽  
Pressure Driven Flow ◽  
Pressure Driven

Systematic asymptotic expansions are used to find the leading-order equations for the pressure-driven flow of a thin sheet of viscous fluid. Assuming the fluid geometry to be slender with non-negligible curvatures, the Navier–Stokes equations with appropriate free-surface conditions are simplified to give a ‘shell-theory’ model. The fluid geometry is not known in advance and a time-dependent coordinate frame has to be employed. The effects of surface tension, gravity and inertia can also be incorporated in the model.

Cosserat Modeling of Turbulent Plane-Couette and Pressure-Driven Channel Flows

2007 ◽  
Vol 129 (6) ◽  
pp. 806-810 ◽  
Author(s):  
Amin Moosaie ◽  
Gholamali Atefi
Keyword(s):  
Stokes Equations ◽  
Irreversible Thermodynamics ◽  
Channel Flows ◽  
Navier Stokes ◽  
Flat Plates ◽  
Navier Stokes Equations ◽  
Micropolar Fluids ◽  
Cosserat Model ◽  
Dissipative Boundary ◽  
Pressure Driven

The theory of micropolar fluids based on a Cosserat continuum model is utilized for analysis of two benchmarks, namely, plane-Couette and pressure-driven channel flows. In the obtained theoretical velocity distributions, some new terms have appeared in addition to linear and parabolic distributions of classical fluid mechanics based on the Navier-Stokes equations. Utilizing the principles of irreversible thermodynamics, a new dissipative boundary condition is developed for angular velocity at flat plates by taking the couple-stress vector into account. The obtained results for the velocity profiles have been compared to results of recent and classical experiments. This paper demonstrates that continuum mechanical theories of higher orders, for instance Cosserat model, are able to describe a complex phenomenon, such as hydrodynamic turbulence, more precisely.

Electrokinetic Flow and Measure Method in Microfluidic

2013 ◽  
Vol 275-277 ◽  
pp. 649-653 ◽  
Author(s):  
Lei Gong ◽  
Jian Kang Wu ◽  
Bo Chen
Keyword(s):  
Stokes Equations ◽  
Solid Wall ◽  
Streaming Potential ◽  
Navier Stokes ◽  
Electrokinetic Flow ◽  
Navier Stokes Equations ◽  
Electroviscous Effect ◽  
Poisson Boltzmann Equation ◽  
Electrokinetic Flows ◽  
Pressure Driven

An analytical solution for pressure-driven electrokinetic flows in a narrow capillary is presented based on the Poisson–Boltzmann equation for electrical double layer and the Navier–Stokes equations for incompressible viscous fluid. The analytical solutions indicate that pressure-driven flow of an electrolyte solution in microchannel with charged solid wall induces a streaming potential, which is proportional to the flowrate and induces an electroviscous effect on flow. A device for measuring the electrokinetic flow rate and streaming potential is proposed.

Analytical Solution of Mixed Electroosmotic and Pressure-Driven Flow in Rectangular Microchannels

2011 ◽  
Vol 483 ◽  
pp. 679-683 ◽  
Author(s):  
Da Yong Yang
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Microfluidic Chips ◽  
Layer Potential ◽  
Rectangular Microchannels ◽  
Navier Stokes Equations ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Pressure Driven Flow ◽  
Pressure Driven

Analytical solutions for potential distributions, velocity distributions of the mixed electroosmotic and pressure-driven flow in rectangular microchannels are discussed. To simulate the flow, a mathematical model, which includes the Poisson-Boltzmann equation and the modified Navier-Stokes equations, is presented and solved using the finite element method based on the Matlab software. The results show that the velocity distribution of mixed flow is compound of the “plug-like” and paraboloid at the steady state, and the pure electroosmotic flow is “plug-like”, which is similar with the electric double layer potential profile. The results provide the guidelines for the application of mix driven flow in microfluidic chips.

