A multiple scales approach to evaporation induced Marangoni convection

This paper considers the stability of thin liquid layers of binary mixtures of a volatile (solvent) species and a non-volatile (polymer) species. Evaporation leads to a depletion of the solvent near the liquid surface. If surface tension increases for lower solvent concentrations, sufficiently strong compositional gradients can lead to Bénard-Marangoni-type convection that is similar to the kind which is observed in films that are heated from below. The onset of the instability is investigated by a linear stability analysis. Due to evaporation, the base state is time dependent, thus leading to a non-autonomous linearised system, which impedes the use of normal modes. However, the time scale for the solvent loss due to evaporation is typically long compared to the diffusive time scale, so a systematic multiple scales expansion can be sought for a finite dimensional approximation of the linearised problem. This is determined to leading and to next order. The corrections indicate that sufficient separation of the top eigenvalue from the remaining spectrum is required for the validity of the expansions, but not the magnitude of the eigenvalues themselves. The approximations are applied to analyse experiments by Bassou and Rharbi with polystyrene/toluene mixtures [Langmuir 2009 (25) 624–632]

Thin film dynamics on a vertically rotating disk partially immersed in a liquid bath

The axisymmetric flow of a thin liquid film is considered for the problem of a vertically rotating disk that is partially immersed in a liquid bath. A model for the fully three-dimensional free-boundary problem of the rotating disk, that drags a thin film out of the bath is set up. From this, a dimension-reduced extended lubrication approximation that includes the meniscus region is derived. This problem constitutes a generalization of the classic drag-out and drag-in problem to the case of axisymmetric flow. The resulting nonlinear fourth-order partial differential equation for the film profile is solved numerically using a finite element scheme. For a range of parameters steady states are found and compared to asymptotic solutions. Patterns of the film profile, as a function of immersion depth and angular velocity are discussed.Comment: 31 pages, 19 figures accepted: Applied Mathematical Modellin

A thin film model for corotational Jeffreys fluids under strong slip

We derive a thin film model for viscoelastic liquids under strong slip which obey the stress tensor dynamics of corotational Jeffreys fluids.Comment: 3 pages, submitted to Eur. Phys. J.

Degenerate Mobilities in Phase Field Models are Insufficient to Capture Surface Diffusion

Phase field models frequently provide insight to phase transitions, and are robust numerical tools to solve free boundary problems corresponding to the motion of interfaces. A body of prior literature suggests that interface motion via surface diffusion is the long-time, sharp interface limit of microscopic phase field models such as the Cahn-Hilliard equation with a degenerate mobility function. Contrary to this conventional wisdom, we show that the long-time behaviour of degenerate Cahn-Hilliard equation with a polynomial free energy undergoes coarsening, reflecting the presence of bulk diffusion, rather than pure surface diffusion. This reveals an important limitation of phase field models that are frequently used to model surface diffusion

Spin coating of an evaporating polymer solution

We consider a mathematical model of spin coating of a single polymer blended in a solvent. The model describes the one-dimensional development of the thin layer of the mixture as the layer thins due to flow created by a balance of viscous forces and centrifugal forces and due to evaporation of the solvent. In the model both the diffusivity of the solvent in the polymer and the viscosity of the mixture are very rapidly varying functions of the solvent volume fraction. Guided by numerical solutions an asymptotic analysis reveals a number of different possible behaviours of the thinning layer dependent on the nondimensional parameters describing the system.\ud \ud The main practical interest is in controlling the appearance and development of a ``skin'' on the polymer where the solvent concentration reduces rapidly on the outer surface leaving the bulk of the layer still with high concentrations of solvent. The critical parameters controlling this behaviour are found to be $\epsilon$ the ratio of the diffusion to advection time scales, $\delta$ the ratio of the evaporation to advection time scales and $\exp(\gamma)$, the ratio of the diffusivity of the initial mixture and the pure polymer. In particular, our analysis shows that for very small evaporation with $\delta << \exp(-3/(4\gamma)) \epsilon^{3/4}$ skin formation can be prevented

Hydrogen tunneling in the perovskite ionic conductor BaCe(1-x)Y(x)O(3-d)

We present low-temperature anelastic and dielectric spectroscopy measurements on the perovskite ionic conductor BaCe(1-x)Y(x)O(3-x/2) in the protonated, deuterated and outgassed states. Three main relaxation processes are ascribed to proton migration, reorientation about an Y dopant and tunneling around a same O atom. An additional relaxation maximum appears only in the dielectric spectrum around 60 K, and does not involve H motion, but may be of electronic origin, e.g. small polaron hopping. The peak at the lowest temperature, assigned to H tunneling, has been fitted with a relaxation rate presenting crossovers from one-phonon transitions, nearly independent of temperature, to two-phonon processes, varying as T^7, to Arrhenius-like. Substituting H with D lowers the overall rate by 8 times. The corresponding peak in the dielectric loss has an intensity nearly 40 times smaller than expected from the classical reorientation of the electric dipole associated with the OH complex. This fact is discussed in terms of coherent tunneling states of H in a cubic and orthorhombically distorted lattice, possibly indicating that only H in the symmetric regions of twin boundaries exhibit tunneling, and in terms of reduction of the effective dipole due to lattice polarization.Comment: submitted to Phys. Rev.

Slip vs viscoelasticity in dewetting thin films

Ultrathin polymer films on non-wettable substrates display dynamic features which have been attributed to either viscoelastic or slip effects. Here we show that in the weak and strong slip regime effects of viscoelastic relaxation are either absent or not distinguishable from slip effects. Strong-slip modifies the fastest unstable mode in a rupturing thin film, which questions the standard approach to reconstruct the effective interface potential from dewetting experiments.Comment: 4 pages, submitted to Eur. Phys. J.

Slip-controlled thin film dynamics

In this study, we present a novel method to assess the slip length and the viscosity of thin films of highly viscous Newtonian liquids. We quantitatively analyse dewetting fronts of low molecular weight polystyrene melts on Octadecyl- (OTS) and Dodecyltrichlorosilane (DTS) polymer brushes. Using a thin film (lubrication) model derived in the limit of large slip lengths, we can extract slip length and viscosity. We study polymer films with thicknesses between 50 nm and 230 nm and various temperatures above the glass transition. We find slip lengths from 100 nm up to 1 micron on OTS and between 300 nm and 10 microns on DTS covered silicon wafers. The slip length decreases with temperature. The obtained values for the viscosity are consistent with independent measurements.Comment: 4 figure

The structure of a dewetting rim with strong slip: the long-time evolution

When a thin viscous film dewets from a solid substrate, the liquid forms a characteristic rim near the contact line as the contact line retracts. The shape of the rim and also the retraction rate vary strongly with the amount of slip that occurs at the liquid-solid substrate. If the slip length is very large compared to the thickness of the film, extensional stresses dominate the shear stresses, and the film evolution can be modelled by a thin-film model similar to the ones that occur in freely suspended films, with a correction from the viscous friction due to the large but finite slip. Asymptotic investigation of this model reveals that the rim has an amazingly rich asymptotic structure that moreover changes as the solution passes through four distinct time regimes. This paper continues previous work that focused on the first of these regimes [Evans, King, Münch, AMRX 2006:25262, 2006]. The structure of the solution is analyzed in detail via matched asymptotics and then the predictions for the contact line and profile evolution are compared with numerical results