Explicit analytical expressions for the drag and diffusion coefficients of a spherical particle attached to the flat interface between two immiscible fluids are constructed for the case of a vanishing viscosity ratio between the fluid phases. The model is designed to account explicitly for the dependence on the contact angle between the two fluids and the solid surface. The Lorentz reciprocal theorem is applied in the context of geometric perturbations from the limiting cases of $90^{\circ }$and $180^{\circ }$contact angles. The model agrees well with the experimental and numerical data from the literature. Also, an advantage of the method utilized is that the drag and diffusion coefficients can be calculated up to one order higher in the perturbation parameter than the known velocity and pressure fields. Extensions to other particle shapes with known velocity and pressure fields are straightforward.

The dynamics of spherical particles driven along an interface between two immiscible fluids is investigated asymptotically. Under the assumptions of a pinned three-phase contact line (TCL) and very different viscosities of the two fluids, a particle assumes a tilted orientation. As it moves, it causes a deformation of the fluid interface which is also computed. The case of two interacting driven particles is studied via the linear superposition approximation. It is shown that the capillary interaction force resulting from the particle motion is dipolar in terms of the azimuthal angle and decays with the fifth power of the inter-particle separation, similar to a capillary quadrupole originating from undulations of the TCL. The dipolar interaction is demonstrated to exceed the quadrupolar interaction at moderate particle velocities.

The line tension of an electrolyte wetting a non-polar substrate is computed analytically and numerically. The results show that, depending on the value of the apparent contact angle, positive or negative line tension values may be obtained. Furthermore, a significant difference between Young's contact angle and the apparent contact angle measured several Debye lengths remote from the three-phase contact line occurs. When applying the results to water wetting highly charged surfaces, line tension values of the same order of magnitude as found in recent experiments can be achieved. Therefore, the theory presented may contribute to the understanding of line tension measurements and points to the importance of the electrostatic line tension. Being strongly dependent on the interfacial charge density, electrostatic line tension is found to be tunable via the pH value of the involved electrolyte. As a practical consequence, the stability of nanoparticles adsorbed at fluid-fluid interfaces is predicted to be dependent on the pH value. The theory is suited for future incorporation of effects due to surfactants where even larger line tension values can be expected.

Based on the notion of a construction process consisting of the stepwise addition of particles to the pure fluid, a discrete model for the apparent viscosity as well as for the maximum packing fraction of polydisperse suspensions of spherical, noncolloidal particles is derived. The model connects the approaches by Bruggeman and Farris and is valid for large size ratios of consecutive particle classes during the construction process, appearing to be the first model consistently describing polydisperse volume fractions and maximum packing fraction within a single approach. In that context, the consistent inclusion of the maximum packing fraction into effective medium models is discussed. Furthermore, new generalized forms of the well-known Quemada and Krieger–Dougherty equations allowing for the choice of a second-order Taylor coefficient for the volume fraction (ϕ2-coefficient), found by asymptotic matching, are proposed. The model for the maximum packing fraction as well as the complete viscosity model is...