Slow flow of a non‐newtonian fluid past a droplet

The problem of slow flow past a droplet is considered where both materials may be represented as fluids of grade 3 and where the outer fluid is of infinite extent. Both non‐Newtonian and inertial effects are included in the analysis. A double perturbation technique and the method of matched asymptotic expansions are employed to obtain solutions to the equation of motion. Solutions, in the form of Legendre polynomial series, are obtained for the stream function (both outside and inside the droplet), for the drag force exerted on the droplet, and for the shape of the droplet. The results obtained are in complete agreement with those obtained by other workers for the flow of a Newtonian fluid past a Newtonian droplet and for the flow of a fluid of grade 3 past a solid sphere. Droplet shape predictions are in qualitative agreement with experimentally observed shapes.