Modelling the Rolling Motion of a Momentum Driven Droplet

Abstract

Abstract Free surfaces, with their associated surface tension energy, play a prominent role in many areas of fluid dynamics. The motions of these free surfaces and the effects of the controlling forces become particularly relevant when considering small droplets or small scale flows in micro-structural domains. Surface tension, in conjunction with structural interaction (as characterised by the contact angle), may also give rise to tractions that are capable of driving the motion of the fluid (as seen in porous media). The effects of surface tension on the momentum driven motion of a small droplet of honey were first investigated by Dussan and Davis (1974). The qualitative experimental observations made by these authors led to the formulation of a kinematic analysis in which the basic assumption was that the interface rolls onto or off of the solid substrate. In the present work we initially look at how numerical Computational Fluid Dynamic (CFD) modelling can be used to repeat the previous authors’ work, and subsequently, we use the basic model to extend their analysis. The motion of a small droplet of honey (1 cm3), moving under the influence of gravity, is modelled. The droplet is initially at rest in a semi-hemispherical configuration upon a plane inclined at 30° to the horizontal. Massless computational particles are introduced in a semicircular configuration close to the droplet surface. The particles are at a constant radial distance from the centre of the droplet and are used to mimic dye or marker particles at the free surface. The motion of the droplet and associated particles, in time, is presented. The resulting motions are compared with existing experimental data (Dussan and Davis, 1974). Using CFD modelling and marker particles we represent numerically the experimental work of Dussan and Davis (1974). Using CFD modelling, dimensional analysis and marker particles within the fluid domain gives an improved insight into the tractions and motions present within the droplet fluid flow.