Effective viscosity of an ordered suspension of small drops

We employ a method of singularity distribution to determine the effective viscosity of a suspension of small neutrally buoyant drops of one fluid in another viscous fluid. We assume that the interfacial tension is relatively large so that the drops may be considered nearly spherical and consider an instantaneous configuration in which the centers of drops coincide with the lattice points of a periodic cubic array. Under these conditions, the effective viscosity tensor is characterized by only two scalars, and, which we determine for the complete range ofc andK wherec is the volume fraction of the drops andK is the ratio of viscosities. Our numerical results, given for the simple, body-centered and face-centered cubic arrays, are in excellent agreement with those obtained for the rigid particles (K=) by Nunan and Keller except for for the face-centered cubic array where our results appear to be more accurate. The results are also in agreement with the asymptotic expressions for the dilute arrays (c1) for allK. The accuracy of the numerical results is also adequate in most cases to yield the formulas for concentrated arrays of very viscous drops (K1).

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Zusammenfassung Mit einer Singularitäten-Methode wird die effektive Viskosität einer Lösung von kleinen neutral schwimmenden Tropfen einer Flüssigkeit in einer anderen viskosen Flüssigkeit bestimmt. Wir setzen voraus daß die Oberflächenspannung verhältnismäßig groß ist, so daß man annehmen kann, daß die Tropfen fast kugelförmig sind, und wir betrachten eine Anordnung in der die Mittelpunkte der Tropfen mit den Gitterpunkten eines periodischen Kubischen Gitters zusammenfallen. Der wirksame Viskositätstensor ist in diesem Fall durch nur zwei Skalare und charakterisiert, welche wir für den gesamten Bereich vonc undK bestimmen. Hierbei istc der Volumenanteil der Tropfen, undK ist das Verhältnis der Viskositäten. Unsere numerischen Ergebnisse für die einfache kubische, raumzentriert kubische und flächenzentriert kubische Anordnung sind in ausgezeichneter Übereinstimmung mit Resultaten von Nunan und Keller für feste Teilchen (K=), ausgenommen für im flächenzentrierten System, wo unsere Resultate genauer zu sein scheinen. Die Resultate sind ebenfalls in Übereinstimmung mit asymptotischen Ausdrücken für verdünnte Suspensionen (c1) für alle Werte von K. Die Genauigkeit der numerischen Ergebnisse für konzentrierte Suspensionen von sehr viskosen Tropfen (K1) ist in den meisten Fällen ausreichend.

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On leave from Academia Sinica, Beijing, China.     

The effects of an electric field on an autocatalytic ionic reaction in a system with high ionic strength

The effects of an applied electric field on an ionic autocatalyticreaction with a quadratic rate law are considered, where thereacting species, A⁺ and B⁺, are present in a system which alsoincludes non-reacting species C^- and D⁺. The conditions areestablished under which the general terms which describe theelectric field effects in the reaction-diffusion equations canbe simplified to those used in previous studies, where theseeffects are modelled by linear advection terms. The resultingequations are then studied in detail by first obtaining conditionsfor the existence of travelling waves of permanent form. Thisdiscussion shows that _B, the ratio of the diffusion coefficientsof B⁺ and A⁺, is a critical parameter, with different formsof behaviour arising for _B < 1 and _B > 1. This analysisis augmented by obtaining solutions valid for large times andlarge values of (the dirnensionless applied field). Numericalsolutions of initial-value problems are obtained for a rangeof values of and _B, guided by and interpreted through the analysispreviously obtained. These numerical integrations show the formationof reaction fronts, with the possibility of greatly increasedreaction rates caused by the applied electric field, as wellas propagating electrophoretic fronts in B⁺ being formed incases where a reaction front is also initiated. There is alsothe possibility of separate electrophoretic fronts in A⁺ andB⁺ being formed, which become increasingly separated as timeincreases with the reaction being completely inhibited.     

The deformation of a liquid drop by an electric field

Summary The shape and stability of an incompressible dielectric drop which is stressed by a uniform external electric field are re-examined by considering small perturbations from a prolate spheroid. Compared with the shapes predicted by other approximations it is found that, for a given field strength, the drops should be a little longer and consequently a little flatter at the equator in order to satisfy the equilibrium conditions. It is also shown that beyond a certain drop deformation the L. P. E. (Legendre polynomial expansion) method fails because the equilibrium conditions at the surface of the drop are not satisfied.     

Influence of an electric field on the rheological behavior of a dilute suspension of dipolar dumbbells in a viscoelastic oldroyd liquid

Conclusions 1. Rheological equations of state of a dilute suspension of dipolar dumbbels in a viscoelastic Oldroyd liquid have been obtained for a stationary orientation of suspended particles in steady flows and electric fields.2. Study of the rheological properties of such a medium in simple shear flow in the presence of an electric field, the intensity vector of which lies in the shear plane and is perpendicular to the velocity vector, has shown that the medium examined conducts itself as a viscoelastic liquid. This is the result of both the viscoelastic properties of the dispersion medium and the orientation of the suspended particles under the action of frictional forces and the electric field. The effective viscosity of the suspension and difference in normal stresses resulting from the presence of the suspended particles are greater if one does not take the elastic properties of the dispersion medium into account.T. G. Shevchenko Kiev State University. Translated from Mekhanika Polimerov, No. 3, pp. 519–524, May–June, 1978.     