Analysis for Incompressible Flow in Annular Pressure Seals

1992 ◽  
Vol 114 (3) ◽  
pp. 431-438 ◽  
Author(s):  
F. Simon ◽  
J. Freˆne
Keyword(s):  
Incompressible Flow ◽  
Stokes Equations ◽  
Steady State Solution ◽  
Navier Stokes ◽  
Zeroth Order ◽  
Navier Stokes Equations ◽  
First Order ◽  
Rotordynamic Coefficients ◽  
The Moment ◽  
Flow Variables

An analysis is developed to calculate the static and dynamic characteristics of annular eccentric seals. Effects of inertia forces in the film, tapered geometry and rotor misalignment are taken into account. Derivation of the governing equations for incompressible flow is based on the Navier-Stokes equations, the continuity equation and a turbulence model using the nonlinear analysis developed by Elrod and Ng. The inlet boundary conditions define the initial swirl and the pressure drop due to the fluid acceleration. Perturbation of the flow variables yields a set of zeroth-order and first-order equations. Integration of the zeroth-order equations yields the steady-state solution which defines the seal leakage, the static load and the moment of misalignment. The eccentric and misaligned rotordynamic coefficients are obtained by integration of the first-order pressure equations. Comparisons are made between the stiffness, damping and inertia coefficients derived herein and both theoretical results based on other models and experimental data which were previously published.

On the asymptotic behaviour of viscous fluid flow at a great distance from a cylindrical body, with special reference to Filon’s paradox

1951 ◽  
Vol 208 (1095) ◽  
pp. 487-516 ◽  
Keyword(s):  
Viscous Fluid ◽  
Asymptotic Behaviour ◽  
Successive Approximation ◽  
Stokes Equations ◽  
Cylindrical Body ◽  
Flow Region ◽  
Great Distance ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
The Moment

The asymptotic behaviour of flow at a considerable distance from an arbitrary cylindrical obstacle immersed in an otherwise uniform flow of an incompressible viscous fluid is considered on the basis of the Navier-Stokes equations. Carrying out the Oseen type of successive approximation to the third stage, the expression for the stream function is exactly determined to the order of r -1 , where r is the distance from some fixed point in or near the cylinder. Then, by considering the conservation of linear and angular momenta of the fluid enclosed between the cylinder and a large contour, exact analytical formulae for the lift, drag and moment acting on the cylinder are obtained. Thus Filon’s well-known paradoxical result that the moment of a cylinder immersed in a viscous flow comes out to be logarithmically infinite with increasing extent of the flow region is given a complete explanation, and the usefulness of the Oseen type of successive approximation in dealing with the Navier-Stokes equations is confirmed.

Dynamics of Unstable Stokes Waves: A Numerical and Experimental Study

2014 ◽  
Author(s):  
Amin Chabchoub ◽  
Robinson Perić ◽  
Norbert P. Hoffmann
Keyword(s):  
Water Waves ◽  
Stokes Equations ◽  
Rogue Waves ◽  
Surface Flow ◽  
Navier Stokes ◽  
Ocean Engineering ◽  
Navier Stokes Equations ◽  
Stokes Waves ◽  
Finite Volume Approach ◽  
Short Term Prediction

Being an appropriate prototype to describe oceanic rogue waves, the Peregrine breather solution of the nonlinear Schrödinger equation is investigated numerically and experimentally to analyze the dynamics of modulationally unstable Stokes waves. The evolution of the water surface elevation is studied numerically by solving the Navier-Stokes equations using a finite-volume approach and a volume of fluid method. The comparison of the numerical results with wave tank experiments show a very good agreement. The results confirm the ability of the chosen method to model the modulation instability of Stokes waves, in particular, breather dynamics in water waves with high accuracy even up to the onset of breaking. We also investigate the sub-surface flow fields, which may be of significance for the short-term prediction of extreme wave focusing in narrow-banded sea state conditions and therefore, for ocean engineering applications.

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