Motion of a magnetizable liquid in a rotating magnetic field

Moskowitz and Rosensweig [1] describe the drag of a magnetic liquid — a colloidal suspension of ferromagnetic single-domain particles in a liquid carrier — by a rotating magnetic field. Various hydrodynamic models have been proposed [2, 3] to describe the macroscopic behavior of magnetic suspensions. In the model constructed in [2] it was assumed that the intensity of magnetization is always directed along the field so that the body torque is zero. Therefore, this model cannot account for the phenomenon under consideration. We make a number of simplifying assumptions to discuss the steady laminar flow of an incompressible viscous magnetizable liquid with internal rotation of particles moving in an infinitely long cylindrical container in a rotating magnetic field. The physical mechanism setting the liquid in motion is discussed. The importance of unsymmetric stresses and the phenomenon of relaxation of magnetization are emphasized. The solution obtained below is also a solution of the problem of the rotation of a polarizable liquid in a rotating electric field according to the model in [3].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 40–43, July–August, 1970.     

Layered model of electrorheological fluid under flow

We present a theoretical model of the behavior of a concentrated electrorheological fluid (ERF) which explicitly takes into account the effects of conductivity. The increase in shear viscosity under an electric field is due to a layered structure between the electrodes, made up of the remnants of particle chains adhering to the electrodes by electrostatic image forces, and a freely flowing liquid layer where all the shear flow is concentrated. This layered model can explain the variation of electric current with shear rate, as well as the rheological response of a dynamic yield stress proportional to the square of the applied electric field.     

Field-induced gelation, yield stress, and fragility of an electro-rheological suspension

 Electro-rheological suspensions (ERS) are known to undergo liquid-to-solid transition under the application of an electric field. Long-range interaction between neighboring particles results in sample-spanning particulate structures which behave as soft solids. Here, we studied the rheological expression of this field-induced transition which has many similarities with chemical gelation. This similarity shows in mechanical spectroscopy on a suspension of monodisperse silica in PDMS as model ERS. Upon application of the electric field, dynamic moduli G′, G′′ grow by orders of magnitude and evolve in a pattern which is otherwise typical for gelation of network polymers (random chemical or physical gelation). At the gel point, the slow dynamics is governed by power-law relaxation behavior (frequency-independent tan δ). A low field strength is sufficient to reach the gel point and, correspondingly, the percolating particle structure at the gel point is still very fragile. It can be broken by the imposition of low stress. For inducing a finite yield stress, the field strength needs to be increased further until the long-range electrostatic interaction generates string-like particle alignments which become clearly visible under the optical microscope. The onset of fragile connectivity was defined experimentally by the tan δ method. The ERS was probed dynamically at low frequencies where the transition is most pronounced, and also in steady shear where the rate of structure formation equals the rate of internal breaking. Received: 1 May 2001 Accepted: 11 August 2001     

An experimental study of electrorheological fluid flow through a packed bed of glass beads

This paper shows that pressure drop-flow rate performance of an electrorheological (ER) fluid flowing through a packed bed of glass beads is consistent with a modified Ergun equation for yield stress flow through a packed bed. ER fluids are of scientific and engineering interest due to the sensitivity of their rheological properties on the applied electric field. As far as we know ER fluids have not been studied for flows through porous media. In this work a silica particle–silicone oil suspension is pumped through a rectangular packed bed of glass beads with applied electric fields. The silica particles are observed to form fibrous structures parallel to the electric field that stretch between the beads and extend between the electrodes. The pressure drop-flow rate performance agrees well with the expected performance calculated from a modified Ergun equation for a yield stress fluid flow through the packed bed with the viscosity and yield stress as functions of the applied electric field.     

