Hydrodynamic Interactions In Suspensions Research Articles

Particle mesh Ewald Stokesian dynamics simulations for suspensions of non-spherical particles

A particle mesh Ewald (PME) Stokesian dynamics algorithm has been developed to model hydrodynamic interactions in suspensions of non-spherical dicolloidal particles. Dicolloids, which have recently been synthesized by a number of independent research groups (Johnson, van Kats & van Blaaderen (Langmuir, vol. 21, 2005, p. 11510), Mocket al. (Langmuir, vol. 22, 2006, p. 4037), Kim, Larsen & Weitz (J. Am. Chem. Soc., vol. 128, 2006, p. 14374)), consist of two intersecting spheres of varying radii and centre-to-centre separation. One-body resistance tensors and disturbance velocity fields are computed for general linear flows using a superposition of Stokes singularities along the symmetry axis of the dicolloid particles. The coefficients and the locations of the singularities are optimized to minimize the norm of the velocity error on the particle surface. The one-body solution provides all coefficients required for the far-field many-body interactions in the Stokesian dynamics algorithm. These generalize the analytical results for spheres employed in the classic algorithm. Modified lubrication interaction tensors are developed for dicolloids for the singular near-field lubrication interactions. Accuracy of the one-body solutions and two-body generalized Stokesian dynamics solutions are validated by comparison with high-precision numerical solutions computed with the spectral boundary element method of Muldowney & Higdon (J. Fluid Mech., vol. 298, 1995, p. 167). The newly developed PME Stokesian dynamics algorithm was used to study transport properties in dicolloidal suspensions over a range of volume fractions (φ ≤ 0.5). The effects of the degree of anisotropy on the properties of the suspension are discussed. For these mildly anisotropic particles, the transport properties remain close to those of spheres, however certain interesting trends emerge, with non-monotonic viscosity dependence as a function of increasing aspect ratio. The minimum viscosity in concentrated suspensions is lower than that for spheres with equal volume fraction over a range of volume fractions.

Effective screening of hydrodynamic interactions in charged colloidal suspensions.

We investigate the hydrodynamic interaction in suspensions of charged colloidal silica spheres. The volume fraction as well as the range of the electrostatic repulsion between the spheres is varied. Using a combination of dynamic x-ray scattering, cross-correlated dynamic light scattering, and small angle x-ray scattering, the hydrodynamic function H(q) is determined experimentally. The effective hydrodynamic interactions are found to be screened, if the range of the direct interaction is relatively long and the static density correlations are strong. This observation of effective hydrodynamic screening is in marked contrast to hard-sphere-like systems.

Rheology of concentrated suspensions of viscoelastic particles

The viscoelastic properties of particles strongly influence the rheology of many concentrated industrial or biological dispersions (emulsions, paints or blood). The deformation-orientation of interacting particles under flow enhances the maximum packing fraction of particles and leads to a non-linear rheological behaviour. We first present a Kelvin Voigt model to describe the deformation and stable orientation of a viscoelastic particle in a simple shear field. We then use a viscosity law for concentrated suspensions of hard particles in purely hydrodynamic interactions and relate the maximum packing concentration to the component of the particle deformation tensor in the direction of the flow. In the range of small deformations and diluted suspensions, the model gives a viscosity law similar to the relation obtained by Lhuillier [Phenomenology of hydrodynamic interactions in suspensions of weakly deformable particles, J. de Phys. 48 (1987) 1887–1902]. In concentrated suspensions, a self-consistent theory based on an effective medium approximation yields a non-linear equation for the relative shear viscosity. The rheological law describes the viscosity of concentrated suspensions of viscoelastic particles such as red cells in saline solution and allows information about the non-linear viscoelastic properties of the cell membrane.

Green's function approach to the theory of hydrodynamic interactions in suspensions

A new approach to the theory of many-sphere hydrodynamic interactions in suspensions is developed starting from the linearized Navier-Stokes equations reformulated in terms of the induced force formalism. This approach is based on the idea of the direct series expansion of the Green's function involved which leads in a very straightforward and controlled manner to the presentation of the velocity moments by means of the irreducible multipoles of the induced forces. To utilize this idea the calculation of the Green's function surface and volume moments of arbitrary order is performed using the method of generating functions. In principle, this offers the possibility to evaluate the translational and rotational mobility tensors in a power series expansions in two natural (for the system under consideration) parameters, namely, a/R and αa where a is a typical radius of the spheres, R a typical distance between spheres and α is expressed through the fluid density π and the viscosity of the fluid η as α=−iωρ/η. The correspondence between our and earlier theories of hydrodynamic interactions is discussed up to the seventh order in parameter (a/R) in the quasistatic limit and up to the third order in combination of both parameters, a/R and αa, in the case of finite frequencies.

