Capture of small drops by large drops in an electric field

In the investigation of the process of the breakdown of emulsions by the coalescence of drops, up to the present time, use has been made of the theory of the coagulation of colloids (for example, [1]). However, there is a considerable difference between colloids and emulsions. Forces of attraction, bringing about the coalescence of two colloidal particles, become predominant at distances much greater than the particle size, so that, in a hydrodynamic sense, it can be assumed that colloidal particles do not interact. On the contrary, the disperse phase in emulsions consists of molecularly smooth spherical drops with a size from a few tenths of a micron or more and, with approach of the drops, forces of hydrodynamic interaction, inhibiting coalescence, become substantial. As a rule, the drops can be regarded as rigid undeformed spheres since their surface is stabilized by surface-active substances. With the approach of such spheres, the layer of liquid between them generates a braking force proportional to the rate of approach of the drops and inversely proportional to the distance between their surfaces. As a result, the approach of drops under the action of a finite force takes place over an infinite time. It follows from this that the process of the coalescence of drops requires the presence of a force of attraction, rising to infinity with approach of the drops, and any theory of coalescence must take simultaneous account of the forces of attraction of the drops and of the hydrodynamic forces.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 61–68, September–October, 1973.     

Hydrodynamic interactions in quasi-two-dimensional colloidal suspensions

Dynamical correlations between colloidal particles, in a quasi-two-dimensional geometry, are measured by optical microscopy. The system consists of charged polystyrene spheres suspended in water and confined between two parallel plates. The long-range electrostatic interaction is screened and the interparticle direct interaction becomes an effective excluded volume interaction. Thus, the observed long-range correlations, between the motion of pairs of particles, are due to the solvent mediated hydrodynamic interactions. Such correlations are observed as a dependence in the interparticle distance of the diffusion coefficients for the normal modes, collective and relative, for which results are presented here for a range of particle concentrations.     

Interaction of two spherical particles in a steady flow of viscous fluid when the Reynolds number is not small

The problem of the interaction of two or more particles moving in a viscous incompressible fluid at small Reynolds numbers (Re 1) has been well studied. The linearity of the Stokes equations makes it possible to develop effective methods of solution of the problem for two and many particles [1]. If the Reynolds number is not small, the inertia forces in the Navier-Stokes equations cannot be ignored, and the problem becomes nonlinear, i.e., much more complicated. The present note is devoted to the problem of the interaction of two spherical particles in a steady uniform flow of a viscous incompressible fluid when the Reynolds number is not small. Asymptotic expressions are obtained for the interaction forces between the particles when the distances between them are large compared with their radius.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 142–144, May–June, 1983.     

Calculation of the rate of coalescence of an emulsion in a turbulent flow

The central moment of the theory describing the merging (coalescence) of the drops of an emulsion is determination of the time of the approach of a drop or a number of drops colliding with a given drop in unit time. In the stage immediately preceding the merging of the drops the forces of the hydrodynamic braking of the approaching drops are found to be considerable. The role of these forces has been analyzed earlier for the case of the capture of small drops by large drops in an oncoming flow in the presence of an external electrical field [1] and for the problem of the Brownian coalescence of drops, taking account of the effect of the electric double layer and of surface forces of interaction [2–4]. The present article considers the approach of drops with turbulent diffusion in an electrical field. Of the greatest interest is the sharp slowing of the approach due to the hydrodynamic interaction of the drops, considerably sharper than in the case of molecular diffusion [2]. As a result, the sharp acceleration of the approach and coalescence of drops with the action of an electrical field on an emulsion in a turbulent flow becomes understandable.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 47–55, May–June, 1976.The authors are grateful to G. I. Barenblatt, A. I. Leonov, V. I. Loginov, and L. P. Smirnov for their evaluation and criticism of the work.     