Internal rotation in the hydrodynamics of weakly conducting dielectric suspensions

Hydrodynamic phenomena in weakly conducting single-phase media due to interphase electric stresses are reviewed in [1]. In the present paper, a model is constructed of a dielectric suspension with body couples due to the field acting on free charges distributed on the surface of the particles of the suspension. Averaging of the microscopic fields yields macroscopic equations for the field and the polarization of the dielectric suspension with allowance for the finite relaxation time of the distribution of the free charge on the phase interface. The developed model is used to consider the occurrence of spontaneous rotation of a dielectric cylinder in a weakly conducting suspension in the presence of an electric field; compared with the case of single-phase media [2], this is characterized by a significant reduction in the threshold intensity of the electric field with increasing concentration of the particles [3]. In the present model of a dielectric suspension, the destabilization of the cylinder is due to the occurrence of rotations of the particles of the suspension due to the interaction between the polarization and the motion of the medium. The relaxation equation for the polarization for the given model is analogous to the corresponding equation for media which can be magnetized [4–6].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 86–93, March–April, 1980.     

Suspension of layered particles: an optimum electrorheological fluid for d.c. applications

 A comparison is made between two types of solid particles used in electrorheological fluids: particles with homogeneous electrical properties versus layered particles with a semi-conducting core surrounded by an outer layer of lower conductivity. Rheological measurements of these suspensions under steady shear and d.c. electric field show that the layered particle system produces the same yield stress but with a substantially reduced electric current. X-ray spectroscopic analysis confirms that these particles have a thin layer of SiO_x on the outer surface which causes the reduction in conductivity. Measurement of the dielectric permittivity followed by analysis using the Maxwell-Wagner model of polarization indicates that the conductivity of the outer layer is about 0.62 times that of the core region. Received: 13 January 1999 Accepted: 26 July 1999     

Hydrodynamic diffusivity of spherical particles in polymer solution

In this research experiments were performed to examine the hydrodynamic diffusion of spherical particles in a highly filled suspension. The suspension consisted of nearly monodisperse polymethylmethacrylate spheres in a density matched polymer solution. The polymer solution was prepared by dissolving 0–700 ppm of polyacrylamide in a mixture of ethyleneglycol and glycerine. The polymer solution did not show appreciable shear thinning. The particle loading was varied from 30 to 55%. The hydrodynamic diffusivity was estimated by measuring the time-dependent viscosity when the suspension was subjected to a circular Couette flow with an air bubble trapped under the rotor of the Couette apparatus. The results show that the dimensionless diffusivity (D/γ˙a ²) of particles in polymer solution is not proportional to shear rate (γ˙), as in the case of a Newtonian fluid, but that it decreases with increasing shear rate. The diffusivity also decreases with increasing polymer concentration. It is suggested that the elongational thickening behaviour and the increased lubrication force due to the first normal stress difference may be responsible for the reduction of diffusivity in the polymer solution. Received: 18 January 2000 Accepted: 6 April 2000     

Measuring static yield stress of electrorheological fluids using the slotted plate device

An electrorheological (ER) response is defined as the dramatic change in rheological properties of a suspension of small particles due to the application of a large electric field transverse to the direction of flow. ER fluids are typically composed of nonconducting or semiconducting particles dispersed in a nonconducting continuous phase. A sufficiently large electric field will cause ER fluids to solidify, giving rising to a yield stress. Many applications in torque and stress transfer devices were proposed employing the reversible yielding behavior of ER fluids. Successful applications depend on a large yield stress of ER fluids and therefore accurate measurements of the yield stress of ER fluids are required. Reported experimental yield stresses of ER fluids have been dynamic yield stresses obtained by extrapolating the shear stress–shear rate data to zero-shear rate. It would be very helpful to the understanding of ER behaviors and the applications of ER fluids to be able to measure the static yield stress of ER fluids accurately. The slotted plate technique has been shown to be a successful method to determine the static yield stress of suspensions. The values obtained via the slotted plate method are static yield stress as the platform is designed for extremely low-speed motion. In this study, we modified the slotted plate device for the application of large electric fields and measured the static yield stress of TiO₂ ER fluids under various electric fields. The measured static yield stress values are also compared with the static yield stress values from a commercial rheometer.     

