Acta. lleohanioa. 66, 233 -249 (1987) ACTA MECHANICA ® by SpriDger-Verlag 1987 Interface Shapes in a Torsionally Oscillating, Layered Medium of Viscoelastic Liquids• By A. Siginer, Auburn, .A1aba.ma With 1 Figure (Received Ja,nirmrg 9, 1986: ret1Uw Hard. Summary The :free surface motion of a layered medium of liquids in a gravitationally sta.ble configuration, resting on top of a layer of mercury, driven by a toraionally oecillating, cyHndrioeJ outer wa.Il is investigated. The non-linea.r problem in the unknown physical domain is expressed a.s a series of linear problema in the rest state by mee.na of a domain perturbation method. The flaw vari&blea a.n.d the stress are expa.nded into series in terms of the amplitude of the of the cylinder. The sh&pes in the mean of the interfa.ces between layers and the flow field are determined up to second order in the perturbation parameter, the amplitude of the oacilla.tion. (I) a J.l c. {J, l¥ 1] lfi s "'1- 012 ,.. To I u "· "· w 8 Nomenclature Density Modified pressure field Amplitude of the oscillation Frequency of the oscillation Interfacial value of the surface tension Dyna.mic visooaity Material functionB Complex visooBity Stream function Poaition vector at time I = -c Tb.e first two Rivlin-Eriolaen oonata.nts Quadratic shear rela.xa.tion modulus Time Velocity vector Velocity oomponents Extra stress tenaor * Presented at the Xth Ca.ruJ.dian. of Applied MeehanicB, The Universit y of Western Ontario, London. Onta.rio. Canada, June 2-7, 1985.