I present observations of interfacial tension between miscible pairs o
f silicate liquid and propose a theoretical model that quantitatively
accounts for them. Viscoelastic rheology of the liquids permits the es
tablishment of gradient stress completely analogous to thermal stress
in Maxwell solids; this is expected whenever the time scale of diffusi
on is shorter than the Maxwell relaxation time. The existence of gradi
ent stress may profoundly affect interface processes during mixing of
miscible fluids.