Wetting phenomena are ubiquitous in nature and technology. A solid substrate exposed to the environment is almost invariably covered by a layer of fluid material. In this review, the surface forces that lead to wetting are considered, and the equilibrium surface coverage of a substrate in contact with a drop of liquid. Depending on the nature of the surface forces involved, different scenarios for wetting phase transitions are possible; recent progress allows us to relate the critical exponents directly to the nature of the surface forces which lead to the different wetting scenarios. Thermal fluctuation effects, which can be greatly enhanced for wetting of geometrically or chemically structured substrates, and are much stronger in colloidal suspensions, modify the adsorption singularities. Macroscopic descriptions and microscopic theories have been developed to understand and predict wetting behavior relevant to microfluidics and nanofluidics applications. Then the dynamics of wetting is examined. A drop, placed on a substrate which it wets, spreads out to form a film. Conversely, a nonwetted substrate previously covered by a film dewets upon an appropriate change of system parameters. The hydrodynamics of both wetting and dewetting is influenced by the presence of the three-phase contact line separating "wet" regions from those that are either dry or covered by a microscopic film only. Recent theoretical, experimental, and numerical progress in the description of moving contact line dynamics are reviewed, and its relation to the thermodynamics of wetting is explored. In addition, recent progress on rough surfaces is surveyed. The anchoring of contact lines and contact angle hysteresis are explored resulting from surface inhomogeneities. Further, new ways to mold wetting characteristics according to technological constraints are discussed, for example, the use of patterned surfaces, surfactants, or complex fluids.

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Wetting and Spreading

Intermolecular And Surface Forces

The dynamics and stability of thin liquid films have fascinated scientists over many decades: the observations of regular wave patterns in film flows down a windowpane or along guttering, the patterning of dewetting droplets, and the fingering of viscous flows down a slope are all examples that are familiar in daily life. Thin film flows occur over a wide range of length scales and are central to numerous areas of engineering, geophysics, and biophysics; these include nanofluidics and microfluidics, coating flows, intensive processing, lava flows, dynamics of continental ice sheets, tear-film rupture, and surfactant replacement therapy. These flows have attracted considerable attention in the literature, which have resulted in many significant developments in experimental, analytical, and numerical research in this area. These include advances in understanding dewetting, thermocapillary- and surfactant-driven films, falling films and films flowing over structured, compliant, and rapidly rotating substrates, and evaporating films as well as those manipulated via use of electric fields to produce nanoscale patterns. These developments are reviewed in this paper and open problems and exciting research avenues in this thriving area of fluid mechanics are also highlighted.

Dynamics and stability of thin liquid films

Let X(t) be the number of tumor cells at time t, and Pr{X(t) = n} = pn(t) is the density of X. A “birth”, i.e., an increase of one of the total population of cancer cells, can occur either by mutation of a normal cell caused by the action of the carcinogen, consisting of randomly (Poisson) distributed hits, or by reproduction of existing cancer cells. A death of a tumor cell occurs as an additive combination of non-immunological and immunological elements. Once a tumor is initiated by carcinogenic action, it undergoes a birth and death process with infinitesimal birth rate linear and infinitesimal death rate composed of a linear and a nonlinear term, the former due to non-immunological deaths, the latter to immunological feedback. The death rate per tumor cell due to immunological response is proportional to the total number of antigen-producing (tumor) cells; thus, the total death rate is quadratic. Although this assumes a very simple mechanism for the action of immunological feedback, it is nevertheless a first step.

The Mathematical Model

The development of microfluidic devices has recently revived the interest in “old” problems associated with transport at, or across, interfaces. As the characteristic sizes are decreased, the use of pressure gradients to transport fluids becomes problematic, and new, interface driven, methods must be considered. This has lead to new investigations of flow near interfaces, and to the conception of interfaces engineered at various scales to reduce flow friction. In this review, we discuss the present theoretical understanding of flow past solid interfaces at different length scales. We also briefly discuss the corresponding phenomenon of heat transport, and the influence of surface slip on interface driven (e.g. electro-osmotic) flows.

