Coupled heat and moisture transport in paper with application to a warm print surface

Zapata, Paula Andrea Marin; Fransen, M. A. L. J.; Boonkkamp, Jan ten Thije; Saes, Louis

doi:10.1016/j.apm.2013.02.032

Cited by 19 publications

(9 citation statements)

References 21 publications

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“…In refs. [1,2,4,5] the exchange/dissipation can be reasoned by evaporation-condensation, or adsorption of water and the moisture exchange inside the porous structure, between the pores and fibers, with capillary effects. In ref.…”

Section: State Of the Art In The Heat-moisture Transfer Modeling And ...mentioning

confidence: 99%

“…According to refs. [1,2,4], the heat-conduction equation for the temperature 𝑇 is coupled with the diffusion of moisture concentration, 𝜔 𝑓 , via evaporation. For 𝑥 ∈ Ω 𝜀 , 𝑡 ∈ [0, 𝑇 𝑓𝑖𝑛𝑖 ], we consider the following problem:…”

Section: Mathematical Statement Of the Problemmentioning

confidence: 99%

“…In this paper, we show, that the effective models discussed above, for example [1, 2], in fact, can be obtained from the rigorous passing to the limit in variational inequalities with the heat conduction and the moisture transport through the porous fiber material with a dissipation on the pore interface. This problem on the micro‐structure is formulated in Section 2.…”

Section: Introductionmentioning

confidence: 99%

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Homogenization based heating control for moist paperboard with evaporation on the pore surface

Orlik,

Khilkov,

Rief

et al. 2023

Z Angew Math Mech

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A control problem for the heating of moist paperboard with the evaporation of moisture from the inner pore surface is considered. The microstructure of the paperboard is known from the CT images. It is easily parametrized w.r.t. the volume fraction of the pores, the surface area of the pores related to the unit volume, averaged area of the contact surfaces between two fibers and the unsupported fiber length between two contact nodes, fiber thickness, and tortuosity. Simple averaging formulas are provided for the computation of the effective coefficients in the coupled diffusion‐heat problem and the dissipation energetic balance was analyzed and we pass to the limit w.r.t. the small parameter, the relation between the pore size and the paper‐board thickness. The limit model is similar to those models, recently available in the literature. However, it provides more understanding and different limiting models and the thresholds for them. Also, the limitation on the heating is derived from the solvability criteria, which means, that the evaporation should not overtake the heating. The model is validated by experimental and numerical results found in the literature.

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Section: State Of the Art In The Heat-moisture Transfer Modeling And ...mentioning

confidence: 99%

Section: Mathematical Statement Of the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Homogenization based heating control for moist paperboard with evaporation on the pore surface

Orlik,

Khilkov,

Rief

et al. 2023

Z Angew Math Mech

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show abstract

“…The model explicitly accounts for the presence of permeable fibers by means of a dual-porosity description. The moisture content Θ f inside the fibers is assumed immobile . Consequently, the dynamic equation for Θ f (units kg/m 2 ) contains only flux terms but no transport terms Here, s pf is the pore–fiber moisture exchange rate and j ev,f the evaporative flux from the fibers to the ambient atmosphere.…”

Section: Theoretical Modelmentioning

confidence: 99%

Chromatographic Effects in Inkjet Printing

2021

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We have studied the chromatographic separation of solvents and dyes after deposition of a dye solution on a paper substrate. Due to their larger molecular size, dyes typically exhibit a stronger interaction with the paper constituents. Consequently, the imbibition process of the dye is usually delayed compared to that of the solvent. This impacts the achievable resolution and color homogeneity in inkjet printing. We present experiments and a comprehensive numerical model to illustrate and quantify these effects. The model accounts for the solvent evaporation, heat transfer, multicomponent unsaturated flow, and dye adsorption, as well as the presence of permeable fibers in the paper substrate. We identify the key parameters that can be tuned to optimize the pattern fidelity of the printing process.

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“…Apart from this, no external influences are at play. Though diffusion of the moisture content is slow in the case under consideration ( Marin Zapata, 2010 ), it does play a role in reality ( Chester and Anand, 2011 ). We assume that paper exhibits elastic behavior, which, according to Niskanen (2012 , Ch.…”

Section: Introductionmentioning

confidence: 99%