Maria L. Ekiel-Jeżewska

Streaming potential studies of colloid, polyelectrolyte and protein deposition

Recent developments in the electrokinetic determination of particle, protein and polyelectrolyte monolayers at solid/electrolyte interfaces, are reviewed. Illustrative theoretical results characterizing particle transport to interfaces are presented, especially analytical formulae for the limiting flux under various deposition regimes and expressions for diffusion coefficients of various particle shapes. Then, blocking effects appearing for higher surface coverage of particles are characterized in terms of the random sequential adsorption model. These theoretical predictions are used for interpretation of experimental results obtained for colloid particles and proteins under convection and diffusion transport conditions. The kinetics of particle deposition and the structure of monolayers are analyzed quantitatively in terms of the generalized random sequential adsorption (RSA) model, considering the coupling of the bulk and surface transport steps. Experimental results are also discussed, showing the dependence of the jamming coverage of monolayers on the ionic strength of particle suspensions. In the next section, theoretical and experimental results pertaining to electrokinetics of particle covered surfaces are presented. Theoretical models are discussed, enabling a quantitative evaluation of the streaming current and the streaming potential as a function of particle coverage and their surface properties (zeta potential). Experimental data related to electrokinetic characteristics of particle monolayers, mostly streaming potential measurements, are presented and interpreted in terms of the above theoretical approaches. These results, obtained for model systems of monodisperse colloid particles are used as reference data for discussion of experiments performed for polyelectrolyte and protein covered surfaces. The utility of the electrokinetic measurements for a precise, in situ determination of particle and protein monolayers at various interfaces is pointed out.

Lubrication corrections for three-particle contribution to short-time self-diffusion coefficients in colloidal dispersions

It is shown that the standard treatment of lubrication effects in many-particle hydrodynamic interactions leads to divergent three-particle contributions to the short-time translational self-diffusion coefficient. To resolve the problem the improved method to account for lubrication is proposed. The translational and rotational self-diffusion coefficients of the Brownian semidilute suspension are then evaluated up to terms of the second order in volume fraction.

On the linearized relativistic Boltzmann equation. I. Existence of solutions

The linearized relativistic Boltzmann equation inL2(r,p) is investigated. The detailed analysis of the collision operatorL is carried out for a wide class of scattering cross sections.L is proved to have a form of the multiplication operatorv(p) plus the compact inL2(p) perturbationK. The collisional frequencyv(p) is analysed to discriminate between relativistic soft and hard interactions. Finally, the existence and uniqueness of the solution to the linearized relativistic Boltzmann equation is proved.

Global existence proof for relativistic Boltzmann equation

The existence and causality of solutions to the relativistic Boltzmann equation inL1 and inLloc1 are proved. The solutions are shown to satisfy physically naturala priori bounds, time-independent inL1. The results rely upon new techniques developed for the nonrelativistic Boltzmann equation by DiPerna and Lions.

Short-time dynamics of permeable particles in concentrated suspensions

We study short-time diffusion properties of colloidal suspensions of neutral permeable particles. An individual particle is modeled as a solvent-permeable sphere of interaction radius a and uniform permeability k, with the fluid flow inside the particle described by the Debye-Bueche-Brinkman equation, and outside by the Stokes equation. Using a precise multipole method and the corresponding numerical code HYDROMULTIPOLE that account for higher-order hydrodynamic multipole moments, numerical results are presented for the hydrodynamic function, H(q), the short-time self-diffusion coefficient, D(s), the sedimentation coefficient K, the collective diffusion coefficient, D(c), and the principal peak value H(q(m)), associated with the short-time cage diffusion coefficient, as functions of porosity and volume fraction. Our results cover the full fluid phase regime. Generic features of the permeable sphere model are discussed. An approximate method by Pusey to determine D(s) is shown to agree well with our accurate results. It is found that for a given volume fraction, the wavenumber dependence of a reduced hydrodynamic function can be estimated by a single master curve, independent of the particle permeability, given by the hard-sphere model. The reduced form is obtained by an appropriate shift and rescaling of H(q), parametrized by the self-diffusion and sedimentation coefficients. To improve precision, another reduced hydrodynamic function, h(m)(q), is also constructed, now with the self-diffusion coefficient and the peak value, H(q(m)), of the hydrodynamic function as the parameters. For wavenumbers qa>2, this function is permeability independent to an excellent accuracy. The hydrodynamic function of permeable particles is thus well represented in its q-dependence by a permeability-independent master curve, and three coefficients, D(s), K, and H(q(m)), that do depend on the permeability. The master curve and its coefficients are evaluated as functions of concentration and permeability.

