Electrohydrodynamic rotation of drops at large electric Reynolds numbers

2016 ◽  
Vol 788 ◽  
Author(s):  
Ehud Yariv ◽  
Itzchak Frankel
Keyword(s):  
Electric Fields ◽  
Numerical Solutions ◽  
Fluid Velocity ◽  
Reynolds Numbers ◽  
Mirror Image ◽  
Liquid Drops ◽  
Weakly Conducting ◽  
Strong Electric Fields ◽  
Quincke Rotation ◽  
Asymmetric Solution

When subject to sufficiently strong electric fields, particles and drops suspended in a weakly conducting liquid exhibit spontaneous rotary motion. This so-called Quincke rotation is a fascinating example of nonlinear symmetry-breaking phenomena. To illuminate the rotation of liquid drops we here analyse the asymptotic limit of large electric Reynolds numbers, $\mathit{Re}\gg 1$, within the framework of a two-dimensional Taylor–Melcher electrohydrodynamic model. A non-trivial dominant balance in this singular limit results in both the fluid velocity and surface-charge density scaling as $\mathit{Re}^{-1/2}$. The flow is governed by a self-contained nonlinear boundary-value problem that does not admit a continuous fore–aft symmetric solution, thus necessitating drop rotation. Furthermore, thermodynamic arguments reveal that a fore–aft asymmetric solution exists only when charge relaxation within the suspending liquid is faster than that in the drop. The flow problem possesses both mirror-image (with respect to the direction of the external field) and flow-reversal symmetries; it is transformed into a universal one, independent of the ratios of electric conductivities and dielectric permittivities in the respective drop phase and suspending liquid phase. The rescaled angular velocity is found to depend weakly upon the viscosity ratio. The corresponding numerical solutions of the exact equations indeed collapse at large $\mathit{Re}$ upon the asymptotically calculated universal solution.

Electrohydrodynamics of Drops and Vesicles

2019 ◽  
Vol 51 (1) ◽  
pp. 305-330 ◽  
Author(s):  
Petia M. Vlahovska
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Lipid Membranes ◽  
Uniform Electric Field ◽  
Dielectric Fluids ◽  
Weakly Conducting ◽  
Strong Electric Fields ◽  
Leaky Dielectric ◽  
Quincke Rotation ◽  
Experimental And Theoretical Studies

The 1969 review by J.R. Melcher and G.I. Taylor defined the field of electrohydrodynamics. Fifty years on, the interaction of weakly conducting (leaky dielectric) fluids with electric fields continues to yield intriguing phenomena. The prototypical system of a drop in a uniform electric field has revealed remarkable dynamics in strong electric fields such as symmetry-breaking instabilities (e.g., Quincke rotation) and streaming from the drop equator. This review summarizes recent experimental and theoretical studies in the area of fluid particles (drop and vesicles) in electric fields, with a focus on the transient dynamics and extreme deformations. A theoretical framework to treat the time evolution of nearly spherical shapes is provided. The model has been successful in describing the dynamics of vesicles (closed lipid membranes) in an electric field, highlighting the broader range of applicability of the leaky dielectric approach.

scholarly journals Dynamics of positrons during relativistic electron runaway

2018 ◽  
Vol 84 (5) ◽  
Author(s):  
O. Embréus ◽  
L. Hesslow ◽  
M. Hoppe ◽  
G. Papp ◽  
K. Richards ◽  
...  
Keyword(s):  
Pair Production ◽  
Electric Fields ◽  
Numerical Solutions ◽  
Production Cross ◽  
Analytical Formula ◽  
Rate Equations ◽  
Annihilation Radiation ◽  
Operational Parameters ◽  
Pair Production Cross Section ◽  
Strong Electric Fields