http://ilm-perso.univ-lyon1.fr/~lbocquet/soft-matter-2007.pdf

Flow boundary conditions from nano- to micro-scales

A new two-phase model for concentrated suspensions is derived that incorporates a constitutive law combining the rheology for non-Brownian suspension and granular flow. The resulting model exhibits a yield-stress behaviour for the solid phase depending on the collision pressure. This property is investigated for the simple geometry of plane Poiseuille flow, where an unyielded or jammed zone of finite width arises in the centre of the channel. For the steady states of this problem, the governing equations are reduced to a boundary value problem for a system of ordinary differential equations and the conditions for existence of solutions with jammed regions are investigated using phase-space methods. For the general time-dependent case a new drift-flux model is derived using matched asymptotic expansions that takes into account the boundary layers at the walls and the interface between the yielded and unyielded region. The drift-flux model is used to numerically study the dynamic behaviour of the suspension flow, including the appearance and evolution of an unyielded or jammed regions.

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Models for the two-phase flow of concentrated suspensions

We address the linear stability of unsteady and nonuniform base states within the class of mass conserving free boundary problems for degenerate and nondegenerate thin film equations. Well-known examples are the finger-instabilities of growing rims that appear in retracting thin solid and liquid films. Since the base states are time dependent and do not have a simple traveling wave or exact self-similar form, a classical eigenvalue analysis fails to provide the dominant wavelength of the instability. However, the initial fronts evolve on a slower time-scale than the typical perturbations. We exploit this time-scale separation and develop a multiple-scale approach for this class of stability problems. We show that the value of the dominant wavelength is rapidly attained once the base state has entered an asymptotically self-similar form. We note that this value is different from the one obtained by the linear stability analysis with "frozen modes," frequently found in the literature. Furthermore, we show that for the present class of stability problems that the dispersion relation is linear in the long wave limit, which is in contrast to many other instability problems in thin film flows. © by SIAM.

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Stability Analysis of Unsteady, Nonuniform Base States in Thin Film Equations

We study numerically and analytically the instabilities associated with phase separation in a solid layer on which an external material flux is imposed. The first instability is localized within a boundary layer at the exposed free surface by a process akin to spinodal decomposition. In the limiting static case, when there is no material flux, the coherent spinodal decomposition is recovered. In the present problem, stability analysis of the time-dependent and nonuniform base states as well as numerical simulations of the full governing equations are used to establish the dependence of the wavelength and onset of the instability on parameter settings and its transient nature as the patterns eventually coarsen into a flat moving front. The second instability is related to the Mullins-Sekerka instability in the presence of elasticity and arises at the moving front between the two phases when the flux is reversed. Stability analyses of the full model and the corresponding sharp-interface model are carried out and compared. Our results demonstrate how interface and bulk instabilities can be analyzed within the same framework which allows us to identify and distinguish each of them clearly. The relevance for a detailed understanding of both instabilities and their interconnections in a realistic setting is demonstrated for a system of equations modeling the lithiation and delithiation processes within the context of lithium ion batteries.

Localized instabilities and spinodal decomposition in driven systems in the presence of elasticity.

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Response to “Comment on ‘Degenerate mobilities in phase field models are insufficient to capture surface diffusion’” [Appl. Phys. Lett. 108, 036101 (2016)]

It is important to understand the operational aspects which affect the continuous fabrication of alginate gel fibers. These can be formed from a cross-linking reaction of an alginate precursor injected into a coaxial annular pipe flow with a calcium chloride solution. This is an example of an emerging solid interface that interacts with the flow in its neighborhood. We advance on earlier works by relaxing assumptions of a fixed spatial domain to explore and observe mechanisms controlling gel radius. We use two different models. The first one represents the gel layer as a capillary interface between two immiscible liquids and captures the effect of surface tension. A second model is introduced to treat the cross-linking chemical reaction and its effect on the viscosity as the alginate gel forms. Through numerical simulations and analytical approximations of the downstream behavior, we determine the shape of the fiber in the pipe flow and its impact on the flow velocity as well as on the total production of gel.

Andreas Münch

Papers

Models for the two-phase flow of concentrated suspensions

Stability Analysis of Unsteady, Nonuniform Base States in Thin Film Equations

Localized instabilities and spinodal decomposition in driven systems in the presence of elasticity.

Response to “Comment on ‘Degenerate mobilities in phase field models are insufficient to capture surface diffusion’” [Appl. Phys. Lett. 108, 036101 (2016)]

Modeling Gel Fiber Formation in an Emerging Coaxial Flow From a Nozzle