On the spreading of liquid lenses over rheologically complex liquid films

Droplet spreading over non-Newtonian liquid substrates occurs in a variety of technological and biological applications. A characteristic example of the latter is the delivery of aerosol drugs with droplet spreading taking place along the airway mucus of the lungs.. Here, we investigate the spreading dynamics of a liquid lens over a thin fluid layer which exhibits rheolgically complex behaviour. We consider liquids films following the Ostwald-de Waele constitutive equation or the Oldroyd-B model in the limit of weak viscoelasticity. In the limit of both a thin droplet and a thin subphase, we employ lubrication theory to derive a coupled system of evolution equations for the interface positions and the resulting governing equations are solved numerically using the finite element method. The results of an extensive parametric analysis to examine the effects of the physical parameters and rheological characteristics on the flow will be discussed.