Effect of inertia on the hydrodynamic interaction between two liquid capsules in simple shear flow

Three-dimensional numerical simulations using front-tracking method are performed to study the hydrodynamic interaction between two liquid capsules suspended in simple shear flow in presence of inertia. Capsules are modeled as liquid drops surrounded by neo-Hookean elastic membranes. In the limit of zero inertia, it has been known from past research that the hydrodynamic interaction between two deformable particles (drops/capsules) suspended in shear flow results in an irreversible shift in the trajectories of the particles as one particle rolls over the other. In this article, we show that the presence of inertia can significantly alter the capsule trajectories. When inertia is small but finite, the capsules do undergo an irreversible displacement, but the lateral separation between them first decreases before they roll over each other, unlike in Re ? 1. For moderate to high inertia, the capsules reverse their directions of motion before coming close to each other. The reversal of motion occurs progressively earlier in time (that is, the capsules come less closer to each other) with increasing inertia. The long-time behavior of the capsule–capsule interaction at finite inertia showed that the capsules engage in spiraling motions. Based on our simulations, four different regimes of capsule–capsule interaction at finite inertia are identified: (i) a self-diffusive type interaction, (ii) an outwardly spiraling motion, (iii) a fixed-orbit spiraling motion, and (iv) an inwardly spiraling motion in which the capsules settle with zero relative velocity. The reversal of motion, and the spiraling trajectories at finite inertia have no analogy in the limit of zero inertia. Such motions are explained by analyzing the flow field around a deformed capsule which shows reverse flow regions and off-surface stagnation points, similar to those previously reported in case of rigid spheres and cylinders under torque-free condition.     

Electrostatic probe for detecting charged particles in a gas-dynamic flow

The theoretical and practical aspects of detection of large (r 50 m) charged particles in a gas-dynamic flow by means of an electrostatic probe are considered. The basic equation that describes the interaction between such a particle and the probe is derived. A model problem that permits one to determine the electrostatic charge induced on the probe is formulated and solved. The interaction with the probe of charged conducting particles and dielectric particles is analyzed. It is shown that one can not only detect individual charged particles in a gas stream but also determine their charge and velocity by analyzing the time distributions of the measured signal. Actual constructions of an electrostatic probe and the corresponding measuring complexes are described. Methods are indicated for raising the sensitivity and resolution of the probe. The results are presented of diagnostics of charged gas-dynamic flows in a laboratory experiment, and also under test and full-scale conditions (measurement of charged particles in jet exhausts).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 72–81, January–February, 1980.We thank V. I. Grabovskii, D. G. Dubravskii, I. I. Il'yushenkovaya, and A. P. Strekalov for assistance during this work.     

Adhesive contact of a fluid-filled membrane driven by electrostatic forces

Adhesion of a particle with a substrate in presence of electrostatic interaction is an appealing area of research because of its significance in many biological and industrial applications. In this work, we study an interesting problem in which a charged flexible particle located in an electrolytic environment adheres to an oppositely charged rigid substrate due to the electrostatic attraction between them. The particle is a membrane filled with incompressible fluid and can undergo large deformation. Continuum theories are used to model the mechanics of the membrane and the electric potential in the electrolytic solution. The developed model allows us to examine the nature of the coupling between the electrostatic interaction and the deformation of the membrane. In particular, the deformation of the membrane causes non-uniform distribution of charges on its surface and significant electrostatic repulsion between these charges. This repulsion is most pronounced within and near the contact zone and provides a source of resistance to its further deformation and contact formation. As a result, the coupling between electrostatics and deformation is most significant for moderate deformation and becomes weaker for very large deformation. The relation between the total electrostatic adhesive force and the contact area shows similar scaling $(F～a^n$, where $n=3)$ to the classical Hertz theory of contact at small deformation, but the value of n increases as deformation increases. The dependence of this relation on the Debye length of the solution and the initial fluid pressure in the membrane is also investigated.     

