Interaction of two spheres in an unbounded stratified fluid

The motion of two spherical particles translating with equal velocities in an unbounded and vertically stratified viscous fluid is considered. The for ce experienced by each sphere is determined using the method of matched asy mptotic expansions to small values of the stratification parameter alpha. T he distance between the particle centres is assumed very much larger than t he particle radius a and the particles are supposed to be sufficiently sepa rated so that the second sphere is located in the outer region of expansion of the first sphere. The lift and the drag on the spheres are found up to first order of calculation and plotted against the distance between the sph eres. The effect of inertia is studied through the variation in low values of the Reynolds number whose order has been taken as O(/alpha/(1/3)). The v elocity components are computed when the spheres are aligned along the axes . It has been found that the drag is increased due to stratification. The s pheres are found to experience no lift when they are aligned in the horizon tal plane. The presence of the second sphere is found to reduce the drag on the first sphere and the contributions of stratification and fluid inertia compensate each other exactly when the spheres are sufficiently close i.e. up to the order O(a/alpha/(1/3)).