Under a simple shearing flow, the effective viscosity of solid suspensions can be reduced by controlling the inclusion particle size or the number of inclusion particles in a unit volume. Based on the Stokes equation, the transformation field method is used to model the reduction behaviour of effective viscosity of solid suspensions theoretically by enlarging the particle size at a given high concentration of particles. With a lot of samples of random cubic particles in a unit cell, our statistical results show that at the same higher concentration, the effective viscosity of solid suspensions can be reduced by increasing the particle size or reducing the number of inclusion particles in a unit volume. This work discloses the viscosity reduction mechanism of increasing particle size, which is observed experimentally.
Under an external uniform electric field, the dielectric response of graded cylindrical composites having generalized dielectric profile inclusions is investigated. The generalized dielectric profile of graded cylindrical inclusion is expressed in the form, εi（r） = c（b ＋ r）^keβr where r is the radial variable of the cylindrical inclusions and c, b, k and β are parameters. The local potential solution of generalized dielectric profile graded composites is derived by means of the power series method and the effective dielectric response is predicted in the dilute limit. Moreover, from the result of generalized profile, the analytical solutions of local potentials and the effective responses of graded composites having three cases of dielectric profiles, i.e., the exponential profile εi（r） = ce^βr, the general power law profile εi（r） = c（b ＋ r）^k and the profile εi（r） = cr^keβr, are sorted out, respectively. In the dilute limit, our exact results are used to test the validity of differential effective dipole approximation （DEDA） for estimating the effective response of graded cylindrical composites, and it is shown that the DEDA is in excellent agreement with the exact result.
Based on the effective medium approximation theory of composites, the whitecap-covered sea surface is treated as a medium layer of dense seawater droplets and air. Two electromagnetic scattering models of randomly rough surface are applied to the investigation of microwave backscattering of breaking waves driven by strong wind. The shapes of seawater droplets are considered by calculating the effective dielectric constant of the whitecap layer. The responses of seawater droplets shapes, such as sphere and ellipsoid, to the backscattering coefficient are discussed. Numerical results of the models are in good agreement with the experimental measurements of horizontally and vertically polarized backscattering at microwave frequency 13.9GHz and different incidence angles.