The growth of ice crystals in an electric field

Zusammenfassung Das Wachstum von Eiskristallen in einer Diffusionswolkenkammer wird durch ein elektrisches Feld von über 500 V/cm wesentlich geändert. Die Kristalle wachsen sehr schnell in Form langer, dünner Nadeln. Die Ursache des beschleunigten Wachstums ist noch nicht völlig erkannt; aber die Beobachtungen stimmen mit der Hypothese überein, dass die Kristalle durch Einbau von neutralen Wassermolekülen wachsen.     

The effect of an electric field on the local stoichiometry of front waves in an ionic chemical system

A model based on an autocatalytic, two-step reaction mechanismincluding two ionic components (of the same charge) and twonon-ionic components, where both reactions are of second orderoverall, is considered when an electric field is applied tothe system. The model is motivated by experimental observationson the iodate-arsenous acid system. The travelling wave equationsare examined first and conditions obtained for the existenceand form of these waves. These conditions are then used to interpretthe results obtained from numerical simulations of the fullsystem. These results display all the main features observedexperimentally, the change in the local stoichiometry and thepossible wave annihilation for sufficiently strong fields. Themodel provides a clear explanation for these features as wellas predicting new features not reported from the experiments.The main one of which is the occurrence of an internal wavepropagating in the reacted part of the system in the directioninduced by the applied field.     

Degenerate plasma in a half-space under an external electric field

An analytic solution is found for the problem on the behavior of a collisional plasma in a variable external electric field. We elucidate the structure of the screened electric field and investigate the case where the frequency of the external field is close to the plasma oscillation frequency (resonance). We show that there are two near-surface layers where the behavior of the screened field differs essentially. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 3, pp. 487–502, June, 2006.     

Semicrystal with a singular potential in an accelerating electric field

We study the Schrödinger equation describing the one-dimensional motion of a quantum electron in a periodic crystal placed in an accelerating electric field. We describe the asymptotic behavior of equation solutions at large values of the argument. Analyzing the obtained asymptotic expressions, we present rather loose conditions on the potential under which the spectrum of the corresponding operator is purely absolutely continuous and spans the entire real axis.     

Scattering on an anisotropic potential in a constant electric field

The scattering of a particle on an anisotropic potential in a constant electric field is considered. Conditions on the anisotropic decay of the potential that insure asymptotic completeness without modifications of the wave operators are obtained. The paper uses the mixed approach wherein the Enss method is applied to one part of the variables, whereas the other part is treated using the smoothness technique. Bibliography: 12 titles. Translated fromZapiski Naucnykh Seminarov POMI, Vol. 230, 1995, pp. 203–214. Translated by A. B. Pushnitskii.     

Propagating reaction fronts in an ionic autocatalytic system: The effects of electric field intensity and ionic strength

An ionic chemical system which has two components, A⁺ and B⁺, reacting with a quadratic autocatalytic rate law and two further, nonreacting components C⁻ and D⁺ is considered. The system is shown to be characterized by the dimensionless parameters δ_B, I and d₀ representing the ratio of the diffusion coefficients of B⁺ and A⁺, the (constant) applied electric current and the ionic strength of the system (the initial concentration of D⁺), respectively. The travelling wave equations for this system are discussed first, and parameter ranges identified where forward-propagating kinetic waves can exist. These are then seen, from numerical integrations of the original initial-value problem, to be the long time structures, when this is the case. When this is not the case, qualitatively different behaviour is observed depending on whether δ_b > 1 or δ_B <1, the form of which is dependent on the size and direction of the applied electric field as well as on the ionic strength. This is described in detail and shown to agree with previous studies for d₀ = 0 and do large.     

Absence of bound states for a two-particle system in the external constant electric field

One proves the absence of bound states of a two-particle system in the external constant electric field. The conditions on the potential coincide basically with the conditions that ensure the existence of the wave operators.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 152, pp. 18–20, 1986.     

The interaction of a system of weakened zones at the interface of elastic media in a tensile stress field

The interaction of a system of crack-like defects with distributed cohesive forces over the whole surface of the edges, located at the interface of two elastic half-planes and which open under the action of forces at infinity, is considered. A dislocation approach is used to describe the model of each defect: the discontinuity in the asymmetric shifts is specified in the form of a basis function with free parameters that satisfies a number of physical constraints. The free parameters of the model are determined when finding an analytical solution of the problem. The key questions are: what is the minimum load at which just one of these weakened zones is converted into the nucleus of a crack or when one of the connecting bridges separating these zones is fractured and, also, under what conditions can the interaction of the defects be neglected ? The model is extended with a relation which enables an explicit opening - bonding force dependence to be obtained.     

Electric field near the surface of a plasma with an arbitrary degree of degeneracy as a response to an external alternating electric field

Theoretical and Mathematical Physics - We analytically solve a boundary value problem for the behavior $$($$ oscillation $$)$$ of an electron plasma with an arbitrary degree of degeneracy of the...     

Transversal line defects induced by an electric field in a period-2 oscillatory medium

The dynamical behavior of spiral waves in a period-2 oscillatory medium is investigated under the influence of an external applied alternating current field. Open and closed transversal line defects which wiggle along the direction parallel to the wave fronts, are generated in the spiral-wave patterns when the stimulus frequency of the electric field is equal to one, three or five times of the local oscillatory frequency in the period-2 state. Their generations are directly related with the change in the spatial wavelength induced by the electric field. These wigglings proliferate along the transverse direction parallel to the wave fronts as the stimulus strength increases, and become denser when the stimulus frequency increases by multiples of the period-2 oscillatory frequency.