Search results for "Hele-Shaw flow"
showing 9 items of 9 documents
Stability of melt flow due to a traveling magnetic field in a closed ampoule
2004
The linear three-dimensional instability of the flow due to a low frequency traveling magnetic field in a regular cylinder is studied numerically for height-to-diameter ratios in the range [0.5:2.5]. The first instability has the form of an azimuthal wave with wave numbers between 1 and 6 depending on the aspect ratio. It is shown that the flow is stable if the Reynolds number is below 290. Even stronger stationary flows may be obtained in a flattened cylinder.
Magnetic forces in 2D foams
2005
The asymptotic expression for the ponderomotive force in the magnetic liquid film is derived and a role of the disjoining pressure in 2D magnetic foam formation is considered. New equation for the force balance at the vertex of 2D magnetic foam is proposed and modified Plateau rule for the films is obtained. The theoretical relation for the angle between films fits the experimental data for small magnetic Bond numbers very well.
Magnetic field driven micro-convection in the Hele-Shaw cell
2013
AbstractMicro-convection caused by ponderomotive forces of the self-magnetic field of a magnetic fluid in the Hele-Shaw cell under the action of a vertical homogeneous magnetic field is studied both experimentally and numerically. It is shown that a non-potential magnetic force at magnetic Rayleigh numbers greater than the critical value causes fingering at the interface between the miscible magnetic and non-magnetic fluids. The threshold value of the magnetic Rayleigh number depends on the smearing of the interface between fluids. Fingering with its subsequent decay due to diffusion of particles significantly increases the mixing at the interface. Velocity and vorticity fields at fingering…
Magnetic field driven micro-convection in the Hele-Shaw cell: the Brinkman model and its comparison with experiment
2015
International audience; The micro-convection caused by the ponderomotive forces of the self-magnetic field in a magnetic fluid is studied here both numerically and experimentally. The theoretical approach based on the general Brinkman model substantially improves the description with respect to the previously proposed Darcy model. The predictions of both models are here compared to finely controlled experiments. The Brinkman model, in contrast to the Darcy model, allows us to describe the formation of mushrooms on the plumes of the micro-convective flow and the width of the fingers. In the Brinkman approach, excellent quantitative agreement is also obtained for the finger velocity dynamics …
2D shape relaxation dynamics in amphiphile monolayers
2007
The shape relaxation dynamics of the droplets in amphiphile monolayers is studied in Darcy approximation. It is shown by numerical experiments that relaxation from the highly extended dumbbell configurations can be described by simple physical model according to which the dissipation is concentrated on circular tips. By numerical simulation it is illustrated that longrange dipolar interactions lead to the stabilization of the shape relaxation process with respect to the formation of a narrow neck causing the rupture of the droplet when dipolar forces are absent. Effect of the dipolar forces on the shape-relaxation process can be accounted by the slope of the relaxation curve at small deviat…
Flow perturbations: a tool to study and characterize heterogeneous deformation
2005
The classification of the myriad of small-scale structures that are used in tectonic analysis is presently based on their geometry, which makes it difficult to discover transitions and groups amongst them. An alternative would be to classify structures according to the flow type by which they form, but this is difficult. Although most structures form by heterogeneous flow, modelling studies are often focussed on bulk homogeneous flow, since the mathematical treatment of heterogeneous flow is cumbersome. Also, heterogeneous deformation patterns seem to occur in as many types as there are small-scale structures. This paper introduces the use of the geometry of flow perturbations to improve ou…
Viscous fingering in magnetic fluids: numerical simulation of radial Hele–Shaw flow
1999
Abstract In this paper, the viscous fingering phenomena of the magnetic liquids in the case when the magnetic field is applied normally to the Hele–Shaw cell is investigated by the numerical simulation technique. It is shown that the magnetic field causes additional destabilization of the free interface arising at the air injection in the magnetic liquid. Here the peculiarities of the interface dynamics – inward motion of the tips of the fjords, the gyration radius dependence on the perimeter found by the numerical simulations are in good accordance with the experiments.
Labyrinthine instability of miscible magnetic fluids
2002
Abstract We consider an inhomogeneous magnetic fluid (MF), modeling a miscible MF pair, in a Hele–Shaw cell under a normal field. A linear stability analysis for the sharp straight interface (analytically) and for the diffused one (numerically) is performed. For the former case, the neutral curves and the stability diagram are found along with the critical wavelength and parameter values. Oscillatory or monotonous instabilities are shown to occur. For the diffused interface, we recognize the importance of 2D flow viscous effects along with the conventional wall friction and observe that in strong fields the dominant wavelength scales as the cell gap.
Shapes of a gas bubble rising in the vertical Hele–Shaw cell with magnetic liquid
2005
Abstract Dynamics of the bubble rising in the vertical Hele–Shaw cell with magnetic liquid in the normal magnetic field is studied. Linear stability analysis of the circular shape is carried out. Development of the instability with respect to the lowest symmetric mode is simulated by the boundary integral equation technique.