Effect of Stationary Particles on the Phase Separation of Binary Fluids
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Effect of Stationary Particles on the Phase Separation of Binary Fluids Domenico Suppa, Olga Kuksenok, Anna C.Balazs and J.M.Yeomans1 Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, PA 15261, U.S.A. 1 Theoretical Physics, University of Oxford, 1 Keble Road, Oxford, OX1 3NP, U.K. ABSTRACT Phase separating binary fluids with the addition of immobile particles, which act as osmotic force centres, were simulated using a Lattice Boltzmann model in two dimensions. In the hydrodynamic over-damped limit, where the flow is entirely driven by capillary effects, the presence of particles that are preferentially wetted by one of the fluid components significantly affects the kinetics of the growth of the fluid domains. The late time dynamics is governed by the wetting interactions and the final size of the domains can be tailored by varying the strength of the particles-fluid interaction as well as the particles concentration. These features are predicted within a simple theoretical model and are amenable of experimental checks. INTRODUCTION The introduction of particles or “fillers” into a binary fluid-like polymeric material can represent a feasible way to control the phase separation dynamics of the system and therefore its properties and practical utility [1-3]. In particular, recent cell-dynamical simulations [4] show that in the late stage of the coarsening process, particles which are preferentially wetted by one of the fluid component can cause the domains to be pinned at a finite size. The researchers also introduced a scaling function in order to describe the dependence of the final size on the coupling constant, which controls the particle-fluid interaction as well as from the concentration of particles. However, a full verification of the proposed relation was not carried out with the simulation method used in [4]. In the present study, a lattice Boltzmann approach was developed and successfully used to explicitly show the possibility of tailoring the domain size by altering the chemical nature and the concentration of the fillers. THEORY We consider a 50:50 A/B binary mixture containing N immobile colloidal particles. We define the order parameter ϕ(r, t) as the difference in concentration between the two components of the mixture. Moreover, we assume that the system is in thermal equilibrium with a thermal bath at temperature T and neglect thermal fluctuations. The equilibrium properties of the system are described by the following free energy functional F[ϕ] = FG.L. [ϕ] + Σ i=1,N U i [ϕ]
(1)
DD6.7.1
where FG.L. [ϕ] is the usual Ginzburg-Landau free energy
τ u k r 2 r FG .L. = ∫ (− φ 2 + φ 4 + ∇φ )dr 2 4 2
(2)
that describes a single homogeneous phase for τ > 0, while it yields two-phase coexistence for τ < 0; the others coefficients u > 0 and k > 0 are phenomenological parameters. At T < Tc the two minima of the polynomial part of FG.L. represent the pure states of the mixture ϕA = ϕeq. = - ϕB. The term Ui[ϕ] , i=1,N is a potential suitable to describe the coupling i
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