Convective instabilities in concurrent two phase flow: Part I. Linear stability

The linear stability of thermally stratified horizontal two‐phase Couette flow is analyzed for the case of a constant vertical temperature gradient. Instabilities driven by buoyancy, surface tension gradients, or shear are allowed for. It is shown that the instability can take three possible forms: streamwise oriented roll vortices, long interfacial waves, and short Tollmien‐Schlichting waves. It is shown that the stability limits for rolls are identical to those for plane, stagnant layers. A long wave expansion is presented and the stability limits for this mode are given algebraically. The nonexistence of a Squire's Theorem is demonstrated and some numerical experiments at moderate Reynolds numbers are described. Detailed comparisons with previous work are possible for only one fluid pair, but it is shown that reasonably accurate statements may be made to determine which mode may manifest itself in any given experimental situation.