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In this paper, a two phase model to compute liquid-liquid flows is presented. We consider that one phase is a highly viscous thermodependent liquid (polymer phase), whereas the second one is a low viscosity low temperature fluid (water). The first part of this paper concerns capture of the interface between the water and the polymer (or determination of the phase field function). Classical VOF and Level set techniques have been implemented and were ameliorated using mesh adaptation techniques.doi:10.1063/1.2740838 fatcat:ys5xakh2yvgetkt6spdrg4tro4