电解质吸附对水基带电表面黏着的影响

为研究界面黏着,利用表面力仪在高离子强度电解质水溶液中测量负电云母表面之间的法向力.在纯水中,因范德华吸引,两表面跳跃至直接接触(间距0?),分离两表面时测得界面黏着力为-46.7 m N/m.在0.1 mol/L K₂SO₄中,因K₊离子牢固吸附于云母,表面间距稳定于5?,黏着力仅-2.9 m N/m;在0.1 mol/L Ca(NO₃)₂中,云母表面吸附的Ca₂⁺离子产生显著短程水合排斥,但在较低载荷下解吸附,导致两表面直接接触,黏着力高达-40.7 m N/m.加入Ca(OH)₂于0.1 mol/L K₂SO₄仅产生微弱短程排斥,黏着状态几乎与纯K₂SO₄水溶液中相同.聚电解质PCE从0.1 mol/L K₂SO₄中吸附于云母表面且诱导远程空间位阻排斥,但在中等载荷下解吸附,导...     

Numerical modelling of the entrainment of particles in inviscid supersonic flow

The interaction between particles situated in close proximity and moving at supersonic speeds is investigated computationally. The simplest case of the motion of a single particle travelling behind a lead particle is used to elucidate the role of aerodynamic forces in the motion of a group of particles. The effect of the following parameters on the drag and lift forces acting on each of two particles of equal diameter in proximity is investigated: the free-stream Mach number, and the axial and lateral displacements of the trailing particle. The two-dimensional flow field is numerically simulated using an unsteady Euler CFD code to find the steady-state drag and lift coefficients for both particles. Three static zones of aerodynamic influence in the wake of the lead particle are identified, which are denoted as the entrainment, lateral attraction, and ejection zones. A non-dimensional representation of the zones of influence is given. It is shown that the dynamic entrainment of particles can occur even when the path of the trailing particle originates outside the entrainment and lateral attraction zones.     

A cell model theory of the shear viscosity of a concentrated suspension of interacting spheres in a non-Newtonian fluid

A theoretical approach to the shear viscosity of concentrated suspensions of small particles in a non-Newtonian fluid has been developed using a cell theory model involving particle-particle interaction. The cell theory of Frankel and Acrivos was first generalized to power-law fluid matrices without particle interaction. Particle-particle interaction was then taken into consideration. The theory suggests that the flow behavior of such systems at low shear rates is chiefly dependent upon non-hydrodynamics interparticle interaction such as van der Waals—London and electrostatic forces which induce flocculation and yield stresses. The flow properties at high shear rates are determined by hydrodynamics interaction essentially dependent upon particle concentration and shape.     

Sedimentation acceleration of remanent iron oxide by magnetic flocculation

Sedimentation based processes are widely used in industry to separate particles from a liquid phase. Since the advent of the ＂Nanoworld＂ the demand for effective separation technologies has rapidly risen, calling for the development of new separation concepts, one of which lies in hybrid separation using the superposition of a magnetic field for magnetic particles. Possible product portfolio of such separation consists of pigment production, nanomagnetics production for electronics and bio separation, A promising step in that direction is magnetic field enhanced cake filtration, which has by now progressed from batch to continuous ooeration. In sedimentation processes in a mass force field the settling behaviour of particles strongly depends on physico-chemical properties, concentration and size distribution of the particles. By adjusting the pH, the interparticle forces, in particular the electrostatic repulsion, can be manipulated. For remanent magnetic particles such as magnetite, pre-treatment in a magnetic field could lead to a change of interparticle interactions. By magnetizing the particles apart from van der Waals attraction and electrostatic repulsion, an additional potential is induced, the magnetic attraction, which could easily dominate the other potentials and result in agglomeration in the primary minimum. By sedimentation analysis, a wide spectrum of parameters like pH, magnetic field strength and concentration have been investigated. The results show a strong increase of sedimentation velocity by magnetic flocculation of the raw suspension. This leads to a rise in throughput due to the acceleration of sedimentation kinetics by imparting a non-chemical interaction to the physico-chemical properties in the feed stream of the separation apparatus.     

