On the shape of a rotating liquid drop in an electric field

Summary The axisymmetric relative equilibrium shape of a finite dielectric liquid mass held together by surface tension and rotating uniformly in a uniform axial electric field is determined by expressing the slope of its tangent in terms of confluent hypergeometric functions and following a numerical integration.

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Zusammenfassung Die axialsymmetrische, relative Gleichgewichtsfigur einer endlichen, dielektrischen, durch die Oberflächenspannung zusammengehaltenen Flüssigkeitsmasse, welche gleichförmig in einem axialen elektrischen Feld konstanter Feldstärke rotiert, wird untersucht. Die Steigung der Tangente wird mittels konfluenter hypergeometrischer Funktionen ausgedrückt, und die Gestalt des Flüssigkeitstropfens durch numerische Integration bestimmt.

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With 1 Figure

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Presented at the Fifth United States National Congress of Applied Mechanics, University of Minnesota, Minneapolis, Minnesota, USA, June 1966; an abstract appears on page 764 of the proceedings.     

On an asymptotic case of plane turbulent motion of a weakly conducting rotating fluid in the presence of a magnetic field

Summary The final period of decay of homogeneous turbulence in a weakly conducting rotating fluid in the presence of a magnetic field is investigated. By asymptotic expansion techniques, the expressions of the kinetic and magnetic energy tensors are established. After a first stage similar to the non-rotating case, it is shown that modulated plane turbulence occurs when both the applied magnetic field and the axis of rotation are parallel.Aspirant au Fonds National Belge de la Recherche Scientifique.     

On the stability for a rate-type electric conducting medium

In this article we prove the existence, uniqueness and asymptotic behaviour of the solutions for an electromagnetic non-homogeneous medium, which is characterized by a rate-type equation for the electric conduction and by dissipative boundary conditions. A domain of dependence inequality is derived and the exponential decay of the solutions is proved by the methods of the semi-group theory.     

On the stability of a hot rotating layer of micropolar fluid

The convective stability of a horizontal layer of incompressible micropolar fluid heated from below and rotating about a vertical axis has been investigated on the basis of linear theory, using normal mode analysis. The boundaries are assumed to be free. After introducing the corrections to the basic equations considered by Sastry and Rao [1], it has been found that the rotation has a destabilizing effect which contradicts the earlier assertion presented in [1].Moreover, microinertia, which does not affect the stability of a hot horizontal layer of incompressible micropolar fluid in the absence of rotation [2], is found to have destabilizing effect.     

Electric action of a flame and a conducting liquid jet in an electric field

Expressions are obtained for the charge and potential of a spheroid-shaped burner with the flame on its top situated in an external field parallel to its rotation axis. Simple expressions for potentials of the burner are obtained in terms of the external field for the sphere, strongly oblate, and strongly stretched ellipsoids. In an analogous manner, electrification, of a spherical tank with the outflowing conducting liquid is considered, and the charges and potentials of the field strength gauge are determined.Notation E field strength - a, b, , and semiaxes of the ellipsoid - surface charge density - Q ₁ andQ ₂ charges of the tanks - g charge of the droplet - n _x shape coefficient - I current strength - C capacity - R resistance - r radius - relaxation time - u flow rate Moscow State Institute of Electronics and Mathematics (Technical University), Moscow, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal Vol. 68, No. 4, July–August 1995, pp. 589–593.     

Nonlinear dynamics of the free surface of a conducting liquid in an electric field

The nonlinear dynamics of the free surface of an ideal conducting liquid in an external electric field is investigated. It is found that in the absence of gravity and surface tension the equations of the two-dimensional motion of the medium can be solved in the approximation of small angles of inclination of the surface. It is shown that singularities of the square-root type, for which the curvature is infinite but the surface itself remains smooth, can form on the surface of a conducting liquid over a finite time. Pis’ma Zh. Tekh. Fiz. 24, 25–29 (June 26, 1998)     

Streamlining of a cylinder with an electric arc rotating in a magnetic field

Streamlining of a circular cylinder with a localized heat source modeling an MHD actuator in which the plasma arc channel moves along the cylinder surface under the action of the Lorentz force in a radial magnetic field is studied experimentally and simulated numerically. It is shown that the presence of a moving heat release region leads to a break in the symmetry in cylinder streamlining by the external flow and the appearance of a nonzero lift force and circulation.     

Explosive growth of perturbations of the surface of a conducting liquid in an electric field

An analysis is made of the behavior of the free surface of a conducting liquid in an external electric field near the Tonks-Frenkel instability threshold assuming that the incipient wave is one-dimensional. It is shown that the surface dynamics is described by the nonlinear Klein-Gordon equation. This equation is used to formulate criteria for the explosive growth of perturbation amplitudes. Pis’ma Zh. Tekh. Fiz. 25, 65–69 (November 12, 1999)     

On the motion of a micropolar fluid drop in a viscous fluid

Summary The problems of the flow of a viscous fluid past a micropolar fluid sphere and the flow of a micropolar fluid past a viscous fluid drop are discussed. The expressions for the stream functions, velocities, spins and the drag are obtained in each case and are compared with the classical (viscous fluid past a viscous fluid sphere) results. It is found that the viscosity ratios and the parameters, which arises in connection with the boundary condition, have significant effect upon the drag on the sphere in each case.     

