This study investigates the flow of a thin annular film driven by an axial force in a microtube. Partial wetting is taken into account using the diffuse interface theory and the film dynamics is approximated by a long-wave mesoscopic model. Using time integration and path-following method, we study the different traveling waves. A rich behavior is brought to light and notably the existence of drop train with a complex spatial organization. We determine the genesis of the drop train related to the coarsening phenomenon. Increasing the domain size, the complexity of these pattern increases by breaking the translation symmetry. Thus, for low mean water content, flow in a microtube occurs via drop train patterns.

This paper analyzes the possibility to obtain selective transport of microparticles depending their size. The particles are suspended in a fluid confined in modulated channels and a periodic pumping moves back and forth the fluid without net displacement. Using numerical simulation and bifurcation analysis tools, we show the existence of particle drift under the Stokes assumption of the fluid flow. For specific parameter ranges, the particle transport can be selective. The transport solution and the selectivity are related to (de)synchronization transitions in forced non-linear oscillators. We reveal that chaotic transitions are a key factor to drop from a bounded dynamics to a net transport. This transport phenomenon can be relevant for heavy particles in suspended in the air in microgravity environnement.

This work focuses on the simulation and experimental study of directional wicking of water on a surface structured by open microchannels. Stainless steel was chosen as the material for the structure motivated by industrial applications as fuel cells. Inspired by nature and literature, we designed a fin type structure. Using Selective Laser Melting (SLM) the fin type structure was manufactured additively with a resolution down to about 30 μm. The geometry was manufactured with three different scalings and both the experiments and the simulation show that the efficiency of the water transport depends on dimensionless numbers such as Reynolds and Capillary numbers. Full 3D numerical simulations of the multiphase Navier-Stokes equations using Volume of Fluid (VOF) and Lattice-Boltzmann (LBM) methods reproduce qualitatively the experimental results and provide new insight into the details of dynamics at small space and time scales. The influence of the static contact angle on the directional wicking was also studied. The simulation enabled estimation of the contact angle threshold beyond which transport vanishes in addition to the optimal contact angle for transport.

This paper analyzes the possibility of obtaining the selective transport of microparticles suspended in air in a microgravity environment through modulated channels without net displacement of air. Using numerical simulation and bifurcation analysis tools, we show the existence of intermittent particle drift under the Stokes assumption of the fluid flow. The particle transport can be selective and the direction of transport is controlled only by the kind of pumping used. The selective transport is interpreted as a deterministic ratchet effect due to spatial variations in the flow and the particle drag. This ratchet phenomenon could be applied to the selective transport of metal particles during the short duration of microgravity experiments.

Liquid film or drop wicking on solid surface without any external energy input is highly desirable in specific industrial processes. This paper proposes a numerical study of the dynamics of liquid wicking on geometrically structured flat surface. We consider structures deduced from flat surface by super-imposing a series of identical parallel channels, the ensemble being made of the same material. Channels exhibit arrow-shaped patterns. We analyse drop wicking on such a structure using numerical simulation and experiment. Both approaches reveal non symmetric wicking clearly exhibiting a privileged direction. The simulation captures the evolution of the liquid/air interface at smaller time scales and reveals wicking with rapid pulses suggested by the experiment.

Chapter 2 Soil Wettability Philippe Beltrame, Philippe BeltrameSearch for more papers by this author Philippe Beltrame, Philippe BeltrameSearch for more papers by this author Book Editor(s):Guilhem Bourrié, Guilhem BourriéSearch for more papers by this author First published: 30 November 2018 https://doi.org/10.1002/9781119438045.ch2 AboutPDFPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShareShare a linkShare onFacebookTwitterLinked InRedditWechat Summary Wettability is a factor particularly important in areas having a climate characterized by extreme events: periods of drought interspersed with intense rain. In soil science, a fundamental consequence of wettability is the phenomenon of capillarity. This chapter conveys the notion of wettability and its interpretation for flat surfaces. It illustrates the impact on water transfer in soils and presents current methods for measuring wettability. The interaction between molecules of two media is not localized at the interface it has a range that can be quite long, for van der Waals forces in particular. Therefore, for very thin films of 10-100 nm, these interactions are not negligible. The chapter outlines the key results that will be useful to understand wetting dynamics in porous environments. Finally, the chapter explains why conventional models are inadequate and gives a few avenues concerning recent models still in their development process. Soils as a Key Component of the Critical Zone 3: Soils and Water Circulation, Volume 3 RelatedInformation

