Dynamics of a viscous thread surrounded by another viscous fluid in a cylindrical tube under the action of a radial electric field: breakup and touchdown singularities

2011 ◽  
Vol 683 ◽  
pp. 27-56 ◽  
Author(s):  
Q. Wang ◽  
D. T. Papageorgiou
Keyword(s):  
Viscous Fluid ◽  
Electric Field ◽  
Electric Fields ◽  
Viscosity Ratio ◽  
Cylindrical Tube ◽  
Radial Electric Field ◽  
Boundary Element Methods ◽  
Annular Region ◽  
Two Fluids ◽  
Jet Breakup

AbstractThe nonlinear dynamics of a viscous filament surrounded by a second viscous fluid arranged in a core-annular configuration when a radial electric field acts in the annular region, are studied analytically and computationally using boundary element methods. The flow is characterized by the viscosity ratio, an electric Weber number measuring the strength of the electric field, a geometrical parameter measuring the thickness of the undisturbed annular region, as well as a computational parameter that fixes the wavenumber of the undulations. Axisymmetric solutions are computed by direct numerical simulations in the Stokes limit for general values of the parameters when the two fluids have equal viscosities, and an asymptotic theory is carried out to produce a novel evolution equation for thin film dynamics valid when the undisturbed annular thickness is small and the viscosity ratio is of order one. It is established (in agreement with previous computations in the absence of electric fields) that a sufficiently thick annulus enables thread breakup while a sufficiently thin one (approximately one fifth of the undisturbed thread radius for the case of equal viscosities, for instance) suppresses pinching and drives the interface to approach the tube wall asymptotically without actually touching it. The present simulations show that the electric field affects the dynamics drastically in several ways. First, it promotes interfacial wall touchdown in finite time and a comparison between direct simulations and the asymptotic solutions are in fair agreement. Second, the electric field acts to suppress pinching in the sense that solutions that lead to jet breakup due to a thick enough viscous annulus are driven to wall touchdown. When pinching takes place we find that the ultimate pinching solutions are self-similar and recover the non-electrified ones to leading order for the range of parameters studied.

scholarly journals Nonlinear electroelasticity: material properties, continuum theory and applications

2017 ◽  
Vol 473 (2204) ◽  
pp. 20170311 ◽  
Author(s):  
Luis Dorfmann ◽  
Ray W. Ogden
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Material Characterization ◽  
Cylindrical Tube ◽  
Continuum Theory ◽  
Radial Electric Field ◽  
Short Account ◽  
Elastomeric Materials ◽  
History Of ◽  
Circular Cylindrical Tube

In the last few years, it has been recognized that the large deformation capacity of elastomeric materials that are sensitive to electric fields can be harnessed for use in transducer devices such as actuators and sensors. This has led to the reassessment of the mathematical theory that is needed for the description of the electromechanical (in particular, electroelastic) interactions for purposes of material characterization and prediction. After a review of the key experiments concerned with determining the nature of the electromechanical interactions and a discussion of the range of applications to devices, we provide a short account of the history of developments in the nonlinear theory. This is followed by a succinct modern treatment of electroelastic theory, including the governing equations and constitutive laws needed for both material characterization and the analysis of general electroelastic coupling problems. For illustration, the theory is then applied to two simple representative boundary-value problems that are relevant to the geometries of activation devices; in particular, (a) a rectangular plate and (b) a circular cylindrical tube, in each case with compliant electrodes on the major surfaces and a potential difference between them. In (a), an electric field is generated normal to the major surfaces and in (b), a radial electric field is present. This is followed by a short section in which other problems addressed on the basis of the general theory are described briefly.

scholarly journals Waves and vibrations in a finitely deformed electroelastic circular cylindrical tube

2020 ◽  
Vol 476 (2233) ◽  
pp. 20190701 ◽  
Author(s):  
Luis Dorfmann ◽  
Ray W. Ogden
Keyword(s):  
Electric Field ◽  
Wave Speed ◽  
Cylindrical Tube ◽  
Radial Electric Field ◽  
Potential Difference ◽  
Axisymmetric Vibration ◽  
End Conditions ◽  
Circular Cylindrical Tube ◽  
Special Case ◽  
Tube Geometry

In two recent papers, conditions for which axisymmetric incremental bifurcation could arise for a circular cylindrical tube subject to axial extension and radial inflation in the presence of an axial load, internal pressure and a radial electric field were examined, the latter being effected by a potential difference between compliant electrodes on the inner and outer radial surfaces of the tube. The present paper takes this work further by considering the incremental deformations to be time-dependent. In particular, both the axisymmetric vibration of a tube of finite length with appropriate end conditions and the propagation of axisymmetric waves in a tube are investigated. General equations and boundary conditions governing the axisymmetric incremental motions are obtained and then, for purposes of numerical evaluation, specialized for a Gent electroelastic model. The resulting system of equations is solved numerically and the results highlight the dependence of the frequency of vibration and wave speed on the tube geometry, applied deformation and electrostatic potential. In particular, the bifurcation results obtained previously are recovered as a special case when the frequency vanishes. Specification of an incremental potential difference in the present work ensures that there is no incremental electric field exterior to the tube. Results are also illustrated for a neo-Hookean electroelastic model and compared with those previously obtained for the case in which no incremental potential difference (or charge) is specified and an external field is required.

