In this article, we study an approximate model for a binary fluid flow in a three-dimensional bounded domain. The governing equations consist of the Allen-Cahn equation for the order (phase) parameter fcoupled with the Lagrange averaged Navier-Stokes-a(LANS-a) system for the velocity u. We analyze the asymptotic behavior of the solution to the associated initial and boundary value problems. In particular, we prove that the system generates a strongly continuous semigroup on a suitable phase space, which possesses a global attractor  Then we establish the existence of an exponential attractor which entails that  has a finite fractal dimension. The model was considered in [13], where the authors studied the convergence of the solution as the parameter agoes to

Lagrange averaged, Navier-Stokes-a, phase transition, global and exponential attractors.