Can hydrodynamic contact line paradox be solved by evaporation--condensation?

We investigate a possibility to regularize the hydrodynamic contact line singularity in the configuration of partial wetting (liquid wedge on a solid substrate) via evaporation-condensation, when an inert gas is present in the atmosphere above the liquid. The no-slip condition is imposed at the solid-liquid interface and the system is assumed to be isothermal. The mass exchange dynamics is controlled by vapor diffusion in the inert gas and interfacial kinetic resistance. The coupling between the liquid meniscus curvature and mass exchange is provided by the Kelvin effect. The atmosphere is saturated and the substrate moves at a steady velocity with respect to the liquid wedge. A multi-scale analysis is performed. The liquid dynamics description in the phase-change-controlled microregion and visco-capillary intermediate region is based on the lubrication equations. The vapor diffusion is considered in the gas phase. It is shown that from the mathematical point of view, the phase exchange relieves the contact line singularity. The liquid mass is conserved: evaporation existing on a part of the meniscus and condensation occurring over another part compensate exactly each other. However, numerical estimations carried out for three common fluids (ethanol, water and glycerol) at the ambient conditions show that the characteristic length scales are tiny

Transient Rayleigh-Benard-Marangoni Convection due to Evaporation : a Linear Non-normal Stability Analysis

The convective instability in a plane liquid layer with time-dependent temperature profile is investigated by means of a general method suitable for linear stability analysis of an unsteady basic flow. The method is based on a non-normal approach, and predicts the onset of instability, critical wave number and time. The method is applied to transient Rayleigh-Benard-Marangoni convection due to cooling by evaporation. Numerical results as well as theoretical scalings for the critical parameters as function of the Biot number are presented for the limiting cases of purely buoyancy-driven and purely surface-tension-driven convection. Critical parameters from calculations are in good agreement with those from experiments on drying polymer solutions, where the surface cooling is induced by solvent evaporation.Comment: 31 pages, 8 figure

Mathematical models for estimating effective diffusion parameters of spherical drug delivery devices

Mathematical modeling of drug delivery is of increasing academic and industrial importance in manyaspects. In this paper, we propose an optimization approach for the estimation of the parameters characterizing the diffusion process of a drug from a spherical porous polymer device to an external finite volume. The approach is based on a nonlinear least-squares method and a novel mathematical model which takes into consideration both boundary layer effect and initial burst phenomenon. Ananalytical solution to the model is derived and a formula for the ratio of the mass released in a given time interval and the total mass released in infinite time is also obtained. The approach has been tested using experimental data of the diffusion of prednisolone 21-hemisuccinate sodium saltfrom spherical devices made of porous poly(2-hydroxyethyl methacrylate) hydrogels. The effectiveness and accuracy of the method are well demonstrated by the numerical results. The model was used to determine the diffusion parameters including the effective diffusion coefficient of the drug from a series of devices that vary in both the porous structure and the drug loading levels. The computed diffusion parameters are discussed in relation to the physical properties of the devices

Continuation for thin film hydrodynamics and related scalar problems

This chapter illustrates how to apply continuation techniques in the analysis of a particular class of nonlinear kinetic equations that describe the time evolution through transport equations for a single scalar field like a densities or interface profiles of various types. We first systematically introduce these equations as gradient dynamics combining mass-conserving and nonmass-conserving fluxes followed by a discussion of nonvariational amendmends and a brief introduction to their analysis by numerical continuation. The approach is first applied to a number of common examples of variational equations, namely, Allen-Cahn- and Cahn-Hilliard-type equations including certain thin-film equations for partially wetting liquids on homogeneous and heterogeneous substrates as well as Swift-Hohenberg and Phase-Field-Crystal equations. Second we consider nonvariational examples as the Kuramoto-Sivashinsky equation, convective Allen-Cahn and Cahn-Hilliard equations and thin-film equations describing stationary sliding drops and a transversal front instability in a dip-coating. Through the different examples we illustrate how to employ the numerical tools provided by the packages auto07p and pde2path to determine steady, stationary and time-periodic solutions in one and two dimensions and the resulting bifurcation diagrams. The incorporation of boundary conditions and integral side conditions is also discussed as well as problem-specific implementation issues

