Thin-flame theory for droplet combustion at low Grashof numbers

The weakly-buoyant, quasi-steady burning of a spherical droplet (of radius a) in an infinite medium is studied theoretically for unity Lewis number and infinite chemical reaction rate, using the Boussinesq model. Approximate solution is given to the non-linear outer equations by applying the Oseen linearization to the unbounded low Grashof number (Gr) flow. This outer solution (scaled as aGr^-1/2) is then matched to the inner convective-diffusive solution treated with the Schvab-Zeldovich formulation. Half-order asymptotic expansions are adopted to describe the temperature and mass-fraction profiles. The flame-sheet position, as a function of polar angle and radial position, and mass burning rate are determined. The results compare favorably with experiments. In our perturbation analysis for small normalized density difference ε, flame characteristics are found to scale with Gr ^1/2.