A challenging problem of water transfer in unsaturated soils is the hydraulic function of the macroporosity as opened cracks, earthworm burrows, and channels left by roots. In macropores, free surface flow can be a dominant process especially for unsaturated soils. In this context, the fluid transfer reveals to be complex [1] and conceptual approaches of film flow (see for instance [2]) are not able to explain the associated flow regimes. Recently, using the Stokes equation and taking into account the macropore surface wettability, a rich range of flow shapes has been identified: droplets, thin films or rivulets and notably, there is a regime of complete wetting for an impervious macropore surface [3]. In the present work, the macropore surface is porous and fluid transfer may appear through the interface between the macropore and the soil matrix. We aim at studying the competition between imbibition and the transport in the macropore. The model is based on the long-wave approximation with a free surface. The soil matrix wettability is taking into account using disjoining and conjoining pressures. Such an approach allows to model contact angle hysteresis if the wettability is not homogeneous [4]. The originality of this contribution is relative to the model of the fluid transfer at the matrix/macropore interface. Indeed, the linear classical flux condition on the liquid/porous interface as used in [5] does not yield if a hydrophobic coating is present: the flux depends on the matrix moisture too [6]. We propose a model taking into account wettability at the surface and also in the porous matrix. We analyse the perturbation via imbibition using continuation techniques and tools of dynamical systems. This analysis displays a rich behaviour and highlights the crucial role of wettability in the fluid transfer.

Ratchet effect refers to the possibility of transporting particles in noisy systems even if the mean force is zero (zero bias). Moreover, if the transport is in the opposite direction to the bias, this transport is called Absolute Negative Mobility (ANM). In the framework of a particle in a ratchet flow, we have showed that the existence of ANM is related to a parity symmetry-breaking and to a crisis of the deterministic problem. However in the literature, ANM seems to emerge from a different scenario. It ensues the open questions of the roles of the parity-symmetry, the crisis transition and more generally the role of chaotic dynamics in the ANM phenomenon? This study provides answering elements to these questions.

The numerical investigation of convective flows in the radial force field caused by an oscillating electric field between spherical surfaces has been performed. A temperature difference (T_{1}>T_{2}) as well as a radial force field triggers a fluid flow similar to the Rayleigh-Bénard convection. The onset of convective flow has been studied by means of the linear stability analysis as a function of the radius ratio η=R_{1}/R_{2}. The influence of the temperature-dependent viscosity has been investigated in detail. We found that a varying viscosity contrast β=ν(T_{2})/ν(T_{1}) between β=1 (constant viscosity) and β=50 decreases the critical Rayleigh number by a factor of 6. Additionally, we perform a bifurcation analysis based on numerical simulations which have been calculated using a modified pseudospectral code. Numerical results have been compared with the GeoFlow experiment which is located on the International Space Station (ISS). Nonturbulent three-dimensional structures are found in the numerically predicted parameter regime. Furthermore, we observed multiple stable solutions in both experiments and numerical simulations, respectively.

Hourly resolution time series of groundwater level fluctuations are analyzed after removing the seasonal cycle. It is found that fluctuations of groundwater levels have fractal scaling and a persistent behavior. We show also that groundwater level fluctuations exhibit non-Gaussian heavy tailed probability distribution that is well fitted by the Lévy stable distribution. Implications of the present results on the groundwater system modeling as a fractional Lévy motion and the connection with the anomalous diffusion inside the soil are discussed.

