A simplified model of the onset of air entrainment in curtain coating at small Capillary number

Blake et al. [Blake, T.D., Clarke, A. and Ruschak, K.J., 1994, Hydrodynamic assist of dynamic wetting. AIChE J, 40(2):229–242; Blake, T.D., Bracke, M. and Shikhmurzaev, Y.D., 1999, Experimental evidence of nonlocal hydrodynamic influence on the dynamic contact angle. Phys Fluids, 11(8):1995–2007] reported a new effect from experimental observations of curtain coating, namely that the wetting line may be unstable for contact angles above some critical contact angle, where this critical angle is less than 180° and typically between 160° and 170°. This experimental observation was unexpected (e.g. see Blake and Ruschak [Blake, T.D. and Ruschak, K.J., 1979, Maximum speed of wetting. Nature, 282:489–491]). Here an unsteady formulation of the interface formation model is used to successfully explain this effect. The results show that the flow becomes unstable when the contact angle is above some critical value, typically between 160° and 175° for parameter values similar to those of Blake et al. [Blake, T.D., Bracke, M. and Shikhmurzaev, Y.D., 1999, Experimental evidence of nonlocal hydrodynamic influence on the dynamic contact angle. Phys Fluids, 11(8):1995–2007].