Viscosity of a suspension of ellipsoidal ferromagnetic particles in a magnetic field

The motion of a suspension of solid magnetized ellipsoids of rotation in a uniform magnetic field is considered. The ellipsoids are assumed to be magnetized along the axes of symmetry. Relaxation processes in the solid phase are not considered. The stress tensor of the suspension is calculated taking into account the rotational Brownian motion of the particles. It is shown that the viscosity tensor contains six independent kinetic coefficients, which are even with respect to the magnetic field. The relation between these coefficients and the field and the ratio of the semiaxes of the ellipsoid is obtained. As an example, the effect of the magnetic field on the symmetrical flow of the suspension in a contractile cylinder is considered.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 75–82, September–October, 1973.     

Effects of a.c. Electric Field and Rotation on Bénard–Marangoni Convection

The coupled buoyancy and thermocapillary instability, the Bénard–Marangoniproblem, in an electrically conducting fluid layer whose upper surface is deformed and subject to a temperature gradient is studied. Both influences of an a.c. electric field and rotation are investigated. Special attention is directed at the occurrence of convection both in the form of stationary motion and oscillatory convection. The linear stability problem is solved for different values of the relevant dimensionless numbers, namely the a.c. electric Rayleigh number, the Taylor, Rayleigh, Biot, Crispation and Prandtl numbers. For steady convection, it is found that by increasing the angular velocity, one reinforces the stability of the fluid layer whatever the values of the surface deformation and the applied a.c. electric field. We have also determined the regions of oscillatory instability and discussed the competition between both stationary and oscillatory convections. This revised version was published online in July 2006 with corrections to the Cover Date.     

Electrorheological behaviour of a starch-oil system

A simple system consisting of a suspension of 10 wt % of starch in silicone oil was subjected to electrorheological testing. The system exhibits a complex behaviour depending on the electrical field. On one hand, the application of an external electric field induced the formation of a linear structure, aligned with the electric field. The formation of that structure was studied by several rheological methods. The rate of modifying the electric field intensity resulted to be related to the electric field value at which percolation is observed. On the other hand, master curves for the structure formation and breakdown in squeeze experiments were obtained.     

Dispersion state and rheology of hectorite particles in water over a broad range of salt and particle concentrations

The relationship between the rheological properties of deionized aqueous suspensions of hectorite particles and the dispersion states of the particles has been studied with a broad range of salt and particle concentrations. The shear viscosity of the hectorite suspensions decreases drastically after exhaustively deionizing the suspensions with ion-exchange resins. By means of DLS measurements, it is clarified that the average size of the flocs of hectorite particles decreases and reaches the Stokes diameter of the individual particle as the degree of deionization advances. This fact strongly supports the idea that the electrical double layer around the hectorite particles expands significantly in the exhaustively deionized state and the particles are well-dispersed individually and do not form a three-dimensional network structure composed of particles, whereas such a network structure forms in the presence of a large amount of salt. In the case of exhaustively deionized state, the suspension forms a glassy state, at high particle fractions. The results show the importance of the electrical double layer that causes a strong repulsive force among the particles on the particle dispersion state, especially in the exhaustive deionization area below 10^− 4 M, and on the rheological properties; the hectorite suspension can be considered a Newtonian liquid in the deionized state, but it becomes elastic-solid in the presence of salt above a certain concentration confirmed by normal stress measurements.     

General Constitutive Equations of an ER Suspension Based on the Internal Variable Theory

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Random close packing and relative viscosity of multimodal suspensions

Multimodal suspensions, consisting of non-colloidal spherical particles and a Newtonian matrix, are considered. A new differential (or multi-scale mean field approach) model for the relative viscosity of multimodal suspensions has been developed. The problem of the random close packing fraction of the solid phase is also investigated. We suppose that the multimodal suspension has a dominant large particle composition and that the smaller particles are embedded in the empty space between the larger particles. The relative viscosity model can therefore be based on the theory of monomodal suspensions. Experimental data of Eveson are compared to the predictions given by using three different models of monomodal suspensions respectively. The Maron–Pierce approach appears to give the best agreement with Eveson’s experiments. However, due to experimental uncertainties, we recommend that the Mendoza and Santamaria-Holek (MSH) formula be adopted.     