This paper is motivated by the transport of suspended particles pumped periodically through a modulated channel filled of water. The resulting flow behaves as a ratchet potential, called ratchet flow, i.e. the particle may drift to a preferential direction without bias. We study the deterministic particle dynamics using continuation of periodic orbits and of periodic transport solutions. The transport exists regardless the parity symmetry of the problem and the bifurcation scenario involve chaotic transitions. Moreover, the influence of the noise is discussed and points out a counter-intuitive consequence. The noise triggers a particle transport in the opposite direction to the bias (Absolute Negative Mobility). We show that this phenomenon is generic for slightly biased ratchet flow problem.

This study is motivated by the issue of the pumping of particle through a periodic modulated channel. We focus on a simplified deterministic model of small inertia particles within the Stokes flow framework that we call "ratchet flow." A path-following method is employed in the parameter space in order to retrace the scenario which from bounded periodic solutions leads to particle transport. Depending on whether the magnitude of the particle drag is moderate or large, two main transport mechanisms are identified in which the role of the parity symmetry of the flow differs. For large drag, transport is induced by flow asymmetry, while for moderate drag, since the full transport solution bifurcation structure already exists for symmetric settings, flow asymmetry only makes the transport effective. We analyzed the scenarios of current reversals for each mechanism as well as the role of synchronization. In particular we show that, for large drag, the particle drift is similar to phase slip in a synchronization problem.

The onset of convection for spherically invariant Rayleigh-B\'enard fluid flow is driven by marginal modes associated with spherical harmonics of a certain degree $\ell$, which depends upon the aspect ratio of the spherical shell. At certain critical values of the aspect ratio, marginal modes of degrees $\ell$ and $\ell+1$ coexist. Initially motivated by an experiment of electrophoretic convection between two concentric spheres carried in the International Space Station (GeoFlow project), we analyze the occurrence of intermittent dynamics near bifurcation in the case when marginal modes with $\ell=3, 4$ interact. The situation is by far more complex than in the well studied $\ell=1, 2$ mode interaction, however we show that heteroclinic cycles connecting equilibria with octahedral as well as axial symmetry can exist near bifurcation under certain conditions. Numerical simulations and continuation (using the software AUTO) on the center manifold help understanding these scenarios and show that the dynamics in these cases exhibits intermittent behaviour, even though the heteroclinic cycles may not be asymptotically stable in the usual sense.

The hydrodynamic interaction between a channel confinement and a suspended body is an important class of hydrodynamic problems. In this paper, we point out a quantitative study of the effects of the channel boundaries on the drag force exerted by the fluid on the particle surface. As results, we can obtain the drag coefficient as well as the flow in the channel due to the presence or the motion of the particle. We consider a channel with a periodic variation in diameter in which an axisymmetric particle is translating along its axis. Our numerical resolution is performed using the boundary integral formulation of Stokes flow which is solved using a boundary elements method. The numerical results are presented for the cases of spherical and ellipsoidal particles. Different geometric effects like the curvature of the channel, the particle geometry, and the channel size to particle size ratio are handled. Using the second law of Newton, these results enable us to study the existence and kinds of the mechanisms allowing the transport of the suspended particle and experienced by the computed drag force. Key-Words: Spherical and ellipsoidal particle; Periodic channel; Confined geometry; Drag force; Boundary elements method; Singular integrals.