Sufficiently strong electric fields in plasmas can accelerate charged particles to relativistic energies. In this paper we describe the dynamics of positrons accelerated in such electric fields, and calculate the fraction of created positrons that become runaway accelerated, along with the amount of radiation that they emit. We derive an analytical formula that shows the relative importance of the different positron production processes, and show that, above a certain threshold electric field, the pair production by photons is lower than that by collisions. We furthermore present analytical and numerical solutions to the positron kinetic equation; these are applied to calculate the fraction of positrons that become accelerated or thermalized, which enters into rate equations that describe the evolution of the density of the slow and fast positron populations. Finally, to indicate operational parameters required for positron detection during runaway in tokamak discharges, we give expressions for the parameter dependencies of detected annihilation radiation compared to bremsstrahlung detected at an angle perpendicular to the direction of runaway acceleration. Using the full leading-order pair-production cross-section, we demonstrate that previous related work has overestimated the collisional pair production by at least a factor of four.

Lubrication theory for electro-osmotic flow in a non-uniform electrolyte

2007 ◽  
Vol 576 ◽  
pp. 139-172 ◽  
Author(s):  
T. L. SOUNART ◽  
J. C. BAYGENTS
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Numerical Solutions ◽  
Fluid Velocity ◽  
Lubrication Theory ◽  
Debye Screening Length ◽  
Sample Stacking ◽  
Osmotic Flow ◽  
Analytic Expressions ◽  
Electro Osmotic Flow

A lubrication theory has been developed for the electro-osmotic flow of non-uniform buffers in narrow rectilinear channels. The analysis applies to systems in which the transverse dimensions of the channel are large compared with the Debye screening length of the electrolyte. In contrast with related theories of electrokinetic lubrication, here the streamwise variations of the velocity field stem from, and are nonlinearly coupled to, spatiotemporal variations in the electrolyte composition. Spatially non-uniform buffers are commonly employed in electrophoretic separation and transport schemes, including iso-electric focusing (IEF), isotachophoresis (ITP), field-amplified sample stacking (FASS), and high-ionic-strength electro-osmotic pumping. The fluid dynamics of these systems is controlled by a complex nonlinear coupling to the ion transport, driven by an applied electric field. Electrical conductivity gradients, attendent to the buffer non-uniformities, result in a variable electro-osmotic slip velocity and, in electric fields approaching 1 kV cm−1, Maxwell stresses drive the electrohydrodynamic circulation. Explicit semi-analytic expressions are derived for the fluid velocity, stream function, and electric field. The resulting approximations are found to be in good agreement with full numerical solutions for a prototype buffer, over a range of conditions typical of microfluidic systems. The approximations greatly simplify the computational analysis, reduce computation times by a factor 4–5, and, for the first time, provide general insight on the dominant fluid physics of two-dimensional electrically driven transport.

Electrohydrodynamic stability: Taylor–Melcher theory for a liquid bridge suspended in a dielectric gas

2002 ◽  
Vol 452 ◽  
pp. 163-187 ◽  
Author(s):  
C. L. BURCHAM ◽  
D. A. SAVILLE
Keyword(s):  
Surface Tension ◽  
Dielectric Constant ◽  
Electric Fields ◽  
Liquid Bridge ◽  
Numerical Solutions ◽  
Specific Conductivity ◽  
Axisymmetric Deformation ◽  
Aspect Ratios ◽  
The Stability ◽  
Theory And Experiment

A liquid bridge is a column of liquid, pinned at each end. Here we analyse the stability of a bridge pinned between planar electrodes held at different potentials and surrounded by a non-conducting, dielectric gas. In the absence of electric fields, surface tension destabilizes bridges with aspect ratios (length/diameter) greater than π. Here we describe how electrical forces counteract surface tension, using a linearized model. When the liquid is treated as an Ohmic conductor, the specific conductivity level is irrelevant and only the dielectric properties of the bridge and the surrounding gas are involved. Fourier series and a biharmonic, biorthogonal set of Papkovich–Fadle functions are used to formulate an eigenvalue problem. Numerical solutions disclose that the most unstable axisymmetric deformation is antisymmetric with respect to the bridge’s midplane. It is shown that whilst a bridge whose length exceeds its circumference may be unstable, a sufficiently strong axial field provides stability if the dielectric constant of the bridge exceeds that of the surrounding fluid. Conversely, a field destabilizes a bridge whose dielectric constant is lower than that of its surroundings, even when its aspect ratio is less than π. Bridge behaviour is sensitive to the presence of conduction along the surface and much higher fields are required for stability when surface transport is present. The theoretical results are compared with experimental work (Burcham & Saville 2000) that demonstrated how a field stabilizes an otherwise unstable configuration. According to the experiments, the bridge undergoes two asymmetric transitions (cylinder-to-amphora and pinch-off) as the field is reduced. Agreement between theory and experiment for the field strength at the pinch-off transition is excellent, but less so for the change from cylinder to amphora. Using surface conductivity as an adjustable parameter brings theory and experiment into agreement.

