Concentrated Suspensions Of Spherical Particles Research Articles

Wide-angle static and dynamic light scattering under shear.

We develop and characterize a wide angle static and dynamic light scattering under shear setup. The apparatus is suitable for the study of the structure and the dynamics of soft materials systems with a sub-micron characteristic length scale. The shear device consists in two parallel plates, and the optical setup allows us to perform light scattering measurements in any plane that contains the gradient of the velocity field direction. We demonstrate several capabilities of our apparatus: a measurement of the evolution with shear of the first peak of the structure factor of a concentrated suspension of spherical particles, both in the compression and extension quadrants of the shear flow, and the measurement of the velocity profile in dynamic light scattering. We present a theoretical treatment of light scattering under flow that takes into account the Gaussian character of the illumination and detection optical paths, in the case where the scattering volume extension is smaller than the gap of the flow cell, and compare with experimental measurements.

Topological transitions in unconfined vibrated concentrated suspensions

Vertical vibration of a concentrated suspension of spherical particles in a liquid yields an array of intriguing behaviors. Here we report new results for unconfined suspensions on a vibrating plate, and show that under certain conditions the suspension forms depressions or craters, while in other conditions it gathers to form a mound, a conical “volcano”, or even a sphere that sits just above the vibrating plate. This behavior results from a jamming transition as the plate accelerates upward, followed by unjamming as it accelerates downward. The ability of periodic jamming and unjamming to induce topological transitions is confirmed by scaling analysis, and sphere formation is further examined by numerical simulation of a suspension with an acceleration-dependent viscosity.

Ion size effects on the electrokinetics of salt-free concentrated suspensions in ac fields

We analyze the influence of finite ion size effects in the response of a salt-free concentrated suspension of spherical particles to an oscillating electric field. Salt-free suspensions are just composed of charged colloidal particles and the added counterions released by the particles to the solution that counterbalance their surface charge. In the frequency domain, we study the dynamic electrophoretic mobility of the particles and the dielectric response of the suspension. We find that the Maxwell–Wagner–O’Konski process associated with the counterions condensation layer is enhanced for moderate to high particle charges, yielding an increment of the mobility for such frequencies. We also find that the increment of the mobility grows with ion size and particle charge. All these facts show the importance of including ion size effects in any extension attempting to improve standard electrokinetic models.

Microstretch Continuum Mechanical Description of Concentrated Suspension Flow

In this article, the Hagen–Poiseuille flow of a concentrated suspension of spherical particles is solved analytically by utilizing the theory of microstretch fuids. A concise review of concentrated suspension flow analysis by employing microcontinuum mechanical theories of fluid dynamics is given. The governing equations of microstretch fluid dynamics are briefly reviewed. Then, the theory is used to analyze the pipe flow of a concentrated suspension composed of spherical particles dispersed in a liquid as well as a blood–like bio–suspension. In order to improve the accuracy of the presented solution, a material identification process is performed by employing the Levenberg–Marquardt algorithm for nonlinear optimization. Ultimately, an excellent agreement with well–known experimental data is established.

Influence of Double-Layer Overlap on the Electrophoretic Mobility and DC Conductivity of a Concentrated Suspension of Spherical Particles

In this paper, the specific effect of the overlapping of electrical double layers on the electrophoretic mobility and the electrical (DC) conductivity of concentrated suspensions of spherical colloidal particles is considered. Previous work has dealt with the study of such physical quantities for general conditions, including arbitrary zeta potentials, particle volume fractions, double-layer thicknesses (overlapping of double layers was allowed), and ionic properties of the solution. However, the large number of variables involved screened to some extent the specific role and, in many cases, the extraordinary magnitude of the overlapping contribution by itself. This is the reason that we are concerned here with the analysis of the latter effect in more detail. Thus, we present an extensive set of numerical data of both the electrophoretic mobility and the electrical conductivity versus the zeta potential and particle volume fraction for different electrolyte concentrations, specially in the region where overlapping effects are more relevant. Numerical results corresponding to the same theoretical conditions but where the overlapping correction is neglected are also shown for comparison. The treatment is based on the use of a cell model to account for hydrodynamic and electrical interactions between particles. The results show that neglecting double-layer overlapping corrections leads in most cases to an important underestimation of the true values of both the electrophoretic mobility and the electrical conductivity. The differences between both treatments are more pronounced the larger the double layer thickness and/or particle volume fraction are. Concerning DC conductivity, the overlap of double layers might help in interpreting discrepancies generally found between experimental data and standard theoretical values, even in suspensions with particle volume fractions that are typically considered to be dilute.