Derivation of radial electric fields using kinetic theory in tokamak

2013 ◽  
Vol 79 (5) ◽  
pp. 513-517
Author(s):  
K. NOORI ◽  
P. KHORSHID ◽  
M. AFSARI
Keyword(s):  
Kinetic Theory ◽  
Electric Field ◽  
Electric Fields ◽  
Driving Forces ◽  
Radial Electric Field ◽  
Radial Pressure ◽  
Momentum Balance ◽  
Balance Equations ◽  
Radial Pressure Gradient ◽  
Poloidal Rotation

AbstractIn the current study, radial electric field with fluid equations has been calculated. The calculation started with kinetic theory, Boltzmann and momentum balance equations were derived, the negligible terms compared with others were eliminated, and the radial electric field expression in steady state was derived. As mentioned in previous researches, this expression includes all types of particles such as electrons, ions, and neutrals. The consequence of this solution reveals that three major driving forces contribute in radial electric field: radial pressure gradient, poloidal rotation, and toroidal rotation; rotational terms mean Lorentz force. Therefore, radial electric field and plasma rotation are connected through the radial momentum balance.

scholarly journals Exchange flow of two immiscible fluids and the principle of maximum flux

2011 ◽  
Vol 682 ◽  
pp. 132-159 ◽  
Author(s):  
R. R. KERSWELL
Keyword(s):  
Viscous Fluid ◽  
Annular Flow ◽  
Viscosity Ratio ◽  
Cylindrical Tube ◽  
Immiscible Fluids ◽  
Exchange Flow ◽  
Two Phase ◽  
Full Circle ◽  
Flow Situation ◽  
Principle Of Maximum

The steady, coaxial flow in which two immiscible, incompressible fluids of differing densities move past each other slowly in a vertical cylindrical tube has a continuum of possibilities due to the arbitrariness of the interface between the fluids. By invoking the presence of surface tension to at least restrict the shape of any interface to that of a circular arc or full circle, we consider the following question: which flow will maximise the exchange when there is only one dividing interface Γ? Surprisingly, the answer differs fundamentally from the better-known co-directional two-phase flow situation where an axisymmetric (concentric) core-annular solution always optimises the flux. Instead, the maximal flux state is invariably asymmetric either being a ‘side-by-side’ configuration where Γ starts and finishes at the tube wall or an eccentric core-annular flow where Γ is an off-centre full circle in which the more viscous fluid is surrounded by the less viscous fluid. The side-by-side solution is the most efficient exchanger for a small viscosity ratio β ≲ 4.60 with an eccentric core-annular solution optimal otherwise. At large β, this eccentric solution provides 51% more flux than the axisymmetric core-annular flow which is always a local minimiser of the flux.

Extension–torsion–inflation coupling in compressible electroelastomeric thin tubes

2019 ◽  
Vol 25 (3) ◽  
pp. 644-663 ◽  
Author(s):  
Shashank Saxena ◽  
Darius Diogo Barreto ◽  
Ajeet Kumar
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Variational Formulation ◽  
Radial Direction ◽  
Radial Electric Field ◽  
Algebraic Equations ◽  
Deformation Problem ◽  
Thin Tube ◽  
Poling Direction ◽  
Helical Anisotropy

We present an axisymmetric and axially homogeneous variational formulation to obtain coupled extension–torsion–inflation deformation in compressible electroelastomeric tubes in the presence of axial and radial electric fields. We show that such deformations occur under the following two conditions: (1) only the axial electric field is imposed, with the electric poling direction in the tube (if present) lying in the radial plane; and (2) only the radial electric field is imposed within the tube, with the electric poling direction (if present) also along the radial direction. The poling direction in condition (1) generates helical anisotropy in the tube. We then obtain the governing differential equations necessary to solve the above deformation problem for thick tubes. We further apply the thin tube limit to obtain simplified algebraic equations to solve the same deformation problem. The effect of applied electric field parameters on the extension–inflation coupling and induced internal pressure vs. imposed inflation behavior is finally presented through numerical solution of the above obtained algebraic equations. The study will be useful in designing soft electroelastic tubular actuators.