Drying colloidal systems: laboratory models for a wide range of applications

The drying of complex fluids provides a powerful insight into phenomena that take place on time and length scales not normally accessible. An important feature of complex fluids, colloidal dispersions and polymer solutions is their high sensitivity to weak external actions. Thus, the drying of complex fluids involves a large number of physical and chemical processes. The scope of this review is the capacity to tune such systems to reproduce and explore specific properties in a physics laboratory. A wide variety of systems are presented, ranging from functional coatings, food science, cosmetology, medical diagnostics and forensics to geophysics and art

2015/16 seasonal vaccine effectiveness against hospitalisation with influenza a(H1N1)pdm09 and B among elderly people in Europe: Results from the I-MOVE+ project

We conducted a multicentre test-negative caseâ\u80\u93control study in 27 hospitals of 11 European countries to measure 2015/16 influenza vaccine effectiveness (IVE) against hospitalised influenza A(H1N1)pdm09 and B among people aged â\u89¥ 65 years. Patients swabbed within 7 days after onset of symptoms compatible with severe acute respiratory infection were included. Information on demographics, vaccination and underlying conditions was collected. Using logistic regression, we measured IVE adjusted for potential confounders. We included 355 influenza A(H1N1)pdm09 cases, 110 influenza B cases, and 1,274 controls. Adjusted IVE against influenza A(H1N1)pdm09 was 42% (95% confidence interval (CI): 22 to 57). It was 59% (95% CI: 23 to 78), 48% (95% CI: 5 to 71), 43% (95% CI: 8 to 65) and 39% (95% CI: 7 to 60) in patients with diabetes mellitus, cancer, lung and heart disease, respectively. Adjusted IVE against influenza B was 52% (95% CI: 24 to 70). It was 62% (95% CI: 5 to 85), 60% (95% CI: 18 to 80) and 36% (95% CI: -23 to 67) in patients with diabetes mellitus, lung and heart disease, respectively. 2015/16 IVE estimates against hospitalised influenza in elderly people was moderate against influenza A(H1N1)pdm09 and B, including among those with diabetes mellitus, cancer, lung or heart diseases

A model coupling the liquid and gas phases for a totally wetting evaporative meniscus

An hydrodynamic model has been developed to get a complete description of an evaporative meniscus in complete wetting configuration. The coupling between the liquid and gas is explicitly taken into account. Scaling laws are derived for the different domains of the meniscus and validated by numerical simulations. Results are compared with previous models of the literature that use the electrostatic analogy proposed by Deegan and co-authors to describe the evaporative flux. We show that the different approaches differ for the description of the tip of the meniscus in the domain corresponding to the decrease of the evaporative flux but lead to the same scaling for the apparent macroscopic contact angle

Self-patterning induced by a solutal Marangoni effect in a receding drying meniscus

This paper examines through numerical simulations the impact of a solutal Marangoni effect on the deposit obtained from a polymer solution. A hydrodynamical model with lubrication approximation is used to describe the liquid phase in a dip-coating–like configuration. The studied case considers evaporation in stagnant air (diffusion-limited evaporation), which results in a coupling between the liquid and gas phases. Viscosity, surface tension, and saturated vapor pressure depend on the solute concentration. In the evaporative regime, when the surface tension increases with the polymer concentration, the Marangoni effect induces a periodic regime. This results in a self-organized periodic patterning of the dried film in certain control parameter ranges. A morphological phase diagram as well as meniscus and dry-deposit shapes are provided as a function of the substrate velocity and bulk solute concentration

Condensation-induced self-patterning of a thin clayey layer

We show through laboratory experiments that the self-patterning of a thin clayey layer can be triggered by condensation. The natural sediment used in the experiments was a highly polydisperse granular paste with smectite clay in the fine fraction. Under certain physicochemical conditions, condensation induces the solid-to-liquid transition of the sediment layer, resulting in sediment flow and the formation of band structures. These results suggest a physical mechanism for the formation of patterns commonly observed on the humid walls of underground cavities, referred to as vermiculations

Pattern formation during the drying of a colloidal suspension

Receding contact lines of colloidal suspensions are studied in the presence of drying, inside Hele-Shaw cells. At high velocity the contact line movement is continuous and the particle deposition is uniform. At small velocity, a periodic pinning-unpinning of the contact line is observed leading to a patterning of the substrate. We focused on the correlation between the deposition pattern and the pinning force that grows during the pinning. Our results strongly indicate that this pinning force is proportional to the macroscopic slope of the deposit and accounted by a simple capillary balance