Transient normal stress response in a concentrated suspension of spherical particles

The transient normal force response in a concentrated suspension of spherical particles upon startup of shear, following a period of rest, was found to depend on the direction in which shear was restarted. When shear was restarted in the same direction, the normal force signal rapidly grew to its positive steady-state value. However, when shear was restarted in the opposite direction, the normal force signal was initially negative and decreased, within the response time of the instrument, to a negative minimum, from which it gradually increased, passing through zero, to its positive steady-state value. This is believed to be the first experimental confirmation of this phenomenon, which had been suggested by the numerical simulations of previous investigators.

The application of dynamic clustering data to the sedimentation rates of concentrated suspensions

A modified Stokes equation is proposed for the settling of concentrated suspensions of spherical particles in Newtonian fluids. The proposed hindered settling model was derived semi-analytically incorporating data obtained on dynamic particle clustering in concentrated suspensions by Graham and Bird. The approach differs from previous models which either neglected the influence of one particle on another or treated these interactions in an empirical manner with minimal physical or mechanistic basis for their design. The phenomenon of dynamic clustering which has recently been observed experimentally and shown to occur in flowing suspensions and sedimentation provides the basis for this study. Cluster size distributions are estimated based on suspension properties and a summation of Stokes terms provides a settling velocity prediction of concentrated systems. The validity of the model is supported by comparing calculated sedimentation rates with measured values for a number of data sets obtained from a variety of different authors.

Modeling of concentrated suspensions

The constitutive equation of a concentrated suspension of spherical particles in a Newtonian medium is derived. To this end the method of local volume averaging is employed. To calculate the contribution of the particles to the stress tensor it is assumed that the stress generated in the interstitial holes between the particles is negligible compared to the stress generated in !he narrow gaps separating the particles. The use of the resulting expression is demonstrated with two examples on a cubical arrangement of particles: pure shear and simple shear. Furthermore, the validity of the lubrication approximation employed in this work is checked against the results derived by Nunan and Keller for periodic suspensions.

Rheological properties of homogeneous finely dispersed suspensions. Steady flows

Expressions are obtained for the rheological parameters (effective viscosity, force of interphase interaction, etc.) of a moderately concentrated suspension of spherical particles. The equations of motion of the suspension and of its phases are written.

A model to describe the flow curves of concentrated suspensions of spherical particles

The explanation for the very common phenomenon of linearity of double logarithmic plots of stress and shear-rate for shear-thinning concentrated suspensions, proposed in earlier papers, has been much extended. A definite model is proposed which, while not claiming to describe real systems in detail, leads to the linearity of the log-log curves and probably represents fairly well the actual behaviour of such systems as thick fresh dairy creams at low temperatures.

Dependence of Viscosity of Suspensions on Reynolds Number

Calculation has been made of viscosity of concentrated suspensions of spherical particles. A term which is proportional to Re2 is estimated in the viscosity-concentration relation, where Reynolds number Re is composed of the rate of shear, the radius of a particle and the kinematic viscosity of the medium.Based on the cage model presented by R. Simha, a spherical enclosure was placed around a central particle. The disturbance of the original flow by the presence of the particle was considered to vanish on the surface of the cell.The coordinate axes are taken to be unconcerned with the rotation of the particle, so that the Navier-Stokes equation is free from the effect of Coriolis force and centrifugal force. The boundary conditions, however, need to be somewhat changed.The velocity field and the pressure are expanded into power series of the rate of shear. The Navier-Stokes equation and the equation of continuity are solved successively for several values of a/b, the ratio of the radii of the particle and the cell, up to the second approximation, a zeroth approximation being Simha's solution obtained from the Stokes approximation.Calculations have been performed by digital computers, and the final results are as follows:η'/η=1+17.1ξ(1-1.2 Re2+…) for a/b=0.7, η'/η=1+53.0ξ(1-98.3Re2+…) for a/b=0.8, η'/η=1+406ξ(1-5610Re2+…) for a/b=0.9, where η' and η are the viscosities of the suspension and the medium, respectively and ξ is the volume fraction of the particles.

The viscosity of a concentrated suspension of spherical particles

Einstein's viscosity equation for an infinitely dilute suspension of spheres is extended to apply to a suspension of finite concentration. The argument makes use of a functional equation which must be satisfied if the final viscosity is to be independent of the sequence of stepwise additions of partial volume fractions of the spheres to the suspension. For a monodisperse system the solution of the functional equation is ƞ τ = exp 2.5φ 1 − kφ where η r is the relative viscosity, φ the volume fraction of the suspended spheres, and k is a constant, the self-crowding factor, predicted only approximately by the theory. The solution for a polydisperse system involves a variable factor, λ ij , which measures the crowding of spheres of radius r j by spheres of radius r i . The variation of λ ij with r i r j is roughly indicated. There is good agreement of the theory with published experimental data.