Drift Instability in the Presence of Nonuniform Radial Electric Fields

1971 ◽  
Vol 49 (12) ◽  
pp. 1630-1640 ◽  
Author(s):  
C. E. Capjack ◽  
T. E. Stringer
Keyword(s):  
Kinetic Equation ◽  
Electric Field ◽  
Electric Fields ◽  
Numerical Solutions ◽  
Radial Electric Field ◽  
Drift Instability

An equation describing the drift instability in a collisionless low-β plasma, in the presence of a nonuniform radial electric field is derived from guiding center equations for the ions and the drift kinetic equation for the electrons. Numerical solutions to this equation indicate that the influence of a nonuniform radial electric field on the drift instability may be determined from the manner in which this field modifies the macroscopic electron rotation profile.

Rheological Properties of Emulsions Immersed in Electric Fields

2007 ◽  
Author(s):  
Arturo Ferna´ndez
Keyword(s):  
Viscous Fluid ◽  
Electric Field ◽  
Numerical Simulations ◽  
Rheological Properties ◽  
Normal Stress ◽  
Electric Fields ◽  
Fluid Motion ◽  
Fluid Shear ◽  
Normal Stress Differences ◽  
Viscous Fluid Motion

The results of fully three-dimensional direct numerical simulations of the effects of electric fields on emulsions of drops will be displayed. The examination of the rheological properties of these systems is performed by imposing a simple-shear flow between two plates where the drops are immersed. An electric potential difference is applied perpendicular to the plates. The resulting electric field leads to two effects: a polarization of the drops and a viscous fluid motion on the interface between the drops and the suspending fluid. The direction and intensity of the viscous fluid motion depends on the electrical properties of the fluids. Drops more conductive than the suspending fluid exhibit a viscous fluid motion from the equator to the poles, whereas drops less conductive than the suspending fluid exhibit a viscous fluid motion from the poles to the equator. The numerical simulations show that the response of the emulsions is governed by the competition between the electric attraction and the fluid shear. The former leads to the aggregation of the drops in chains parallel to the electric field, while the latter tries to break-up the aggregated chains. The results are presented as a function of the Mason number and the electric capillary number, Mn and Ce. These non-dimensional numbers quantify the strength of the electric forces versus the fluid shear and the capillary forces, respectively. The significance of the electrical field on the viscosity and the normal stress differences will be discussed: At low Mason numbers, Mn<0.1, the application of the electric field results in the aggregation of the drops. This aggregation leads to an increase in the effective viscosity of the system and to an increase in the stresses, which result in higher normal stress differences than in hydrodynamic emulsions. At high Mason numbers, Mn>1.0, the fluid shear breaks up the aggregated structures and the properties are similar to hydrodynamic emulsions. At 0.1<Mn<1.0 the properties of the emulsions exhibit an intermediate behavior.

Modification of electrostatic fluctuations by externally imposed radial electric fields

2000 ◽  
Vol 64 (3) ◽  
pp. 227-233
Author(s):  
C. RICCARDI ◽  
C. BEVILACQUA ◽  
G. CHIODINI ◽  
E. SINDONI ◽  
M. FONTANESI
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Radial Electric Field ◽  
Plasma Parameters ◽  
Electrostatic Fluctuations

This paper concerns experiments on the turbulence of a toroidal magnetoplasma in the presence of a radial electric field. The possibility of reduction of turbulence through the application of an external biasing potential has been evaluated by measuring the electrostatic fluctuations and main plasma parameters.

scholarly journals Analysis of the interaction of an electron with radial electric fields in the presence of a disclination

2019 ◽  
Vol 16 (11) ◽  
pp. 1950172
Author(s):  
Knut Bakke ◽  
Claudio Furtado
Keyword(s):  
Electric Field ◽  
Elastic Medium ◽  
Electric Fields ◽  
Bound States ◽  
Topological Defect ◽  
Radial Electric Field ◽  
Centrifugal Term ◽  
Radial Equation ◽  
Linear Distribution ◽  
Electric Charge Distribution

We consider an elastic medium with a disclination and investigate the topological effects on the interaction of a spinless electron with radial electric fields through the WKB (Wentzel, Kramers, Brillouin) approximation. We show how the centrifugal term of the radial equation must be modified due to the influence of the topological defect in order that the WKB approximation can be valid. Then, we search for bound states solutions from the interaction of a spinless electron with the electric field produced by this linear distribution of electric charges. In addition, we search for bound states solutions from the interaction of a spinless electron with radial electric field produced by uniform electric charge distribution inside a long non-conductor cylinder.

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