Slowly accreting ice due to supercooled water impacting on a cold surface

We study phase separation in thin films using the Navier-Stokes Cahn-Hilliard equations in the lubrication approximation, modeling substrate-film interactions with a van der Waals potential. We investigate the thin-film equations numerically and compare them with experimental results. We find that the model captures the qualitative features of real phase-separating fluids, in particular the tendency of concentration gradients to produce film thinning and surface roughening. The ultimate outcome of the phase separation depends strongly on the dynamical backreaction of concentration gradients on the flow, as we demonstrate when a shear stress is applied at the film's surface. When the backreaction is small, the phase domain boundaries align with the direction of the imposed stress, while as the backreaction is made larger, the domains begin to align in the perpendicular direction.PACS numbers: 47.15.gm, 47.55.-t, 64.75.+g When a binary fluid is cooled below the critical temperature, the homogeneous state is energetically unfavourable and the system spontaneously phase-separates and forms domains rich in either fluid component [1,2]. Due to the relevance of phase-separating thin films in industrial applications [3], many experiments and numerical simulations focus on understanding how phase separation is altered if the binary fluid is confined in a thin layer. We propose a lubrication approximation based on the coupled Navier-Stokes Cahn-Hilliard equations to explain the main features of these studies.Several recent experiments have clarified the different regimes of domain growth in a binary thin film. Wang and Composto [4] have identified early, intermediate, and late stages of evolution. The early stage comprises threedimensional domain growth, while the intermediate stage is characterized by the formation of wetting layers at the film boundaries, the thinning of the middle layer, and significant surface roughening. Due to the thinning of the middle layer, the sandwich-like structure breaks up and matter from the wetting layer flows back into the bulk. Thus, a late stage is reached, consisting of bubbles coated by thin wetting layers. This characterization of the evolution has been seen in other experiments [5,6], although clearly a variety of behaviors is possible, depending on the wetting properties of tnhe mixture. Our model captures the essential features of this evolution, in particular the tendency for concentration gradients to promote film rupture and surface roughening.In a series of papers, Das et al. [7,8] investigate the behaviour of binary fluids with wetting. In [7] they specialize to ultra-thin films. In bulk mixtures, where one of the fluid components is preferentially attracted to the boundary, a layer rich in that component may be established there, followed by depletion layer, and so on. This so-called spinodal wave propagates into the bulk [8]. In * Electronic address: jeanluc@imperial.ac.uk ultra-thin films, the film thickness is less than a single spinodal wavelength and the spinodal wav...

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“…This velocity field may also be obtained by imposing a shear stress τ at the surface, provided τ = ∇σ [20]. We carry out simulations using Eq.…”

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confidence: 99%

Dynamical effects and phase separation in cooled binary fluid films

Náraigh

Thiffeault

2007

Phys. Rev. E

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“…However, quantitative analysis of temporal evolution of spreading diameter, illustrated in Figure 3, shows that the effect of incoming cold air flow has an insignificant effect on wetting dynamics on hydrophilic and hydrophobic surfaces which arise from strong crystallization process at solid-liquid interface combined with sever increase in contact line viscosity up to 8 and 4.3 fold at −30 °C and −20 °C , respectively [41,42]. Furthermore, the effect of the capillary ridge become important where exposed air flow on thin film of super cooled water comes into contact with solid material [46]. On the other hand, due to the fact that both homogeneous nucleation, which weakens surface tension, and heterogeneous nucleation, which results in an increase in hydrophilicity by changing contact angle [17], enhances the chance of pinning on a polished aluminum surface and the resulting normal and shear force of stagnation flow cannot overcome the formed capillary ridge.…”

Section: Resultsmentioning

confidence: 99%

Supercooled Water Droplet Impacting Superhydrophobic Surfaces in the Presence of Cold Air Flow

2017

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Abstract:In the present work, an investigation of stagnation flow imposed on a supercooled water drop in cold environmental conditions was carried out at various air velocities ranging from 0 (i.e., still air) to 10 m/s along with temperature spanning from −10 to −30 • C. The net effect of air flow on the impacting water droplet was investigated by controlling the droplet impact velocity to make it similar with and without air flow. In cold atmospheric conditions with temperatures as low as −30 • C, due to the large increase of both internal and contact line viscosity combined with the presence of ice nucleation mechanisms, supercooled water droplet wetting behavior was systematically affected. Instantaneous pinning for hydrophilic and hydrophobic surfaces was observed when the spread drop reached the maximum spreading diameter (i.e., no recoiling phase). Nevertheless, superhydrophobic surfaces showed a great repellency (e.g., contact time reduction up to 30% where air velocity was increased up to 10 m/s) at temperatures above the critical temperature of heterogeneous ice nucleation (i.e., −24 • C). However, the freezing line of the impacting water droplet was extended up to 2-fold at air velocity up to 10 m/s where substrate temperature was maintained below the aforementioned critical temperature (e.g., −30 • C).

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“…Other approaches which also include the gravity and capillary forces, surface curvature and heat conduction through the ice and water layer have been derived by Myers et al [101,102,103,104].…”

Section: Improved Accretion Methodsmentioning

confidence: 99%

Eulerian method for ice crystal icing in turbofan engines

Norde¹

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Slowly accreting ice due to supercooled water impacting on a cold surface

Cited by 114 publications

References 37 publications

Dynamical effects and phase separation in cooled binary fluid films

Dynamical effects and phase separation in cooled binary fluid films

Supercooled Water Droplet Impacting Superhydrophobic Surfaces in the Presence of Cold Air Flow

Eulerian method for ice crystal icing in turbofan engines

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