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 Journal of Fluid MechanicsJournal Prestige (SJR): 1.591 Citation Impact (citeScore): 3Number of Followers: 150      Hybrid journal (It can contain Open Access articles) ISSN (Print) 0022-1120 - ISSN (Online) 1469-7645 Published by Cambridge University Press  [372 journals]
• Particle fountains in a confined environment
• Authors: Martin C. Lippert; Andrew W. Woods
Pages: 28 - 42
Abstract: We present new experiments and theoretical models of the motion of relatively dense particles carried upwards by a liquid jet into a laterally confined space filled with the same liquid. The incoming jet is negatively buoyant and rises to a finite height, at which the dense mixture of liquid and particles, diluted by the entrainment of ambient liquid, falls back to the floor. The mixture further dilutes during the collapse and then spreads out across the floor and supplies an up-flow outside the fountain equal to the source volume flux plus the total entrained volume flux. The fate of the particles depends on the particle fall speed, $u_{fall}$ , compared to (i) the characteristic fountain velocity in the fountain core, $u_{F}$ , (ii) the maximum upward velocity in the ambient fluid outside the fountain, $u_{u}(0)$ , which occurs at the base of the fountain, and (iii) the upward velocity in the ambient fluid above the top of the fountain associated with the original volume flux in the liquid jet, $u_{BG}$ . From this comparison we identify four regimes. (I) If $u_{fall}>u_{F}$ , then the particles separate from the fountain and settle on the floor. (II) If $u_{F}>u_{fall}>u_{u}(0)$ , the particles are carried to the top of the fountain but then settle as the collapsing flow around the fountain spreads out across the floor; we do not observe particle suspension in the background flow. (III) For $u_{u}(0)>u_{fall}>u_{BG}$ we observe a particle-laden layer outside the fountain which extends from the floor of the tank to a point below the top of the fountain. The density of this lower particle-laden layer equals the density of the collapsing fountain fluid as it passes downwards through this interface. The collapsing fluid then spreads out horizontally through the depth of this particle-laden layer, instead of continuing downwards around the rising fountain. In the lower layer, the negatively buoyant source fluid in fact rises as a negatively buoyant jet, but this transitions into a fountain above the upper interface of the particle-laden layer. The presence of the particles in the lower layer reduces the density difference between fountain and environment, leading to an increase in the fountain height. (IV) If
PubDate: 2018-11-25T00:00:00.000Z
DOI: 10.1017/jfm.2018.645
Issue No: Vol. 855 (2018)

• From electrodiffusion theory to the electrohydrodynamics of leaky
dielectrics through the weak electrolyte limit
• Authors: Yoichiro Mori; Y.-N. Young
Pages: 67 - 130
Abstract: The Taylor–Melcher (TM) model is the standard model for describing the dynamics of poorly conducting leaky dielectric fluids under an electric field. The TM model treats the fluids as ohmic conductors, without modelling the underlying ion dynamics. On the other hand, electrodiffusion models, which have been successful in describing electrokinetic phenomena, incorporate ionic concentration dynamics. Mathematical reconciliation of the electrodiffusion picture and the TM model has been a major issue for electrohydrodynamic theory. Here, we derive the TM model from an electrodiffusion model in which we explicitly model the electrochemistry of ion dissociation. We introduce salt dissociation reaction terms in the bulk electrodiffusion equations and take the limit in which the salt dissociation is weak; the assumption of weak dissociation corresponds to the fact that the TM model describes poor conductors. Together with the assumption that the Debye length is small, we derive the TM model with or without the surface charge convection term depending upon the scaling of relevant dimensionless parameters. An important quantity that emerges is the Galvani potential (GP), the jump in voltage across the liquid–liquid interface between the two leaky dielectric media; the GP arises as a natural consequence of the interfacial boundary conditions for the ionic concentrations, and is absent under certain parametric conditions. When the GP is absent, we recover the TM model. Our analysis also reveals the structure of the Debye layer at the liquid–liquid interface, which suggests how interfacial singularities may arise under strong imposed electric fields. In the presence of a non-zero GP, our model predicts that the liquid droplet will drift under an imposed electric field, the velocity of which is computed explicitly to leading order.
PubDate: 2018-11-25T00:00:00.000Z
DOI: 10.1017/jfm.2018.567
Issue No: Vol. 855 (2018)

serrations: a new control concept
• Authors: P. Chaitanya; P. Joseph, S. Narayanan, J. W. Kim
Pages: 131 - 151
PubDate: 2018-11-25T00:00:00.000Z
DOI: 10.1017/jfm.2018.620
Issue No: Vol. 855 (2018)

