Thin film flow over a spinning disk: Experiments and direct numerical simulations
Jason Stafford, Nwachukwu Uzo, Enrico Piccoli, Camille Petit, Omar K. Matar
Abstract
The dynamics of thin liquid films flowing over a spinning disk is studied through a combination of experiments and direct numerical simulations. We consider a comprehensive range of interfacial flow regimes from waveless to three-dimensional (3D) waves, and for previously unexplored inertia-dominated conditions that have practical relevance. The transition between these regimes is categorized within a phase map based on two governing parameters that correspond to modified inverse Weber ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>λ</a:mi> </a:math> ) and Ekman numbers ( <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:msub> <b:mi>r</b:mi> <b:mtext>disk</b:mtext> </b:msub> </b:math> ). Our findings show that stationary two-dimensional (2D) spiral waves, which unfold in the direction of rotation from the Coriolis effect, transition to 3D waves with the emergence of small perturbations on the wavefronts. These nonstationary structures grow asymmetrically in the 2D-3D transitional region, and detach from the parent spiral wave to form wavelets or so-called <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mi mathvariant="normal">Λ</c:mi> </c:math> solitons. We show that during and after this wave formation process, flow circulations unique to the spinning disk arrangement are present within the main wave hump. Furthermore, when combined with observations of wall strain rates and topology within the film, these findings elucidate the mechanisms that underpin the apparent wave-induced interfacial turbulence effects observed for spinning disk flows.