Electrorheologial properties of hematite/silicone oil suspensions under DC fields

Electrorheological (ER) fluids composed of α-Fe₂O₃ (hematite) particles suspended in silicone oil are studied in this work. The rheological response has been characterized as a function of field strength, shear rate and volume fraction. Rheological tests under DC electric fields elucidated the influence of the electric field strength, E, and volume fraction, ϕ, on the field-dependent yield stress, τ_y. It was found that this quantity scales with E and ϕ with a linear and parabolic dependence, respectively. The viscosities of electrified suspensions were found to increase by several orders of magnitude as compared to the unelectrified suspension at low shear rates, although at high-shear rates hydrodynamic effects become dominant and no effects of the electric field on the viscosity are observed. The work is completed with the analysis of microscopic observations of the structure acquired by the ER fluid upon application of a constant electric field. Electrohydrodynamic convection is found to be the origin of the ER response rather than the commonly admitted particle fibrillation. This fact can provide an explanation to the relationship between yield stress and electric field strength as well as the pattern of periodic structures observed in the measurement geometries.     

Particles for tracing turbulent liquid helium

We address the problem of making quantitative measurements of local flow velocities in turbulent liquid helium, using tracer particles. We survey and evaluate presently available particles and previous work to establish the need to develop new particles for the purpose. We present the first practical solution for visualizing fluid motions using a suspension of solid hydrogen particles with diameters of about 2 μm. The hydrogen particles can be used to study flows with Taylor-microscale Reynolds numbers between 85 and 775. The particles can be used equally well with the PIV, LDV, or particle-tracking techniques.     

Self-assembly of latex particles for colloidal crystals

Self-assembly of latex particles is of great importance for fabricating various functional colloidal crystals. In this paper, we review recent research on the self-assembly of latex particles for colloidal crystals, covering the assembly forces and various assembly approaches of latex particles, including self-assembly by gravity sedimentation, vertical deposition, physical confinement, electric field, and magnetic field. Furthermore, some simple methods for assembling latex particles such as spin coating, spray coating, and printing are also summarized.     

Flow of a yield stress fluid over a rotating surface

We study the flow of yield stress fluids over a rotating surface when both the viscoelastic solid behavior below a critical deformation (γ _c) and liquid properties beyond γ _c can play a significant role. We review the detailed characteristics of the flow in the solid regime in the specific case of a pure elongational strain (large height to radius ratio). We, in particular, show that there exists a critical rotation velocity (ω _c) associated with the transition from the solid to the liquid regime. We then consider the specific case of lubricational regime (small height to radius ratio) in the liquid regime. In that case we describe the different possible evolutions of the equilibrium shape of the material as a function of the rotation velocity (ω), from which we extrapolate the transient shape evolutions as ω increases. We show that for a sufficiently large rotation velocity the sample separates into two parts, one remaining at rest around the rotation axis, the other going on moving radially. These predictions are then compared with systematic spin-coating tests under increasing rotation velocity ramps followed by a plateau at ω _f with typical yield stress fluids. It appears that there exists a critical velocity below which the material undergoes a limited elongation and beyond which it starts to spread significantly over the solid surface. For a larger ω _f value the sample forms a thick peripheral roll, leaving behind it a thin layer of fluid at rest relatively to the disc. These characteristics are in qualitative agreement with the theoretical predictions. Beyond a sufficiently large ω _f value this roll eventually spreads radially in the form of thin fingers. Moreover, in agreement with the theory in the lubricational regime, the different curves of deformation vs ω fall along a master curve when the rotation velocity is scaled by ω _c for different accelerations, different sample radii, or different material yield stress. The final thickness of the deposit seems to be mainly governed by the displacement of the roll, the characteristics of which take their origin in the initial stage of the spreading, including the solid–liquid transition.     

Stability of a liquid layer with bubbling

The article discusses a new type of instability of a horizontal layer of a motionless liquid, due to the motion of bubbles of gas or of particles of a suspension through the layer. It is shown that, when a certain critical mass flow rate of the gas or the suspension is attained, due to the essential inhomogeneity of the velocity of the gas bubbles, the layer becomes unstable and convective flow develops in a Bénard cell. With the motion of bubbles in the field of gravity, the criterion of instability is found to be independent of the size of the bubbles and the kinematic viscosity of the liquid.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, July–August, 1974.