Stress-driven diffusion in a drying liquid paint layer

Abstract

A model is presented for the diffusion-driven drying of a polymeric solution such as liquid paint. Included is a stress build-up and relaxation in the polymer network of the viscoelastic material, which influences the diffusion process. The behaviour of the (one-dimensional) model is analysed by means of the maximum principle and illustrated with numerical calculations.

Analysis and mixed-primal finite element discretisations for stress-assisted diffusion problems

“…Truesdell [33], Podstrigach [27], or Aifantis [2], a number of applicative studies and different models have been developed. Many of these contributions have focused on the modelling of hydrogen diffusion in metals [32], damage of electrodes in lithium ion batteries [5], sorption in fibre-reinforced polymeric materials [30], drying of liquid paint layers [34], gels and general-purpose solute penetration [21,35], anisotropy of cardiac dynamics [9], and several other effects. Irrespective of the specific interaction under consideration, the assumptions in these models convey that the species diffuses on the elastic medium obeying a Fickean law enriched with additional contributions arising from local effects by exerted stresses.…”

“…Although there exist numerous advances on the modelling considerations for stress-assisted and strainassisted diffusion problems, their counterparts from the viewpoint of mathematical and numerical analysis are still far behind. A few punctual references include the study of plane steady solutions [20], asymptotic analysis [11,34], and the very recent general well-posedness theory for static and transient problems in a primal formulation, developed in [24]. Our goal at this stage is to focus on a simple stationary problem that represents the main ingredients of diffusion-deformation interaction models where the Cauchy stress acts as a coupling variable.…”

Spin coating of an evaporating polymer solution

“…19 The first theoretical treatment of spin coating an evaporating solution is due to Meyerhofer 20 and was later extended by Sukanek, 21 Bornside et al, 22 and Reisfeld et al 23,24 Additional effects if a volatile component is added, such as variable viscosity and diffusion coefficients during the thinning of the film and its effects on the stability of the film, have also been intensely studied asymptotically and numerically during the past decade. [25][26][27][28][29][30][31] One important feature that occurs due to the evaporation of the volatile component is the phenomenon of "skin" formation. This has first been studied by Lawrence, 32,33 see also de Gennes 34 and Okuzono et al 35 for further discussions on this aspect.…”

A Generalized Stefan Problem in a Diffusion Model with Evaporation

“…We assume this diffusion coefficient to be strictly positive and bounded. Extensions of the Fickian diffusion may include a contribution due to viscoelastic stress [1,2,3,5,8].…”

“…The model is then a diffusion equation with boundary conditions dictated by conservation of resin and pigment and loss of solvent. A more comprehensive version of this model has been described in [8], where we were interested in stress-driven diffusion rather than evaporation, and in [6].…”