  A model polydisperse fluid represents many real fluids such as colloidal
suspensions and polymer solutions. In this study, considering a concentrated
size-polydisperse hard sphere fluid with size derived from two different
distribution functions, namely, uniform and Gaussian and explore the effect of
polydispersity and mass scaling on the transport properties in general. A
simple analytical solution based on the Boltzmann transport equation is also
presented (together with the solution using Chapman-Enskog (CE) method) using
which various transport coefficients are obtained. The central idea of our
approach is the realization that, in polydisperse system, the collision
scattering cross section is proportional to a random variable \textit{z} which
is equal to the sum of two random variables $\sigma_i$ and $\sigma_j$
(representing particle diameters), and the distribution of \textit{z} can be
written as the convolution of the two distributions $P(\sigma_i)$ and
$P(\sigma_j)$. The obtained transport coefficients are expressed as explicit
function of polydispersity index, $\delta$, and their dependence on the nature
of particle size distribution is explored. It is observed that in the low
polydispersity limit, the transport coefficients are found to be insensitive to
the type of size distribution functions considered. The analytical results (for
diffusion coefficients and thermal conductivity) obtained using Chapman-Enskog
method and our simple analytical approach agrees well with the simulation.
However, for shear viscosity, our analyical approach agress for $\delta \le
20\%$, while it agrees upto $\delta \approx 40\%$ with the result obtained
using CE-method (in the limit $\delta \rightarrow 0$). Interestingly, the
effect of scaling mass (i.e., mass proportional to the particle size and thus a
random variable) produces no significant qualitative difference.
