Droplet absorption and spreading into thin layers of polymer hydrogels

Etzold, Merlin A.; Fortune, George T.; Landel, Julien R.; Dalziel, Stuart B.

doi:10.48550/arxiv.2202.10389

Cited by 2 publications

(2 citation statements)

References 48 publications

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“…The combined result is a computationally efficient model that is able to resolve the spatio-temporal dynamics of drying and bending. In asymptotically reducing the equations for the film, we invoke a poroelastic version of lubrication theory [11,18,22]. Furthermore, we extend our previous work on drying-induced stresses in poroelastic drops [17] by accounting for a wide range of drying regimes that are determined by the magnitude of the Péclet number.…”

Section: Introductionmentioning

confidence: 99%

Time-dependent modelling of thin poroelastic films drying on deformable plates

Hennessy

Matar

2023

Eur. J. Appl. Math

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Understanding the generation of mechanical stress in drying, particle-laden films is important for a wide range of industrial processes. One way to study these stresses is through the cantilever experiment, whereby a thin film is deposited onto the surface of a thin plate that is clamped at one end to a wall. The stresses that are generated in the film during drying are transmitted to the plate and drive bending. Mathematical modelling enables the film stress to be inferred from measurements of the plate deflection. The aim of this paper is to present simplified models of the cantilever experiment that have been derived from the time-dependent equations of continuum mechanics using asymptotic methods. The film is described using nonlinear poroelasticity and the plate using nonlinear elasticity. In contrast to Stoney-like formulae, the simplified models account for films with non-uniform thickness and stress. The film model reduces to a single differential equation that can be solved independently of the plate equations. The plate model reduces to an extended form of the Föppl-von Kármán (FvK) equations that accounts for gradients in the longitudinal traction acting on the plate surface. Consistent boundary conditions for the FvK equations are derived by resolving the Saint-Venant boundary layers at the free edges of the plate. The asymptotically reduced models are in excellent agreement with finite element solutions of the full governing equations. As the Péclet number increases, the time evolution of the plate deflection changes from $t$ to $t^{1/2}$ , in agreement with experiments.

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Section: Introductionmentioning

confidence: 99%

Time-dependent modelling of thin poroelastic films drying on deformable plates

Hennessy

Matar

2023

Eur. J. Appl. Math

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show abstract

“…The combined result is a computationally efficient model that is able to resolve the spatio-temporal dynamics of drying and bending. In asymptotically reducing the equations for the film, we invoke a poroelastic version of lubrication theory [26][27][28]. Furthermore, we extend our previous work on drying-induced stresses in poroelastic drops [29] by accounting for a wide range of drying regimes that are determined by the magnitude of the Péclet number.…”

Section: Introductionmentioning

confidence: 99%

Time-dependent modelling of thin poroelastic films drying on deformable plates

Hennessy¹,

Matar²

2022

Preprint

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Understanding the generation of mechanical stress in drying, particle-laden films is important for a wide range of industrial processes. The cantilever experiment allows the stress in a drying film that has been deposited onto a thin plate to be quantified. Mechanical stresses in the film are transmitted to the plate and drive bending. Mathematical modelling enables the film stress to be inferred from measurements of the plate deflection. The aim of this paper is to present simplified models of the cantilever experiment that have been derived from the time-dependent equations of continuum mechanics using asymptotic methods. The film is described using nonlinear poroelasticity and the plate using nonlinear elasticity. In contrast to Stoney-like formulae, the simplified models account for films with non-uniform thickness and stress. The film model reduces to a single differential equation that can be solved independently of the plate equations. The plate model reduces to an extended form of the Foppl-von Karman (FvK) equations that accounts for gradients in the longitudinal traction acting on the plate surface. Consistent boundary conditions for the FvK equations are derived by resolving the Saint-Venant boundary layers at the free edges of the plate. The asymptotically reduced models are in excellent agreement with finite element solutions of the full governing equations. As the Péclet number increases, the time evolution of the plate deflection changes from t to t 1/2 , in agreement with experiments.

show abstract

Droplet absorption and spreading into thin layers of polymer hydrogels

Cited by 2 publications

References 48 publications

Time-dependent modelling of thin poroelastic films drying on deformable plates

Time-dependent modelling of thin poroelastic films drying on deformable plates

Time-dependent modelling of thin poroelastic films drying on deformable plates

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