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A model polydisperse fluid represents many real fluids such as colloidalsuspensions and polymer solutions. In this study, considering a concentratedsize-polydisperse hard sphere fluid with size derived from two differentdistribution functions, namely, uniform and Gaussian and explore the effect ofpolydispersity and mass scaling on the transport properties in general. Asimple analytical solution based on the Boltzmann transport equation is alsopresented (together with the solution using Chapman-Enskog (CE) method) usingwhich various transport coefficients are obtained. The central idea of ourapproach is the realization that, in polydisperse system, the collisionscattering cross section is proportional to a random variable \textit{z} whichis equal to the sum of two random variables $\sigma_i$ and $\sigma_j$(representing particle diameters), and the distribution of \textit{z} can bewritten as the convolution of the two distributions $P(\sigma_i)$ and$P(\sigma_j)$. The obtained transport coefficients are expressed as explicitfunction of polydispersity index, $\delta$, and their dependence on the natureof particle size distribution is explored. It is observed that in the lowpolydispersity limit, the transport coefficients are found to be insensitive tothe type of size distribution functions considered. The analytical results (fordiffusion coefficients and thermal conductivity) obtained using Chapman-Enskogmethod and our simple analytical approach agrees well with the simulation.However, for shear viscosity, our analyical approach agress for $\delta \le20\%$, while it agrees upto $\delta \approx 40\%$ with the result obtainedusing CE-method (in the limit $\delta \rightarrow 0$). Interestingly, theeffect of scaling mass (i.e., mass proportional to the particle size and thus arandom variable) produces no significant qualitative difference.

Transport properties of polydisperse hard sphere fluid: Effect of distribution shape and mass scaling