Strongly nonlinear interfacial dynamics in core–annular flows

Abstract

Nonlinear stability of a pressure driven core-annular flow is analysed, and a study of the large-amplitude interfacial dynamics is reported in the limit of a small ratio β of the annular clearance to the radius. An asymptotic nonlinear evolution equation for the annular film thickness is derived as a general case which involves shear coupling with the core flow. We discuss the effects of the surface tension parameter and viscosity stratification of various orders in β. The governing equation is investigated by solving it on extended intervals. Long-term simulations in a wide range of parameters reveal rich dynamics of wave patterns and coherent structures. Only in a narrow window of the small control parameters can it be described by the weakly nonlinear dissipative-dispersive equation, exhibiting behaviour of strictly bounded solutions which varies from a spatiotemporal chaos to the quasi-steady wavetrains. For sufficiently high surface tension, some pulses (to which the primary instabilities saturate) can coalesce into stable larger structures. This leads to the formation of solitary humps via cascade absorption. Substantial thickness non-uniformities can cause collapse of the perfect CAFF owing to the lens formation or extreme film thinning. Our critical value of the control parameter is in good agreement with the experimental data by Aul & Olbricht. Under strong coupling of the core flow with a less viscous annular film the interfacial evolution settles to a train of inverted pulses. Long-time behaviour in the intermediate range of parameters is diversified from regular pulse trains, to the formation of wide multi-peak structures or blow-up, depending on the apparent involvement of the core.