Scalable gas-phase processes to create nanostructured particles

The properties of nanoparticles are often different from those of larger grains of the same solid material because of their very large specific surface area. This enables many novel applications, but properties such as agglomeration can also hinder their potential use. By creating nanostructured particles one can take optimum benefit from the desired properties while minimizing the adverse effects. We aim at developing high-precision routes for scalable production of nanostructured particles. Two gas-phase synthesis routes are explored. The first one - covering nanoparticles with a continuous layer - is carried out using atomic layer deposition in a fluidized bed. Through fluidization, the full surface area of the nanoparticles becomes available. With this process, particles can be coated with an ultra-thin film of constant and well-tunable thickness. For the second route - attaching nanoparticles to larger particles - a novel approach using electrostatic forces is demonstrated. The micron-sized particles are charged with one polarity using tribocharging. Using electrospraying, a spray of charged nanoparticles with opposite polarity is generated. Their charge prevents agglomeration, while it enhances efficient deposition at the surface of the host particle. While the proposed processes offer good potential for scale-up, further work is needed to realize large-scale processes.     

Interaction forces of particles dispersed in an electrolyte

Expressions are derived for the forces acting in a disperse medium in the presence of interaction of the double layers surrounding particles or drops of the dispersed phase when the potential of the dispersed particles is small. It is found that the force produced by the presence of double layers is proportional to the concentration gradient of the dispersed particles. It is shown that this force is comparable with the force produced by Brownian motion of the particles and may even exceed it. The equations of motion for the dispersed phase are derived with allowance for the convective terms, the pressure gradient, and the forces caused by Brownian motion and the presence of the double layers. A generalized Fick's law is obtained with effective diffusion coefficient. The equilibrium distribution of the particle concentration in a uniformly rotating cylinder is found with allowance for the interaction of the double layers.Translated from Izvestiya Akademii Nauk SSSR, Meklianika Zhidkosti i Gaza, No. 5, pp. 98–102, September–October, 1984.     

Suspensions of monodisperse spheres in polymer melts: particle size effects in extensional flow

Suspensions in polymeric, viscoelastic liquids have been studied in uniaxial extensional flow. The fibre wind-up technique has been used for this purpose. The effects of particle size and particle volume fraction have been investigated, using monodisperse, spherical particles. The results have been compared with shear flow data on the same materials. The values of the relative extensional viscosities at low stretching rates are in agreement with the relative shear viscosities and relative moduli. This indicates that hydrodynamic forces are stronger than the particle interaction forces. At larger strain rates strain hardening occurs; it is suppressed when particles are added. Small aggregating particles reduce the strain hardening more strongly than larger particles; strain hardening can even be totally eliminated. When further increasing the stretching rate, hydrodynamic effects dominate again and the effect of particle size effect on strain hardening disappears.     

Electrohydrodynamic flow in a two-dimensional channel with an axially disposed electrode-emitter

A study is made of the flow of an incompressible nonviscous unipolar charged liquid in a two-dimensional channel ¦ x ¦ <, ¦ y ¦ h with conducting walls and an axially disposed electrode-emitter (along y = 0). The charged particles have an arbitrary constant mobility. The charge distribution on the emitter is approximated as a unit step function. The problem is solved by linearizing the equations with respect to the electrohydrodynamic interaction. The behavior of the electrical parameters is determined, and the deformed profiles of velocity and pressure downstream of the zone in which the electrostatic forces are rotational in character are calculated. These profiles can be determined without having to solve the linearized partial differential hydrodynamic equations in the entire region occupied by the flow, although the profiles then depend on the distribution of the electrical parameters along the entire length of the channel.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 35–40, November–December, 1970.In conclusion the author wishes to thank A. B. Vatazhin for suggesting the problem and for his constant attention throughout the work.     

