Nonlinear dynamics of a two-dimensional viscous drop under shear flow

2006 ◽  
Vol 18 (7) ◽  
pp. 072106 ◽  
Author(s):  
J. Zhang ◽  
M. J. Miksis ◽  
S. G. Bankoff
Keyword(s):  
Nonlinear Dynamics ◽  
Shear Flow ◽  
Two Dimensional ◽  
Viscous Drop

Nonlinear dynamics of a two dimensional airfoil with freeplay in an inviscid compressible flow

2000 ◽  
Vol 4 (2) ◽  
pp. 125-133 ◽  
Author(s):  
Zoran Dimitrijević ◽  
Guy Daniel Mortchéléwicz ◽  
Fabrice Poirion
Keyword(s):  
Nonlinear Dynamics ◽  
Compressible Flow ◽  
Two Dimensional ◽  
Inviscid Compressible Flow

Numerical study of electric field effects on the deformation of two-dimensional liquid drops in simple shear flow at arbitrary Reynolds number

2009 ◽  
Vol 626 ◽  
pp. 367-393 ◽  
Author(s):  
STEFAN MÄHLMANN ◽  
DEMETRIOS T. PAPAGEORGIOU
Keyword(s):  
Steady State ◽  
Shear Flow ◽  
Electric Field ◽  
Electric Fields ◽  
Simple Shear ◽  
Simple Shear Flow ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Two Dimensional ◽  
Liquid Drops

The effect of an electric field on a periodic array of two-dimensional liquid drops suspended in simple shear flow is studied numerically. The shear is produced by moving the parallel walls of the channel containing the fluids at equal speeds but in opposite directions and an electric field is generated by imposing a constant voltage difference across the channel walls. The level set method is adapted to electrohydrodynamics problems that include a background flow in order to compute the effects of permittivity and conductivity differences between the two phases on the dynamics and drop configurations. The electric field introduces additional interfacial stresses at the drop interface and we perform extensive computations to assess the combined effects of electric fields, surface tension and inertia. Our computations for perfect dielectric systems indicate that the electric field increases the drop deformation to generate elongated drops at steady state, and at the same time alters the drop orientation by increasing alignment with the vertical, which is the direction of the underlying electric field. These phenomena are observed for a range of values of Reynolds and capillary numbers. Computations using the leaky dielectric model also indicate that for certain combinations of electric properties the drop can undergo enhanced alignment with the vertical or the horizontal, as compared to perfect dielectric systems. For cases of enhanced elongation and alignment with the vertical, the flow positions the droplets closer to the channel walls where they cause larger wall shear stresses. We also establish that a sufficiently strong electric field can be used to destabilize the flow in the sense that steady-state droplets that can exist in its absence for a set of physical parameters, become increasingly and indefinitely elongated until additional mechanisms can lead to rupture. It is suggested that electric fields can be used to enhance such phenomena.

scholarly journals Crystal rotations and alignment in spatially varying magma flows: Two-dimensional examples of common subvolcanic flow geometries

2021 ◽  
Author(s):  
Rémi Vachon ◽  
Mohsen Bazargan ◽  
Christoph F Hieronymus ◽  
Erika Ronchin ◽  
Bjarne Almqvist
Keyword(s):  
Shear Flow ◽  
Magma Chamber ◽  
Simple Shear ◽  
Thermal Convection ◽  
Pure Shear ◽  
Simple Shear Flow ◽  
Two Dimensional ◽  
Crystal Orientations ◽  
Volcanic Plumbing System ◽  
Spatially Varying

Summary Elongate inclusions immersed in a viscous fluid generally rotate at a rate that is different from the local angular velocity of the flow. Often, a net alignment of the inclusions develops, and the resulting shape preferred orientation (SPO) of the particle ensemble can then be used as a strain marker that allows reconstruction of the fluid’s velocity field. Much of the previous work on the dynamics of flow-induced particle rotations has focused on spatially homogeneous flows with large-scale tectonic deformations as the main application. Recently, the theory has been extended to spatially varying flows, such as magma with embedded crystals moving through a volcanic plumbing system. Additionally, an evolution equation has been introduced for the probability density function (PDF) of crystal orientations. Here, we apply this new theory to a number of simple, two-dimensional flow geometries commonly encountered in magmatic intrusions, such as flow from a dyke into a reservoir or from a reservoir into a dyke, flow inside an inflating or deflating reservoir, flow in a dyke with a sharp bend, and thermal convection in a magma chamber. The main purpose is to provide a guide for interpreting field observations and for setting up more complex flow models with embedded crystals. As a general rule, we find that a larger aspect ratio of the embedded crystals causes a more coherent alignment of the crystals, while it has only a minor effect on the geometry of the alignment pattern. Due to various perturbations in the crystal rotation equations that are expected in natural systems, we show that the time-periodic behavior found in idealized systems is probably short-lived in nature, and the crystal alignment is well described by the time-averaged solution. We also confirm some earlier findings. For example, near channel walls, fluid flow often follows the bounding surface and the resulting simple shear flow causes preferred crystal orientations that are approximately parallel to the boundary. Where pure shear deformation dominates, there is a tendency for crystals to orient themselves in the direction of the greatest tensile strain rate. Where flow impinges on a boundary, for example in an inflating magma chamber or as part of a thermal convection pattern, the stretching component of pure shear aligns with the boundary, and the crystals orient themselves in that direction. In the field, this local pattern may be difficult to distinguish from a boundary-parallel simple shear flow. Pure shear also dominates along the walls of a deflating magma chamber and in places where the flow turns away from the reservoir walls, but in these locations, the preferred crystal orientation is perpendicular to the wall. Overall, we find that our calculated patterns of crystal orientations agree well with results from analogue experiments where similar geometries are available.

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