Spherical cloud of point particles falling in a viscous fluid

Statistical mechanics is applied to calculate ensemble-averaged particle and fluid velocity fields of a spherical cloud of point particles sedimenting at a low Reynolds number. The analogy with the fall of a liquid drop in another lighter fluid is discussed.

Fibrinogen conformations and charge in electrolyte solutions derived from DLS and dynamic viscosity measurements

Hydrodynamic properties of fibrinogen molecules were theoretically calculated. Their shape was approximated by the bead model, considering the presence of flexible side chains of various length and orientation relative to the main body of the molecule. Using the bead model, and the precise many-multipole method of solving the Stokes equations, the mobility coefficients for the fibrinogen molecule were calculated for arbitrary orientations of the arms whose length was varied between 12 and 18 nm. Orientation averaged hydrodynamic radii and intrinsic viscosities were also calculated by considering interactions between the side arms and the core of the fibrinogen molecule. Whereas the hydrodynamic radii changed little with the interaction magnitude, the intrinsic viscosity exhibited considerable variation from 30 to 60 for attractive and repulsive interactions, respectively. These theoretical results were used for the interpretation of experimental data derived from sedimentation and diffusion coefficient measurements as well as dynamic viscosity measurements. Optimum dimensions of the fibrinogen molecule derived in this way were the following: the contour length 84.7 nm, the side arm length 18 nm, and the total volume 470 nm(3), which gives 16% hydration (by volume). Our calculations enabled one to distinguish various conformational states of the fibrinogen molecule, especially the expanded conformation, prevailing for pH<4 and lower ionic strength, characterized by high intrinsic viscosity of 50 and the hydrodynamic radius of 10.6 nm. On the other hand, for the physiological condition, that is, pH=7.4 and the ionic strength of 0.15M NaCl, the semi-collapsed conformation dominates. It is characterized by the average angle equal to =55°, intrinsic viscosity of 35, and the hydrodynamic radius of 10nm. Additionally, the interaction energy between the arms and the body of the molecule was predicted to be -4 kT units, confirming that they are oppositely charged than the central nodule. Results obtained in our work confirm an essential role of the side chains responsible for a highly anisotropic charge distribution in the fibrinogen molecule. These finding can be exploited to explain anomalous adsorption of fibrinogen on various surfaces.

Streaming current and streaming potential for particle covered surfaces: Virial expansion and simulations

Streaming potential changes induced by deposition of particles at solid/liquid interfaces are considered theoretically. The solution is obtained in terms of a virial expansion of the streaming potential up to the third order of the surface coverage of particles, assumed to be distributed according to the hard sphere equilibrium distribution function. Theoretical methods, including the idea of cluster expansion, are adopted from statistical physics. In the cluster expansion, two-body and three-body hydrodynamic interactions are evaluated with a high precision using the multipole method. The multipole expansion algorithm is also used to perform numerical simulations of the streaming potential, valid for the entire surface coverage range met in practice. Results of our calculations are in good agreement with the experimental data for spherical latex particles adsorbed on a mica surface.

Three-particle contribution to sedimentation and collective diffusion in hard-sphere suspensions

The virial expansion of the collective mobility (sedimentation) coefficient is considered for hard sphere suspensions at equilibrium. The term of the second order in volume fraction, which involves three-particle hydrodynamic interactions, is calculated with high accuracy. To achieve that we represent the collective mobility coefficient as the sum of convergent integrals over particle configurations. In this way the short-wave-number limit k→0 is avoided. Moreover, an efficient numerical procedure is applied to evaluate the hydrodynamic interactions. The algorithm is based on the multipole expansion, corrected for lubrication. The method allows us to analyze contributions to the collective mobility coefficient from different configurations of three particles and to select the dominant part. This suggests a general approximation scheme.

Three-particle contribution to effective viscosity of hard-sphere suspensions

The virial expansion of the high-frequency effective viscosity is considered for hard sphere suspensions at equilibrium. The term of the third order in volume fraction, which involves three-particle hydrodynamic interactions, is calculated with high accuracy and the corresponding coefficient in the Saito representation is also evaluated. The method is based on a regularization procedure, which gives the effective viscosity as the sum of convergent integrals over particle configurations. To calculate the hydrodynamic interactions, we apply the efficient algorithm based on the multipole expansion, corrected for lubrication, which has been earlier applied to evaluate the self-diffusion and the sedimentation coefficients. However, in the context of the effective viscosity, we have faced a slower convergence of the results with the increasing number of the included mulitipoles.