Characteristics of the molecular structure of weakly conducting liquids in an electric field

It is found experimentally that synergetic specific features displayed by weakly conducting liquids in an electric field consist in their cluster (locally ordered) structure, which is achieved due to the charged associates of admixture molecules bound with one another by hydrogen bonding. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 70, No. 5, pp. 757–760, September-October, 1997     

Hydromagnetic flow past a rotating porous plate in a conducting fluid rotating about a noncoincident parallel axis

Summary The hydromagnetic flow of an incompressible viscous electrically conducting fluid past a porous plate is investigated when the plate rotates with a uniform angular velocity about an axis normal to the plate and the fluid at infinity rotates with the same angular velocity about a non-coincident parallel axis. It is shown that in the presence of a uniform magnetic field parallel to the axis of rotation the boundary layer thickness decreases with an increase in either the suction at the plate or the magnetic parameter M. In the presence of suction at the plate, the velocity component u in the direction normal to the plane containing the axis of rotation of the plate and that of the fluid increases with an increase in M, while the velocity component v in the transverse direction parallel to the plane of the plate decreases with an increase in M. For a fixed value of M, at a given location u increases with an increase in the suction parameter S while v decreases with increasing S. For a fixed value of M, at a given location both u and v decrease with an increase in the blowing parameter S₁. Further, for a fixed value of S₁, at a given position u increases with an increase in M but v decreases with increasing M. It is shown that no torque is exerted by the fluid on the plate, and non-coaxial rotations of the plate and the fluid at infinity have no influence on the torque.The solution of the heat transfer equation reveals that for given values of the suction parameter S, Prandtl number P and Eckert number E, the temperature at a given point in the flow increases with increasing M. On the other hand, for fixed values of M, P and E, the temperature at a given point decreases with increasing S. No steady distribution of temperature exists when there is blowing at the plate.     

On shape differentiation of discretized electric field integral equation

This work presents shape derivatives of the system matrix representing electric field integral equation discretized with Raviart–Thomas basis functions. The arising integrals are easy to compute with similar methods as the entries of the original system matrix. The results are compared to derivatives computed with automatic differentiation technique and finite differences, and are found to be in an excellent agreement. Furthermore, the derived formulas are employed to analyze shape sensitivity of the input impedance of a planar inverted F-antenna, and the results are compared to those obtained using a finite difference approximation.     

Effects of uniform radial electric field on the MHD heat and fluid flow due to a rotating disk

The flow and heat transfer of an incompressible electrically conducting fluid over a rotating infinite disk are studied in the present paper. The disk finds itself subjected to a uniform normal magnetic field. The particular interest lies in searching for the effects of an imposed radial electric field on the behavior of the physical flow. The gradient of an electric potential generated on the disk penetrates through the fluid and greatly influences the boundary layer formation. The presented model representing the fluid motion is a general case since it reduces to the traditional Karman’s viscous pump when the electric potential is ignored. The governing Navier–Stokes and Maxwell equations of the constructed model together with the energy equation are converted into self-similar forms using suitable similarity transformations. The flow and thermal boundary layers are shown to be much affected by the presence of a uniform radial electric parameter. Some parameters of fundamental physical significance such as the surface shear stresses in the radial and tangential directions and the heat transfer rate are numerically evaluated. The effects of electric conductivity of the disk on the flow and forced convection heat transfer are further discussed.     

Influence of temperature field on stability of fluid motion between rotating cylinders

The Rayleigh method is used to obtain relations giving the influence of the amount and direction of heat flow on the stability of a fluid between rotating cylinders.     

On the development of characteristics in an oseillating,rotating fluid

Summary A source of fluid with an oscillatory strength, which is situated on the axis of a rotating fluid, commences to act at time t=0. We describe how inviscid, geostrophic forces lead to the development of the characteristic cone when the frequency of oscillation is less than twice the frequency of rotation. Eventually, viscous forces become important when the time is O(E ^-1/3), where E is the small Ekman number, in forming the thin shear layer along the surface of the cone.     

On the capillary instability of a dielectric viscous liquid cylinder surrounded by another viscous fluid in an electric field

Summary The capillary instability of a long, dielectric, incompressible, viscous liquid cylinder when subjected to small axisymmetric disturbances in the presence of a uniform axial electric field is investigated by making a normal mode analysis of the equations describing the perturbed fluid flow. The resulting characteristic equation, which includes the effect of a surrounding unbounded viscous fluid, is solved in order to express graphically the governing dispersion relation as a function of the relative viscous and dielectric properties of the two media when the viscosities of both are dominant. The influence of the various parameters on the modes of capillary instability as well as their effect on the modes of maximum instability are exhibited for this and other special cases.

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Zusammenfassung Die kapillare Instabilität eines langen, dielektrischen, inkompressiblen, zähen Flüssigkeitszylinders wird untersucht, wenn letzterer kleinen axialsymmetrischen Störungen in Gegenwart eines gleichförmigen, elektrischen Axialfeldes ausgesetzt ist. Das zur Behandlung des vorliegenden Problems herangezogene Verfahren macht Gebrauch von einem Normalschwingungsansatz für die das gestörte Strömungsfeld beschreibenden Gleichungen. Die resultierende charakteristische Gleichung, welche den Einfluß der umgebenden, unendlich ausgedehnten, zähen Flüssigkeit berücksichtigt, wird gelöst. Die grundlegende Dispersionsbeziehung wird graphisch als Funktion der relativen zähen und dielektrischen Eigenschaften beider Medien dargestellt, falls der Zähigkeitseinfluß in beiden Medien dominiert. Der Einfluß verschiedener Parameter auf das Schwingungsverhalten der Kapillarinstabilität, ebenso ihr Einfluß auf das Schwingungsverhalten der maximalen Instabilität, wird sowohl für den vorliegenden Fall als auch für verschiedene Sonderfälle dargestellt.

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With 7 Figures

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Presented at the Canadian Congress of Applied Mechanics, Université Laval, Québec, Canada, May 1967; an abstract appears in the proceedings.