Is Unidirectional Drying in a Round Capillary Always Diffusive?

The unidirectional drying of water in cylindrical capillaries has been described since the discovery of Stefan's solution as a vapor diffusion-controlled process with a square root of time kinetics. Here we show that this well-known process actually depends on the way the capillary is closed. Experiments are performed on the evaporation of water in capillaries closed at one end with a solid material or connected to a fluid reservoir. While we recover Stefan's solution in the first case, we show that in the second situation the water plug evaporates at a constant rate with the water-air meniscus remaining pinned at the exit where evaporation proceeds. The presence of the liquid reservoir closing the capillary combined with a capillary pumping effect induces a flow of the water plug toward the evaporation front leading to a constant-rate drying, substantially faster than the prediction of Stefan's equation. Our results show that a transition from a constant-rate evaporation regime at short times to a diffusion-driven evaporation regime at long times can be observed by increasing the viscosity of the fluid in the reservoir blocking the other end of the capillary. Such transition can also be observed by connecting the capillary end to a solidifying fluid like epoxy glue.

Coupling between internal and external mass transfer during stage-1 evaporation in capillary porous media: Interfacial resistance approach.

The coupling boundary condition to be imposed at the evaporative surface of a porous medium is studied from pore network simulations considering the capillary regime. This paper highlights the formation of a thin edge effect region of smaller saturation along the evaporative surface. It is shown that this thin region forms in the breakthrough period at the very beginning of the drying process. The size of this region is studied and shown to be not network size dependent. This region is shown to be the locus of a nonlocal equilibrium effect. The features lead to the consideration of a coupling boundary condition involving an interfacial mass transfer resistance and an external mass transfer resistance. Contrary to previous considerations, it is shown that both resistances depend on the variation of the saturation, i.e., the fluid topology, and the size of the external mass transfer layer, i.e., the mass transfer rate. This is explained by the evolution of the vapor partial pressure distribution at the surface which becomes increasingly heterogeneous during evaporation and depends on both the evolving fluid distribution in the interfacial region and the mass transfer rate. However, the geometric effects due to the configuration of the fluids can be separated from rate effects that arise due to the nonequilibrium mass transport.

Determination of the throat size distribution of a porous medium as an inverse optimization problem combining pore network modeling and genetic and hill climbing algorithms.

The pore size distribution of a porous medium is often estimated from the retention curve or the invading fluid flow rate curve using simple relationships more or less explicitly based on the consideration that the porous medium is made of a bundle of cylindrical parallel tubes. This type of determination is tested using pore network simulations. Starting from two- or three-dimensional networks, the characteristics of which are known a priori, the estimation of the throat size distribution (TSD) is performed using the standard methods in the case of drainage. Results show a significant discrepancy with the input data. The disagreement is more pronounced when the fluid flow rate curve is employed together with the parallel tubes assumption. The physical origins of these shortcomings are identified. A method, based on pore network simulations combined with a genetic algorithm and the hill climbing algorithm, is then designed, which makes simultaneous use of the nonwetting fluid flow rate curve and the retention curve of the medium. Very significant improvement is achieved in the estimation of the TSD using this procedure.

Determination of the transmissivity of a heterogeneous anisotropic fracture in slip flow conditions.

Rough fractures often exhibit a broad spectrum of defect length scales ranging from the microscopic (roughness) scale to a macroscopic one (waviness) and further to the megascopic scale corresponding to the entire fracture. The influence of these multiple scales and their reciprocal interactions are expected to play a significant role on the transport properties at the megascale. Focusing on the pressure-driven slightly compressible gas slip flow, a two-scale method is presented allowing the determination of the global transmissivity of a fracture on the basis of an upscaled Reynolds model. This model is applied on a tessellation of the fracture, each tile being affected by a macroscopic transmissivity tensor which encompasses the microscale transport information as a result of the first upscaling process. Then, the megascale flow problem in this structure, made of a set of tiles characterized by a heterogeneous and anisotropic transmissivity tensor field, is solved using a boundary element method. Numerical results obtained with this two-scale method are compared to the transmissivity computed with direct simulations carried out at the microscale on the whole fracture. This is performed on two model rough fractures, namely, a spiral groove and a fractal fracture, while varying their mean apertures to investigate a wide range of the average Knudsen number characteristic of the flow at the megascale. A good agreement is obtained between the two approaches showing the robustness of the two-scale method to determine the global transmissivity of the fracture while significantly reducing the overall computational time.

Direct observation of pore collapse and tensile stress generation on pore walls due to salt crystallization in a PDMS channel.

The generation of stress on pore walls due to salt crystallization is generally analysed as a compressive stress generation mechanism using the concept of crystallization pressure. We report on a completely different stress generation mechanism. In contrast with the classical picture where the crystal pushes the pore wall, the crystal growth leads to the generation of a local tensile stress. This tensile stress occurs next to a region where a compressive stress is generated, thus inducing also shear stresses. These findings are obtained from direct optical observations in PDMS model pores where the tensile stress generation results in the collapse of the pore region located between the crystal and the pore dead-end. The experiments also reveal other interesting phenomena, such as hyperslow drying in PDMS channels or asymmetrical growth of the crystal during the collapse.

Control of evaporation by geometry in capillary structures. From confined pillar arrays in a gap radial gradient to phyllotaxy-inspired geometry.

Evaporation is a key phenomenon in the natural environment and in many technological systems involving capillary structures. Understanding the evaporation front dynamics enables the evaporation rate from microfluidic devices and porous media to be finely controlled. Of particular interest is the ability to control the position of the front through suitable design of the capillary structure. Here, we show how to design model capillary structures in microfluidic devices so as to control the drying kinetics. This is achieved by acting on the spatial organization of the constrictions that influence the invasion of the structure by the gas phase. Two types of control are demonstrated. The first is intended to control the sequence of primary invasions through the pore space, while the second aims to control the secondary liquid structures: films, bridges, etc., that can form in the region of pore space invaded by the gas phase. It is shown how the latter can be obtained from phyllotaxy-inspired geometry. Our study thus opens up a route toward the control of the evaporation kinetics by means of tailored capillary structures.

Salt stains from evaporating droplets.

The study of the behavior of sessile droplets on solid substrates is not only associated with common everyday phenomena, such as the coffee stain effect, limescale deposits on our bathroom walls , but also very important in many applications such as purification of pharmaceuticals, de-icing of airplanes, inkjet printing and coating applications. In many of these processes, a phase change happens within the drop because of solvent evaporation, temperature changes or chemical reactions, which consequently lead to liquid to solid transitions in the droplets. Here we show that crystallization patterns of evaporating of water drops containing dissolved salts are different from the stains reported for evaporating colloidal suspensions. This happens because during the solvent evaporation, the salts crystallize and grow during the drying. Our results show that the patterns of the resulting salt crystal stains are mainly governed by wetting properties of the emerging crystal as well as the pathway of nucleation and growth, and are independent of the evaporation rate and thermal conductivity of the substrates.