Abstract
Modelling of drying processes without adjustable parameters is still a challenge. As emphasized in several previous works, this might partly be due to the impact of liquid films trapped in corners of the pore space. In this study, we present and analyse a drying experiment with a micromodel, which clearly shows the presence of corner films. In contrast with previous works, however, the corner films do not form a system of interconnected corner films extending over large regions in our micromodel. They rather form isolated capillary rings surrounding the solid blocks of the device, and thus, a quasi-two-dimensional version of liquid bridges often observed in the contact regions between grains in soils and packings of particles. These capillary rings essentially remain confined in the two-phase region. As a result, their impact on drying rate is much smaller than in systems favouring films hydraulically connected over long distances. The capillary liquid ring formation is taken into account in a pore network model of drying leading to satisfactory agreement with the experiment provided that the lateral pinning of liquid phase observed in the experiment is included in the model. Based on this, the model enriches the family of pore network models of drying and can be considered as a step towards the modelling of secondary capillary effects in drying in more complex geometry.
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Abbreviations
- \(A_{\mathrm{i,tot}} \) :
-
Total evaporation surface area (\(\hbox {m}^{2})\)
- \(A_\mathrm{t} \) :
-
Cross-sectional area of throats (\(\hbox {m}^{2})\)
- \(A_\mathrm{r} \) :
-
Ring evaporation surface area (\(\hbox {m}^{2})\)
- h :
-
Film height (m)
- L :
-
Lattice spacing (m)
- \(L_\mathrm{r} \) :
-
Ring width (m)
- \(L_\mathrm{d} \) :
-
Network depth (m)
- \(\tilde{M}\) :
-
Molar mass (\(\hbox {kg kmol}^{-1})\)
- \(\dot{M}\) :
-
Mass flow rate (\(\hbox {kg s}^{-1})\)
- P :
-
Total pressure (Pa)
- \(P_\mathrm{c} \) :
-
Capillary pressure (Pa)
- \(P_\mathrm{l} \) :
-
Liquid pressure (Pa)
- \(P_\mathrm{v} \) :
-
Vapour pressure (Pa)
- \(P_\mathrm{v}^*\) :
-
Saturation vapour pressure (Pa)
- \(P_{\mathrm{v},\infty }\) :
-
Vapour pressure in the bulk air phase (Pa)
- \(r_\mathrm{t} \) :
-
Throat radius (m)
- \(\bar{{r}}_\mathrm{t} \) :
-
Mean throat radius (m)
- \(r_{\mathrm{t,d}} \) :
-
Meniscus radius at ring detachment (m)
- \(\tilde{R}\) :
-
Universal gas constant (kJ kmol\(^{-1}\) K\(^{-1})\)
- \(s_{\mathrm{BL}} \) :
-
Boundary layer thickness (m)
- S :
-
Total network saturation (–)
- t :
-
Time (s)
- T :
-
Temperature (\(^{\circ }\hbox {C}\))
- \(\bar{{T}}\) :
-
Mean temperature (\(^{\circ }\hbox {C}\))
- V :
-
Volume (\(\hbox {m}^{3})\)
- \(\alpha \) :
-
Fitting parameter (–)
- \(\delta \) :
-
Diffusivity (\(\hbox {m}^{2}\,\hbox {s}^{-1})\)
- \(\theta \) :
-
Contact angle (–)
- \(\sigma \) :
-
Surface tension (\(\hbox {N}\,\hbox {m}^{-1})\)
- 0:
-
Initial value
- \(\infty \) :
-
Bulk phase
- i, j, k, l:
-
Pore indices, ring indices
- ij, kl, ik, jl, mk:
-
Throat indices
- p:
-
Pore
- t:
-
Throat
- r:
-
Ring
- v:
-
Vapour
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Acknowledgments
The Si-\(\hbox {SiO}_{2}\) pore network was produced by the Institute of Micro and Sensor Technique at Otto-von-Guericke University. Financial support by Deutsch-Franzoesische Hochschule (DFH-UFA) and DFG (in the frame of GKmm 1554) is gratefully acknowledged. Furthermore, the authors gratefully acknowledge the funding of part of the experimental equipment (CLSM) by the German Federal Ministry of Science and Education (BMBF) as part of the InnoProfile-Transfer project NaWiTec (03IPT701X).
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Vorhauer, N., Wang, Y.J., Kharaghani, A. et al. Drying with Formation of Capillary Rings in a Model Porous Medium. Transp Porous Med 110, 197–223 (2015). https://doi.org/10.1007/s11242-015-0538-1
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DOI: https://doi.org/10.1007/s11242-015-0538-1