3,322 research outputs found
Developed liquid film passing a smoothed and wedge-shaped trailing edge: small-scale analysis and the ‘teapot effect’ at large Reynolds numbers
Recently, the authors considered a thin steady developed viscous free-surface flow
passing the sharp trailing edge of a horizontally aligned flat plate under surface tension
and the weak action of gravity, acting vertically, in the asymptotic slender-layer limit
(J. Fluid Mech., vol. 850, 2018, pp. 924–953). We revisit the capillarity-driven short-scale
viscous–inviscid interaction, on account of the inherent upstream influence, immediately
downstream of the edge and scrutinise flow detachment on all smaller scales. We adhere to
the assumption of a Froude number so large that choking at the plate edge is insignificant
but envisage the variation of the relevant Weber number of O(1). The main focus, tackled
essentially analytically, is the continuation of the structure of the flow towards scales much
smaller than the interactive ones and where it no longer can be treated as slender. As
a remarkable phenomenon, this analysis predicts harmonic capillary ripples of Rayleigh
type, prevalent on the free surface upstream of the trailing edge. They exhibit an increase
of both the wavelength and amplitude as the characteristic Weber number decreases.
Finally, the theory clarifies the actual detachment process, within a rational description of
flow separation. At this stage, the wetting properties of the fluid and the microscopically
wedge-shaped edge, viewed as infinitely thin on the larger scales, come into play. As this
geometry typically models the exit of a spout, the predicted wetting of the wedge is related
to what in the literature is referred to as the teapot effect
The thinning of the liquid layer over a probe in two-phase flow
The draining of the thin water film that is formed between a two dimensional, infinite, initially flat oil-water interface and a smooth, symmetric probe, as the interface is advected by a steady and uniform flow parallel to the probe axis, is modelled using classical fluid dynamics.
The governing equations are nondimensionalised using values appropriate to the oil extraction industry. The bulk flow is driven by inertia and, in some extremes, surface tension while the viscous effects are initially confined to thin boundary layers on the probe and the interface. The flow in the thin water film is dominated by surface tension, and passes through a series of asymptotic regimes in which inertial forces are gradually overtaken by viscous forces. For each of these regimes, and for those concerning the earlier stages of approach, possible solution strategies are discussed and relevant literature reviewed.
Consideration is given to the drainage mechanism around a probe which protrudes a fixed specified distance into the oil. A lubrication analysis of the thin water film may be matched into a capillary-static solution for the outer geometry using a slender transition region if, and only if, the pressure gradient in the film is negative as it meets the static meniscus. The remarkable result is that, in practice, there is a race between rupture in the transition region and rupture at the tip. The analysis is applicable to the case of a very slow far field flow and offers significant insight into the non-static case.
Finally, a similar approach is applied to study the motion of the thin water film in the fully inviscid approximation, with surface tension and a density contrast between the fluids
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Exact solution to a class of functional difference equations with application to a moving contact line flow
A new integral representation for the Barnes double gamma function is derived. This is canonical in the sense that solutions to a class of functional difference equations of first order with trigonometrical coefficients can be expressed in terms of the Barnes function. The integral representation given here makes these solutions very simple to compute. Several well-known difference equations are solved by this method and a treatment of the linear theory for moving contact line flow in an inviscid fluid wedge is given.https://journals.cambridge.org/action/displayAbstract?aid=231870
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Thin-sheet flow between coalescing bubbles
When two spherical bubbles touch, a hole is formed in the fluid sheet between them, and capillary pressure acting on its tightly curved edge drives an outward radial flow which widens the hole joining the bubbles. Recent images of the early stages of this process (Paulsen et al., Nat. Commun., vol. 5, 2014) show that the radius of the hole at time grows proportional to , and that the rate is dependent on the fluid viscosity. Here, we explain this behaviour in terms of similarity solutions to a third-order system of radial extensional-flow equations for the thickness and velocity of the sheet of fluid between the bubbles, and determine the growth rate as a function of the Ohnesorge number . The initially quadratic sheet profile allows the ratio of viscous and inertial effects to be independent of time. We show that the sheet is slender for if , where is the bubble radius, but only slender for if due to a compressional boundary layer of length , after which there is a change in the structure but not the speed of the retracting sheet. For , the detailed analysis justifies a simple momentum-balance argument, which gives the analytic prediction , where is the surface tension and is the density.J.P.M. acknowledges an Engineering and Physical Sciences Research Council studentship. C.R.A. and O.A.B. acknowledge the Donors of the American Chemical Society Petroleum Research Fund for partial support of this research. All data accompanying this publication are directly available within the publication.This is the accepted manuscript of a paper published in the Journal of Fluid Mechanics (Munro JP, Anthony CR, Basaran OA, Lister JR, Journal of Fluid Mechanics, 2015, 773, doi:10.1017/jfm.2015.253). The final version is available at http://dx.doi.org/10.1017/jfm.2015.25
The role of inertia in the rupture of ultrathin liquid films
Theory and numerical simulations of the Navier–Stokes equations are used to unravel the influence of inertia on the dewetting dynamics of an ultrathin film of Newtonian liquid deposited on a solid substrate. A classification of the self-similar film thinning regimes at finite Ohnesorge numbers is provided, unifying previous findings. We reveal that, for Ohnesorge numbers smaller than one, the structure of the rupture singularity close to the molecular scales is controlled by a balance between liquid inertia and van der Waals forces, leading to a self-similar asymptotic regime with hmin ∝ τ2/5 as τ → 0, where hmin is the minimum film thickness and τ is the time remaining before rupture. The flow exhibits a three-region structure comprising an irrotational core delimited by a pair of boundary layers at the wall and at the free surface. A potential-flow description of the irrotational core is provided, which is matched with the vortical layers, allowing us to present a complete parameter-free asymptotic description of inertia-dominated film rupture.This research was funded by the Spanish MINECO, Subdirección General de Gestión de Ayudas a la Investigación, through Project No. RED2018-102829-T and by the Spanish MCIU-Agencia Estatal de Investigación through Project No. DPI2017-88201-C3-3-R, partly financed through FEDER European funds. A.M.-C. also acknowledges support from the Spanish MECD through the Grant No. FPU16/02562.Publicad
Drop spreading with random viscosity
We examine theoretically the spreading of a viscous liquid drop over a thin
film of uniform thickness, assuming the liquid's viscosity is regulated by the
concentration of a solute that is carried passively by the spreading flow. The
solute is assumed to be initially heterogeneous, having a spatial distribution
with prescribed statistical features. To examine how this variability
influences the drop's motion, we investigate spreading in a planar geometry
using lubrication theory, combining numerical simulations with asymptotic
analysis. We assume diffusion is sufficient to suppress solute concentration
gradients across but not along the film. The solute field beneath the bulk of
the drop is stretched by the spreading flow, such that the initial solute
concentration immediately behind the drop's effective contact lines has a
long-lived influence on the spreading rate. Over long periods, solute swept up
from the precursor film accumulates in a short region behind the contact line,
allowing patches of elevated viscosity within the precursor film to hinder
spreading. A low-order model provides explicit predictions of the variances in
spreading rate and drop location, which are validated against simulations
Air-cushioning in impact problems
This paper concerns the displacement potential formulation to study the post-impact influence of an aircushioning layer on the two-dimensional impact of a liquid half-space by a rigid body. The liquid and air are both ideal and incompressible and attention is focussed on cases when the density ratio between the air and liquid is small. In particular, the correction to classical Wagner theory is analysed in detail for the impact of circular cylinders and wedges
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