Thin-flame theory for a fuel droplet in slow viscous flow

Abstract

The equilibrium burning of a spherical drop of pure non-gaseous fuel in a slow convective flow of hot oxidant is examined for Lewis number unity. A Stokes or Oseen flow with modified boundary conditions to permit mass transfer at the drop surface describes the velocity field. The method of inner and outer expansions is then adopted to describe the thermal and mass-fraction profiles under the model of a direct one-step irreversible indefinitely fast chemical reaction. The thin-flame position and surface mass-transfer rate, both functions of polar angle as well as radial position when convection is added to the conventional diffusive transport, are furnished in terms of the Peclet number. It is found that the interaction of the perturbational free-streaming with the asymmetric vaporization it induces can lead to drag coefficients in excess of the Stokes value.