Three particle hydrodynamic interactions in suspensions

We present an outline of a method to determine the components of the grand mobility matrix of a system of three hydrodynamically interacting spherical particles with arbitrary particle configuration. We present the results of a study of some components of the grand mobility matrix in the case of two special configurations. The results derived for one configuration, with the three particles on a line, are compared with some results from the literature. In the other configuration, we have put the particles on the corners of an equilateral triangle. Besides the study of the mobility matrix, we have derived virial expansions for the translational and rotational self-diffusion coefficients up to quadratic order in φ, the volume fraction. Three particle contributions are incorporated in these expressions. We also present virial expansions, where three particle hydrodynamic interactions are included, for the translational and rotational sedimentation velocities. There are some results available in the literature in the case of the translational self-diffusion coefficient and the translational sedimentation velocity, which are different from our results. We discuss these differences. As far as we know, the results of the three particle contribution to the virial expansions of the rotational self-diffusion coefficient and the rotational sedimentation velocity are new. All the virial expansions mentioned above are compared with experimental results and simulation data from the literature.

Retarded hydrodynamic interactions in suspensions

We extend the method to determine the grand mobility matrix presented in a previous article to the problem of two particles in an unbounded fluid satisfying the time dependent linear incompressible Navier-Stokes equations. Use of this method combined with a generalization of the fluctuation dissipation theorem results in the determination of the correlation matrix. We determine the effect of hydrodynamic interactions on the time dependent diffusion coefficients D 11(τ) and D 12(τ). Finally we study the effects of the correlation functions on Brownian motion.

Quasistatic hydrodynamic interactions in suspensions

We present a method to determine the grand mobility matrix for a system of N spherical particles, interacting hydrodynamically, with stick boundary conditions in an unbounded fluid. In the case of a system of two spherical particles we compare the results with those obtained from the reflection method. Finally we determine virial expansions for some diffusion coefficients, the translational sedimentation and the rotational sedimentation. We compare some of them with results available from the literature; other results are new, such as the second order virial coefficient of the short time rotational self-diffusion coefficient and the virial expansion of the rotational sedimentation. Our conclusion is that the method is generally applicable and offers a more systematic convergence than e.g. the reflection method. It leads to satisfactory results in the case of the two particle problem.

Hydrodynamic interactions in suspensions with periodic boundary conditions

We study hydrodynamic interactions in suspensions with periodic boundary conditions with the purpose of performing computer simulations with many particles per unit cell. The use of periodic boundary conditions minimizes surface effects. The formulation of the problem is complicated due to the long range nature of the hydrodynamic interactions. We show how macroscopic considerations may be used to arrive at a periodic solution of the flow equations. We derive expressions for the mobility tensors of freely moving particles, as well as for the friction tensor of a rigid array. Finally we discuss the high frequency effective viscosity of suspensions with periodic boundary conditions.

Many-body hydrodynamic interactions in suspensions

We consider hydrodynamic interactions between N rigid bodies of arbitrary shape immersed in an incompressible fluid. We study the generalized mobility matrix relating the translational and rotational velocities and the symmetric force dipole moments to the forces, the torques and the strain of an incident flow field. We show that the elements of the mobility matrix may be obtained as matrix elements of an operator related to the friction kernel. This allows a multiple scattering expansion of the mobility matrix.

Phenomenology of hydrodynamic interactions in suspensions of weakly deformable particles

What is the influence of hydrodynamic interactions on the equations of motion of a suspension of deformable particles? We propose here a qualitative answer for a neutrally-buoyant suspension with weak particle deformations. We show that the influence of the neighbouring particles can be pictured by only two functions of the particle volume fraction when quadratic deformation terms are neglected. The influence of the viscosity ratio is completely determined by assuming that the particles deform homogeneously. It is suggested that Hand's equations are not the most convenient starting point for discussing hydrodynamic interactions L'influence de particules voisines se manifeste a travers deux fonctions seulement de la concentration quand on neglige les termes quadratiques en deformation. Le role du rapport des viscosites est determine en supposant que les particules se deforment de maniere homogene

Singularity solutions for ellipsoids in low-Reynolds-number flows: With applications to the calculation of hydrodynamic interactions in suspensions of ellipsoids

The disturbance velocity fields due to translational and rotational motions of an ellipsoid in a uniform stream. constant vorticity and constant rate-of-strain. required in fundamental studies of behavior of suspensions. have been obtained by the singularity method. These solutions extend earlier solutions for prolate spheroids. Although equivalent solutions problems were obtained by Oberbeck. Edwardes and Jeffery by separation of variables in ellipsoidal coordinates. the singularity solutions are far more simple in form. Other significant results obtained by the singularity method include the exposition of the unified structure shared by the three boundary value problems and the construction of new forms of the Faxen laws for ellipsoids through application of the reciprocal theorem. The disturbance solutions and Faxen laws. the basis for Smoluchowski's method-of-reflections technique. are used to calculate hydrodynamic interactions between two or more arbitrarily oriented ellipsoids. In particular. mobility problems are solved directly to order R −5 . where R is the centroid-to-centroid separation between the ellipsoids.