Numerical simulations of fingering instabilities in miscible magnetic fluids in a Hele-Shaw cell and the effects of Korteweg stresses

2003 ◽  
Vol 15 (4) ◽  
pp. 1086-1089 ◽  
Author(s):  
Ching-Yao Chen
Keyword(s):  
Numerical Simulations ◽  
Magnetic Fluids ◽  
Korteweg Stresses ◽  
Hele Shaw Cell

Numerical simulations of a viscous-fingering instability in a fluid with a temperature-dependent viscosity

2006 ◽  
Vol 84 (4) ◽  
pp. 273-287 ◽  
Author(s):  
Kristi E Holloway ◽  
John R Bruyn
Keyword(s):  
Growth Rate ◽  
Numerical Simulations ◽  
Viscosity Ratio ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Cell Width ◽  
Inlet Velocity ◽  
Fingering Instability ◽  
Dependent Viscosity ◽  
Hele Shaw Cell

We have performed numerical simulations of the flow of hot glycerine as it displaces colder, more viscous glycerine in a radial Hele–Shaw cell. We find that fingering occurs for sufficiently high inlet velocities and viscosity ratios. The wavelength of the instability is independent of inlet velocity and viscosity ratio, but depends weakly on cell width. The growth rate of the fingers is found to increase with inlet velocity and decrease with the cell width. We compare our results with those from experiments.PACS No.: 47.54.–r

Numerical simulations of sink flow in the Hele-Shaw cell with small surface tension

1997 ◽  
Vol 8 (6) ◽  
pp. 533-550 ◽  
Author(s):  
E. D. KELLY ◽  
E. J. HINCH
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Viscous Fluid ◽  
Numerical Simulations ◽  
Boundary Integral Equation ◽  
Numerical Algorithm ◽  
Boundary Integral ◽  
Inviscid Fluid ◽  
Small Surface ◽  
Hele Shaw Cell

The motion of an initially circular drop of viscous fluid surrounded by inviscid fluid in a Hele-Shaw cell withdrawn from an eccentric point sink is considered. Using a numerical algorithm based on a boundary integral equation, the solution for small, finite surface tension is observed. It is found that the zero-surface-tension formation of a cusp is avoided, and instead a narrow finger of inviscid fluid forms, which then rapidly propagates towards the sink. The scaling of the finger in the sink vicinity is determined.

Miscible displacements in capillary tubes. Part 2. Numerical simulations

1996 ◽  
Vol 326 ◽  
pp. 57-90 ◽  
Author(s):  
Ching-Yao Chen ◽  
Eckart Meiburg
Keyword(s):  
Diffusion Coefficient ◽  
Numerical Simulations ◽  
Capillary Tube ◽  
Plane Channel ◽  
Taylor Dispersion ◽  
Transitional Region ◽  
Global Features ◽  
Miscible Displacements ◽  
Finger Tip ◽  
Korteweg Stresses

Numerical simulations are presented which, in conjunction with the accompanying experimental investigation by Petitjeans & Maxworthy (1996), are intended to elucidate the miscible flow that is generated if a fluid of given viscosity and density displaces a second fluid of different such properties in a capillary tube or plane channel. The global features of the flow, such as the fraction of the displaced fluid left behind on the tube walls, are largely controlled by dimensionless quantities in the form of a Péclet number Pe, an Atwood number At, and a gravity parameter. However, further dimensionless parameters that arise from the dependence on the concentration of various physical properties, such as viscosity and the diffusion coefficient, result in significant effects as well.The simulations identify two distinct Pe regimes, separated by a transitional region. For large values of Pe, typically above O(10), a quasi-steady finger forms, which persists for a time of O(Pe) before it starts to decay, and Poiseuille flow and Taylor dispersion are approached asymptotically. Depending on the strength of the gravitational forces, we observe a variety of topologically different streamline patterns, among them some that leak fluid from the finger tip and others with toroidal recirculation regions inside the finger. Simulations that account for the experimentally observed dependence of the diffusion coefficient on the concentration show the evolution of fingers that combine steep external concentration layers with smooth concentration fields on the inside. In the small-Pe regime, the flow decays from the start and asymptotically reaches Taylor dispersion after a time of O(Pe).An attempt was made to evaluate the importance of the Korteweg stresses and the consequences of assuming a divergence-free velocity field. Scaling arguments indicate that these effects should be strongest when steep concentration fronts exist, i.e. at large values of Pe and At. However, when compared to the viscous stresses, Korteweg stresses may be relatively more important at lower values of these parameters, and we cannot exclude the possibility that minor discrepancies observed between simulations and experiments in these parameter regimes are partially due to these extra stresses.

A novel approach for estimating the magnetization curve of magnetic fluids

2017 ◽  
Vol 34 (6) ◽  
pp. 2063-2073 ◽  
Author(s):  
Marcin Szczech
Keyword(s):  
Magnetic Field ◽  
Numerical Simulation ◽  
Numerical Simulations ◽  
Magnetic Fluid ◽  
Magnetization Curve ◽  
Magnetic Fluids ◽  
Content Type ◽  
Carrier Fluid ◽  
Novel Approach ◽  
The Difference

Purpose Magnetization is one of the most important parameters of magnetic fluids. The shape of the magnetization curve often determines the application of a fluid in a device. On the basis of the magnetization curve, it is also possible to estimate, for example, the distribution and size of the particles in a magnetic fluid carrier fluid. The aim of this paper is to present a new approach for estimating the magnetization curve. Design/methodology/approach The proposed method is an iterative method based on the measurement of magnetic induction on a test stand. To determine the magnetization curve, a numerical simulation of the magnetic field distributions for the preliminary magnetization curve should also be performed. Numerical simulations for modified forms of the magnetization curve are performed until the difference between the results obtained by the measurement and numerical simulation are the smallest. Findings This paper presents the results of magnetization curve research for ferrofluids and magnetorheological fluids. Originality/value The discussed method shows the possibilities of using numerical simulations of magnetic field distribution to determine the magnetic properties of magnetic fluids. This method may be an alternative for estimating the magnetization curve of the magnetic fluid compared to other methods.

Numerical simulations of convection induced by Korteweg stresses in miscible polymermonomer systems

2005 ◽  
Vol 17 (1) ◽  
pp. 8-12 ◽  
Author(s):  
Nick Bessonov ◽  
Vitaly A. Volpert ◽  
John A. Pojman ◽  
Brian D. Zoltowski
Keyword(s):  
Numerical Simulations ◽  
Korteweg Stresses

Labyrinthine instabilities of miscible magnetic fluids in a rotating Hele-Shaw cell

2017 ◽  
Vol 29 (2) ◽  
pp. 024109 ◽  
Author(s):  
Mei-Yu Chen ◽  
Li-Que Chen ◽  
Huanhao Li ◽  
Chih-Yung Wen
Keyword(s):  
Magnetic Fluids ◽  
Hele Shaw Cell
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