Strong electric fields produce forces that can overcome the surface tension in thin liquid polymer films and in this way induce an instability of the free surface of the film, that triggers the formation of structures on a micrometer length scale. Here, we study experimentally a polymer-air-polymer system for several combinations of polymer films. These results are accompanied by theoretical considerations based on coupled long-wave time evolution equations for the two free surface profiles. The linear stability and nonlinear time evolution are investigated and compared to the experimental findings. The prediction that the instability always evolves through a mirror mode that couples the two surfaces in an anti-phase manner agrees well with the experimental results. The model describes well the linear (early stage) evolution of the instability. In the non-linear (later stage) evolution, topographical differences in the instability pattern occur if the mobilities of the two layers significantly differ and an unpredicted acceleration of growth is seen in thinner less mobile films. Possible reasons for the mismatch are discussed.

We study the drift of suspended micro-particles in a viscous liquid pumped back and forth through a periodic lattice of pores (drift ratchet). In order to explain the particle drift observed in such an experiment, we present an one-dimensional deterministic model of Stokes' drag. We show that the stability of oscillations of particle is related to their amplitude. Under appropriate conditions, particles may drift and two mechanisms of transport are pointed out. The first one is due to an spatio-temporal synchronization between the fluid and particle motions. As results the velocity is locked by the ratio of the space periodicity over the time periodicity. The direction of the transport may switch by tuning the parameters. Noteworthy, its emergence is related to a lattice of 2-periodic orbits but not necessary to chaotic dynamics. The second mechanism is due to an intermittent bifurcation and leads to a slow transport composed by long time oscillations following by a relative short transport to the next pore. Both steps repeat in a quasi-periodic manner. The direction of this last transport is strongly dependent on the pore geometry.

Depinning of two-dimensional liquid ridges and three-dimensional drops on an inclined substrate is studied within the lubrication approximation. The structures are pinned to wetting heterogeneities arising from variations of the strength of the short-range contribution to the disjoining pressure. The case of a periodic array of hydrophobic stripes transverse to the slope is studied in detail using a combination of direct numerical simulation and branch-following techniques. Under appropriate conditions the ridges may either depin and slide downslope as the slope is increased, or first break up into drops via a transverse instability, prior to depinning. The different transition scenarios are examined together with the stability properties of the different possible states of the system.

Transport in unsaturated macropores or fractured porous media displays intermittent water fluxes and preferential flow pathways [1]. Front instabilities play an important role in these dynamics. However, in porous media the modeling of the surface has to take into account chemical heterogeneities and/or topographic roughness. In fact, micro-or mesoscale heterogeneities are expected to affect the macroscopic movement of drops. For instance, they are responsible for contact angle hysteresis, the roughening of contact lines and the stick-slip motion of weakly driven contact lines [2]. The present contribution focusses on the spatio-temporal patterns of capillary-and wettability-dominated flow resulting from the interplay between driving and pinning forces. In particular, we consider a thin free-surface liquid film/drop on a substrate striped by defects driven by gravity. The defects are modeled using a spatially variable wettability leading to an evolution equation for the film height [3]. This approach enables one to (i) study the depinning transition employing tools from dynamical systems theory and bifurcation theory, and (ii) investigate the dynamics of the stick-slip motion that occurs after depinning on substrates with many defects. Recently, a specific numerical code has been developed to perform these tasks for a 3D system [4].

Lubrication equations describe many structuring processes of thin liquid films. We develop and apply a numerical framework suitable for their analysis employing a dynamical systems approach. In particular, we present a time integration algorithm based on exponential propagation and an algorithm for steady-state continuation. Both algorithms employ a Cayley transform to overcome numerical problems resulting from scale separation in space and time. An adaptive time-step allows one to study the dynamics close to hetero- or homoclinic connections. The developed framework is employed, on the one hand, to analyze different phases of the dewetting of a liquid film on a horizontal homogeneous substrate. On the other hand, we consider the depinning of drops pinned by a wettability defect. Time-stepping and path-following are used in both cases to analyze steady-state solutions and their bifurcations as well as dynamic processes on short and long time-scales. Both examples are treated for two- and three-dimensional (2d and 3d) physical settings and prove that the developed algorithms are reliable and efficient for 1d and 2d lubrication equations.