• Newly identified principle for aerodynamic heating in hypersonic flows
• Authors: Yiding Zhu; Cunbiao Lee, Xi Chen, Jiezhi Wu, Shiyi Chen, Mohamed Gad-el-Hak
Pages: 152 - 180
Abstract: Instability evolution in a transitional hypersonic boundary layer and its effects on aerodynamic heating are investigated over a 260 mm long flared cone. Experiments are conducted in a Mach 6 wind tunnel using Rayleigh-scattering flow visualization, fast-response pressure sensors, fluorescent temperature-sensitive paint (TSP) and particle image velocimetry (PIV). Calculations are also performed based on both the parabolized stability equations (PSE) and direct numerical simulations (DNS). Four unit Reynolds numbers are studied, 5.4, 7.6, 9.7 and $11.7\times 10^{6}~\text{m}^{-1}$ . It is found that there exist two peaks of surface-temperature rise along the streamwise direction of the model. The first one (denoted as HS) is at the region where the second-mode instability reaches its maximum value. The second one (denoted as HT) is at the region where the transition is completed. Increasing the unit Reynolds number promotes the second-mode dissipation but increases the strength of local aerodynamic heating at HS. Furthermore, the heat generation rates induced by the dilatation and shear processes (respectively denoted as $w_{\unicode[STIX]{x1D703}}$ and $w_{\unicode[STIX]{x1D714}}$ ) were investigated. The former item includes both the pressure work $w_{\unicode[STIX]{x1D703}1}$ and dilatational viscous dissipation $w_{\unicode[STIX]{x1D703}2}$ . The aerodynamic heating in HS mainly arose from the high-frequency compression and expansion of fluid accompanying the second mode. The dilatation heating, especially $w_{\unicode[STIX]{x1D703}1}$ , was more than five times its shear counterpart. In a limited region, the underestimated $w_{\unicode[STIX]{x1D703}2}$ was also larger than $w_{\unicode[STIX]{x1D714}}$ . As the second-mode waves decay downstream, the low-frequency waves continue to grow, with the consequent shear-induced heating increasing. The latter brings about a second, weaker growth of surface-temperature HT. A theoretical analysis is provided to interpret the temperature distribution resulting from the aerodynamic heating.
PubDate: 2018-11-25T00:00:00.000Z
DOI: 10.1017/jfm.2018.646
Issue No: Vol. 855 (2018)

• Marangoni-enhanced capillary wetting in surfactant-driven superspreading
• Authors: Hsien-Hung Wei
Pages: 181 - 209
Abstract: Superspreading is a phenomenon such that a drop of a certain class of surfactant on a substrate can spread with a radius that grows linearly with time much faster than the usual capillary wetting. Its origin, in spite of many efforts, is still not fully understood. Previous modelling and simulation studies (Karapetsas et al. J. Fluid Mech., vol. 670, 2011, pp. 5–37; Theodorakis et al. Langmuir, vol. 31, 2015, pp. 2304–2309) suggest that the transfer of the interfacial surfactant molecules onto the substrate in the vicinity of the contact line plays a crucial role in superspreading. Here, we construct a detailed theory to elaborate on this idea, showing that a rational account for superspreading can be made using a purely hydrodynamic approach without involving a specific surfactant structure or sorption kinetics. Using this theory it can be shown analytically, for both insoluble and soluble surfactants, that the curious linear spreading law can be derived from a new dynamic contact line structure due to a tiny surfactant leakage from the air–liquid interface to the substrate. Such a leak not only establishes a concentrated Marangoni shearing toward the contact line at a rate much faster than the usual viscous stress singularity, but also results in a microscopic surfactant-devoid zone in the vicinity of the contact line. The strong Marangoni shearing then turns into a local capillary force in the zone, making the contact line in effect advance in a surfactant-free manner. This local Marangoni-driven capillary wetting in turn renders a constant wetting speed governed by the de Gennes–Cox–Voinov law and hence the linear spreading law. We also determine the range of surfactant concentration within which superspreading can be sustained by local surfactant leakage without being mitigated by the contact line sweeping, explaining why only limited classes of surfactants can serve as superspreaders. We further show that spreading of surfactant spreaders can exhibit either the $1/6$ or $1/2$ power law, depending on the ability of interfacial surfactant to transfer/leak to the bulk/substrate. All these findings can account for a variety of results seen in experiments (Rafai et al. Langmuir, vol. 18, 2002, pp. 10486–10488; Nikolov & Wasan, Adv. Colloid Interface Sci., vol. 222, 2015, pp. 517–529) and simulations (Karapetsas et al. 2011). Analogy to thermocapillary spreading is also made, reverberating the ubiquitous role of the Marangoni effect in enhancing dynamic wetting driven by non-uniform surface tension.
PubDate: 2018-11-25T00:00:00.000Z
DOI: 10.1017/jfm.2018.626
Issue No: Vol. 855 (2018)

• Two-dimensional pulse dynamics and the formation of bound states on
electrified falling films
• Authors: M. G. Blyth; D. Tseluiko, T.-S. Lin, S. Kalliadasis
Pages: 210 - 235
Abstract: The flow of an electrified liquid film down an inclined plane wall is investigated with the focus on coherent structures in the form of travelling waves on the film surface, in particular, single-hump solitary pulses and their interactions. The flow structures are analysed first using a long-wave model, which is valid in the presence of weak inertia, and second using the Stokes equations. For obtuse angles, gravity is destabilising and solitary pulses exist even in the absence of an electric field. For acute angles, spatially non-uniform solutions exist only beyond a critical value of the electric field strength; moreover, solitary-pulse solutions are present only at sufficiently high supercritical electric-field strengths. The electric field increases the amplitude of the pulses, can generate recirculation zones in the humps and alters the far-field decay of the pulse tails from exponential to algebraic with a significant impact on pulse interactions. A weak-interaction theory predicts an infinite sequence of bound-state solutions for non-electrified flow, and a finite set for electrified flow. The existence of single-hump pulse solutions and two-pulse bound states is confirmed for the Stokes equations via boundary-element computations. In addition, the electric field is shown to trigger a switch from absolute to convective instability, thereby regularising the dynamics, and this is confirmed by time-dependent simulations of the long-wave model.
PubDate: 2018-11-25T00:00:00.000Z
DOI: 10.1017/jfm.2018.592
Issue No: Vol. 855 (2018)

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