  In this paper, we consider the field model for complex ionic fluids with an
energy variational structure, and analyze the well-posedness to this model with
regularized kernels. Furthermore, we deduce the estimate of the maximal density
function to quantify the finite size effect. On the numerical side, we adopt a
finite volume scheme to the field model, which satisfies the following
properties: positivity-preserving, mass conservation and energy dissipation.
Besides, series of numerical experiments are provided to demonstrate the
properties of the steady state and the finite size effect by showing the
equilibrium profiles with different values of the parameter in the kernel.
