  While the density functional theory with integral equations techniques are
very efficient tools in numerical analysis of complex fluids, an analytical
insight into the phenomenon of effective interactions is still limited. In this
paper we propose a theory of binary systems which results in a relatively
simple analytical expression combining arbitrary microscopic potentials into
the effective interaction. The derivation is based on translating many particle
Hamiltonian including particle-depletant and depletant-depletant interactions
into the occupation field language. Such transformation turns the partition
function into multiple Gaussian integrals, regardless of what microscopic
potentials are chosen. In result, we calculate the effective Hamiltonian and
discuss when our formula is a dominant contribution to the effective
interactions. Our theory allows us to analytically reproduce several important
characteristics of systems under scrutiny. In particular, we analyze the
effective attraction as a demixing factor in the binary systems of Gaussian
particles, effective interactions in the binary mixtures of Yukawa particles
and the system of particles consisting of both repulsive core and
attractive/repulsive Yukawa interaction tail, for which we reproduce the
'attraction-through-repulsion' and 'repulsion-through-attraction' effects.
