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Viscous fluid flows in microstructured optical fibres
Fluid Flow in Helical Channels
Fluid flow in a helical channel has application to spiral particle separators used in the mineral processing industry. A spiral separator consists of an open channel wound around a vertical axis. Flow down the channel is driven by gravity, while the curved geometry induces a secondary cross flow in the channel cross section. Under- standing the flow is central to improving the operation of spiral separators. Due to the generally shallow fluid depth, it is difficult to obtain accurate experimental observations of the flow. Hence, mathematical models are used to provide insight into the effect of both geometric and fluid properties on the flow behaviour. In general, the partial differential equations governing this fluid flow require computationally expensive numerical solution. However, the shallow nature of the flow allows a thin- film approximation to be made which reduces the PDE system to a set of linear differential equations. The derivation of the governing equations is discussed, along with the thin-film approximation. A rectangular geometry is considered as a sim- ple example. Solutions to the simplified system are compared to the full numerical solution and are found to be in good agreement. In this geometry, the thin-film solution may be written in terms of the free surface shape, which is described by an equation involving a single parameter $$. This equation is found to have no solution for $$ > 3.28.