Abstract
We consider the fluid dynamics of the chocolate fountain. Molten chocolate is a mildly shear-thinning non-Newtonian fluid. Dividing the flow into three main domains—the pumped flow up the centre, the film flow over each dome, and the freely falling curtain flow between the domes—we generate a wide-ranging study of Newtonian and non-Newtonian fluid mechanics. The central pumped flow is a benchmark to elucidate the effects of shear-thinning. The dome flow can be modelled as a thin-film flow with the leading-order effects being a simple balance of gravity and viscosity. Finally, the curtain flow is analytically intractable but is related to the existing theory of water bells (both inviscid and viscous). In pipe flow, Newtonian fluids exhibit a parabolic velocity profile; shear-thinning makes the profile more blunted. In thin-film flow over the dome, gravitational and viscous effects balance and the dome shape is not important beyond the local slope. We find that the chocolate thins and slows down as it travels down the dome. Finally, in the curtain flow, we predict the shape of the falling sheet for an inviscid fluid, and compare this with the literature to predict the shape for a viscous fluid, having shown that viscous forces are too great to ignore. We also find that the primary effect driving the shape of the curtain (which falls inwards towards the axis of the fountain) is surface tension. We find that the three domains provide excellent introductions to non-Newtonian mechanics, the important mathematical technique of scaling, and how to manipulate existing data to make our own predictions. We also find that the topic generates interest among the public in our engagement work.
Highlights
Chocolate fountains (see figure 1(a)) are a popular feature at special events
The resulting mixture of chocolate fondue poses an interesting fluid mechanics problem, as it is non-Newtonian: this is to say, its viscosity depends on how it moves through the fountain
We investigate each regime in turn: the upwards flow through the centre of the fountain; the film flow over each dome; and the freely
Summary
Chocolate fountains (see figure 1(a)) are a popular feature at special events. From table-top machines that are 30 cm tall, to large displays several metres tall, fountains normally consist of a series of stacked dome-shaped tiers over which melted chocolate flows, after being pumped up through a central tube from a basin at the bottom. How well the chocolate runs through the fountain is largely dictated by the viscosity of the fondue. In order to keep it flowing smoothly and generating aesthetic curtains, operators are often seen to add liquids such as vegetable oil. The resulting mixture of chocolate fondue poses an interesting fluid mechanics problem, as it is non-Newtonian: this is to say, its viscosity depends on how it moves through the fountain
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