Investigation of the hydrodynamics of a two component lattice Bhatnagar-Gross-Krook fluid.

We present results from a computer simulation of an immiscible two component fluid, using a Lattice Boltzmann BGK D2Q9 scheme. Each fluid component is identified by a colour tag (either red or blue), and the immiscible behaviour arises from the implementation of colour segregation imposed on the lattice fluid. For two dimensional, microcurrent free planar interfaces between the two immiscible fluids we derive expressions for static interfacial tensions and interfacial distributions of the two fluids. Extending our analysis to curved interfaces, we propose a scheme for incorporating the influence of interfacial microcurrents that is based upon general symmetry arguments and is correct to second order in lattice velocity. The analysis demonstrates that the interfacial microcurrents have only second order influence upon the macroscopic behaviour of the model. We find good agreement between our calculations and simulation results based on the microcurrent stream function and surface tension results from the pressure tensor or Laplace law.We examine the tangential stress transmission in the immiscible interface, by the investigation of the relationship between fluid shear and fluid viscosity across a plar nar symmetric interface. We find comprehensive agreement with theory, for the tangential hydrodynamic boundary condition. The examination of normal stress transmission in our two dimensional simulation is facilitated from correct behaviour of tangential stress. We develop a Fourier analysis technique which allows a quanti-tative analysis of the anisotropy of the interface. This technique has facilitated the development of a further modification to the interface perturbation, which improves the macroscopic surface tension isotropy and reduces the magnitude of the parasitic microcurrent.As an application of our model we simulate the induced deformation and burst of neutrally buoyant fluid drops subjected to external simple shear and solenoidal irrotational flow. Qualitatively the drops are seen to deform and orientate correctly, with respect to the external flow. Measuring the dependence of critical shear rate for drop rupture on flow parameters, our results validate the method over a range of simulation variables. The model's interfacial tension parameter < 7, undeformed drop radius R, and BGK relaxation parameter u are all found to have the correct influence upon the burst process as required by hydrodynamic theory. We note that the macroscopic surface tension and fluid viscosity are coupled, however this does not limit the application of the model.