Calculation of the probability of optical transitions in strong electric fields

2000 ◽  
Vol 91 (5) ◽  
pp. 945-951 ◽  
Author(s):  
S. V. Bulyarskii ◽  
N. S. Grushko ◽  
A. V. Zhukov
Keyword(s):  
Electric Fields ◽  
Optical Transitions ◽  
Strong Electric Fields

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.

On steady compressible flows with compact vorticity; the compressible Hill's spherical vortex

1998 ◽  
Vol 374 ◽  
pp. 285-303 ◽  
Author(s):  
D. W. MOORE ◽  
D. I. PULLIN
Keyword(s):  
Finite Difference ◽  
Compressible Flows ◽  
Numerical Solutions ◽  
Flow Direction ◽  
Fluid Velocity ◽  
Major Axis ◽  
Sonic Point ◽  
Euler Flow ◽  
Compressible Euler ◽  
Spherical Vortex

We consider steady compressible Euler flow corresponding to the compressible analogue of the well-known incompressible Hill's spherical vortex (HSV). We first derive appropriate compressible Euler equations for steady homentropic flow and show how these may be used to define a continuation of the HSV to finite Mach number M∞=U∞/C∞, where U∞, C∞ are the fluid velocity and speed of sound at infinity respectively. This is referred to as the compressible Hill's spherical vortex (CHSV). It corresponds to axisymmetric compressible Euler flow in which, within a vortical bubble, the azimuthal vorticity divided by the product of the density and the distance to the axis remains constant along streamlines, with irrotational flow outside the bubble. The equations are first solved numerically using a fourth-order finite-difference method, and then using a Rayleigh–Janzen expansion in powers of M2∞ to order M4∞. When M∞>0, the vortical bubble is no longer spherical and its detailed shape must be determined by matching conditions consisting of continuity of the fluid velocity at the bubble boundary. For subsonic compressible flow the bubble boundary takes an approximately prolate spheroidal shape with major axis aligned along the flow direction. There is good agreement between the perturbation solution and Richardson extrapolation of the finite difference solutions for the bubble boundary shape up to M∞ equal to 0.5. The numerical solutions indicate that the flow first becomes locally sonic near or at the bubble centre when M∞≈0.598 and a singularity appears to form at the sonic point. We were unable to find shock-free steady CHSVs containing regions of locally supersonic flow and their existence for the present continuation of the HSV remains an open question.

A Numerical and Experimental Investigation of Turbulent Heat Transport Downstream From an Abrupt Pipe Expansion

1983 ◽  
Vol 105 (4) ◽  
pp. 862-869 ◽  
Author(s):  
R. S. Amano ◽  
M. K. Jensen ◽  
P. Goel
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Separated Flow ◽  
Flow Region ◽  
Reynolds Numbers ◽  
Turbulent Heat ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Pipe Expansion

An experimental and numerical study is reported on heat transfer in the separated flow region created by an abrupt circular pipe expansion. Heat transfer coefficients were measured along the pipe wall downstream from an expansion for three different expansion ratios of d/D = 0.195, 0.391, and 0.586 for Reynolds numbers ranging from 104 to 1.5 × 105. The results are compared with the numerical solutions obtained with the k ∼ ε turbulence model. In this computation a new finite difference scheme is developed which shows several advantages over the ordinary hybrid scheme. The study also covers the derivation of a new wall function model. Generally good agreement between the measured and the computed results is shown.

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