Motion of a cylinder in a viscous electroconductive medium with a magnetic field

The method of force sources is used to consider the planar problem of the motion of a circular cylinder in a viscous electroconductive medium with a magnetic field. The conventional and magnetic Reynolds numbers are assumed to be small. Expressions are obtained for the hydrodynamic reaction forces of the medium, acting on the moving cylinder. It is shown that as a result of the flow anisotropy in the medium, caused by the magnetic field, in addition to the resistance forces on bodies moving at an angle to the field, there are deflecting forces perpendicular to the velocity vector. The velocity field disturbances at great distances from the moving cylinder are determined.The problems of viscous electroconductive flow about solid bodies in the presence of a magnetic field constitute one of the divisions of magnetohydrodynamics. Motion of an electroconductive medium in a magnetic field gives rise to inductive electromagnetic fields and currents which interact with the velocity and pressure hydrodynamic fields in the medium [1, 2]. Under conditions of sufficiently strong interaction, the number of independent flow similarity parameters in MHD is considerably greater than in conventional hydrodynamics. This circumstance complicates the theoretical analysis of MHD flow about bodies, and therefore we must limit ourselves to consideration of individual particular flow cases.Here we consider the linear problem of the motion of an infinite circular cylinder in a viscous incompressible medium with finite electroconductivity located in a uniform magnetic field.There are many studies devoted to the flow of a viscous electroconductive medium with a magnetic field about solid bodies (see, for example, [3–5]). Because of this, some of the results obtained here include previously known results, which will be indicated below. In contrast to the cited studies, the examination is made by the method of force sources, suggested in [6]. This method permits obtaining integral equations for the distribution of the forces acting on the surface of the moving body. Their solution is obtained for small Reynolds and Hartmann numbers. Then the nature of the velocity disturbances at great distances from the body are determined. These results are compared with conventional viscous flow about a cylinder in the Oseen approximation.     

Geomagnetic flocculation: An explanation of the rheological behaviour of suspended magnetite

Summary The persistent flocculation of magnetite, suspended in water, which is shown by relatively high yield stresses and fast settling, is explained by mutual attraction of magnetite particles as a consequence of magnetic dipoles, induced into them by the earth's magnetic field.The magnitude of this effect is calculated and compared with other forces affecting particle interaction.

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Zusammenfassung Die persistente (nicht vermeidbare) Flockung von Magnetit, suspendiert in Wasser, die sich bei relativ hohen Fließgrenzen und schnellen Absetzen zeigt, wird durch gegenseitige Anziehung der Magnetit-Teilchen als Folge von magnetischen Dipolen, erzeugt durch das erdmagnetische Feld, erklärt.Die Größe dieses Effektes wird berechnet und mit anderen Kräften, die die Wechselwirkung der Teilchen beeinflussen, verglichen.

     

Correlation between the high-frequency elastic modulus and the interparticle interaction potential in zirconium oxide colloidal suspensions

In this work, we study the high-frequency elastic modulus of aqueous suspensions made with two kinds of zirconium oxide particles, one commercially available and the other synthesized as monodisperse spheres. The effect of volume fraction of solid, ionic strength (sodium chloride as indifferent electrolyte) and particle geometry is taken into account in the study on this viscoelastic property of the suspensions. Frequency sweeps were performed at a fixed value of the applied shear-stress in order to obtain the frequency-limiting value of the elastic modulus by rheometrical methods. On the other hand, the high-frequency modulus is theoretically calculated independently by means of the models proposed by Buscall and co-workers, Wagner and Bergenholtz and co-workers, which correlate the interaction potential between particles with this rheological parameter. The approach to the interparticle potential is the extended DLVO theory, which considers the electrical repulsion between charged colloidal particles, the van der Waals attraction and the acid–base interaction that can be attractive or repulsive depending on the thermodynamic nature of the solid–liquid interface.     

The impact of non-DLVO forces on the onset of shear thickening of concentrated electrically stabilized suspensions

This paper exposes an extension of an activation model previously published by the authors. When particles arranged along the compression axis of a sheared suspension, they may overcome the electrostatic repulsion and form force chains associated with shear thickening. A percolation-based consideration allows an estimation of the impact of the force chains on a flowing suspension. It suggests that similar to mode coupling models, the suspension becomes unstable before the critical stress evaluated from the activation model is reached. The percolated force chains lead to discontinuous shear thickening. The model predictions are compared with results from two experimental studies on aqueous suspensions of inorganic oxides; in one of them, hydration repulsion and in the other hydrophobic attraction can be expected. It is shown that the incorporation of non-Derjaguin–Landau–Verwey–Overbeek forces greatly improve predictions of the shear thickening instability.