Under flow conditions, the dynamic contact angle replaces the equilibrium contact angle. Correlation of dynamic contact angles as a function of the capillary number in liquid-liquid-solid systems is important in a number of applications. For instance, it is one of the ways used to predict water penetration into an oil-filled porous medium. The Cahn-Thermo device is used to measure the excess force needed to plunge a plate vertically into a liquid-liquid interface or pull it out. This force is used to calculate the dynamic contact angle. Polydimethylsiloxane (PDMS) with different viscosities were used for the upper phase and water for the lower phase (viscosity ratios of 95-485). An algebraic expression that predicts the dynamic contact angles has been derived using the concept that the total viscous dissipation is equal to the surface work in the contact line region. This result, together with a result based on a regular hydrodynamic theory, was compared to the experiments on the advancing dynamic contact angles. The advancing dynamic contact angles measured were from 90° to 105°, agreed with the theory and one adjustable parameter related to the ratio of microscopic to the macroscopic length scale that is recovered is found to depend inversely on the viscosity ratio. The parameter itself varies from 2 to 70. The receding contact angles showed significant scatter. A closer photographic examination showed the meniscus to be unstable.