Numerical simulations of interfacial instabilities on a rotating miscible magnetic droplet with effects of Korteweg stresses

2005 ◽  
Vol 17 (4) ◽  
pp. 042101 ◽  
Author(s):  
Ching-Yao Chen ◽  
H.-J. Wu
Keyword(s):  
Numerical Simulations ◽  
Interfacial Instabilities ◽  
Korteweg Stresses ◽  
Magnetic Droplet

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.

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

scholarly journals On the generation of nonlinear travelling waves in confined geometries using electric fields

2014 ◽  
Vol 372 (2020) ◽  
pp. 20140066 ◽  
Author(s):  
R Cimpeanu ◽  
D. T Papageorgiou
Keyword(s):  
Numerical Simulations ◽  
Electric Fields ◽  
Travelling Waves ◽  
Travelling Wave ◽  
Direct Numerical Simulations ◽  
Small Scale ◽  
Interfacial Instabilities ◽  
Lower Electrode ◽  
Nonlinear Deformations ◽  
Moving Parts

We investigate electrostatically induced interfacial instabilities and subsequent generation of nonlinear coherent structures in immiscible, viscous, dielectric multi-layer stratified flows confined in small-scale channels. Vertical electric fields are imposed across the channel to produce interfacial instabilities that would normally be absent in such flows. In situations when the imposed vertical fields are constant, interfacial instabilities emerge due to the presence of electrostatic forces, and we follow the nonlinear dynamics via direct numerical simulations. We also propose and illustrate a novel pumping mechanism in microfluidic devices that does not use moving parts. This is achieved by first inducing interfacial instabilities using constant background electric fields to obtain fully nonlinear deformations. The second step involves the manipulation of the imposed voltage on the lower electrode (channel wall) to produce a spatio-temporally varying voltage there, in the form of a travelling wave with pre-determined properties. Such travelling wave dielectrophoresis methods are shown to generate intricate fluid–surface–structure interactions that can be of practical value since they produce net mass flux along the channel and thus are candidates for microfluidic pumps without moving parts. We show via extensive direct numerical simulations that this pumping phenomenon is a result of an externally induced nonlinear travelling wave that forms at the fluid–fluid interface and study the characteristics of the generated velocity field inside the channel.

Saturation mechanism and generated viscosity in gravito-turbulent accretion disks

2020 ◽  
Vol 640 ◽  
pp. A53
Author(s):  
L. Löhnert ◽  
S. Krätschmer ◽  
A. G. Peeters
Keyword(s):  
Growth Rate ◽  
Numerical Simulations ◽  
Accretion Disks ◽  
Gravitational Instability ◽  
Turbulent Viscosity ◽  
Radial Distance ◽  
Maximum Growth ◽  
Wave Number ◽  
Radiative Cooling ◽  
Mixing Length

Here, we address the turbulent dynamics of the gravitational instability in accretion disks, retaining both radiative cooling and irradiation. Due to radiative cooling, the disk is unstable for all values of the Toomre parameter, and an accurate estimate of the maximum growth rate is derived analytically. A detailed study of the turbulent spectra shows a rapid decay with an azimuthal wave number stronger than ky−3, whereas the spectrum is more broad in the radial direction and shows a scaling in the range kx−3 to kx−2. The radial component of the radial velocity profile consists of a superposition of shocks of different heights, and is similar to that found in Burgers’ turbulence. Assuming saturation occurs through nonlinear wave steepening leading to shock formation, we developed a mixing-length model in which the typical length scale is related to the average radial distance between shocks. Furthermore, since the numerical simulations show that linear drive is necessary in order to sustain turbulence, we used the growth rate of the most unstable mode to estimate the typical timescale. The mixing-length model that was obtained agrees well with numerical simulations. The model gives an analytic expression for the turbulent viscosity as a function of the Toomre parameter and cooling time. It predicts that relevant values of α = 10−3 can be obtained in disks that have a Toomre parameter as high as Q ≈ 10.

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