Hostname: page-component-848d4c4894-2xdlg Total loading time: 0 Render date: 2024-06-21T23:51:56.309Z Has data issue: false hasContentIssue false

Dynamics of directional soluble wicking

Published online by Cambridge University Press:  16 March 2021

Sohyun Jung
Affiliation:
Department of Mechanical Engineering, Seoul National University, Seoul08826, Korea
Wonjung Kim*
Affiliation:
Department of Mechanical Engineering, Sogang University, Seoul04107, Korea
Ho-Young Kim*
Affiliation:
Department of Mechanical Engineering, Seoul National University, Seoul08826, Korea
*
Email addresses for correspondence: wonjungkim@sogang.ac.kr, hyk@snu.ac.kr
Email addresses for correspondence: wonjungkim@sogang.ac.kr, hyk@snu.ac.kr

Abstract

Liquids can invade fibrous porous media when the fibres are either wettable or soluble, and the infiltration rate can differ depending on spatial distribution of fibres as well as liquid properties. With continuing developments in dissolution-driven release mechanisms of porous drugs and chemical pattern formations, the understanding of how liquids spontaneously infiltrate into soluble fibrous media is strongly called for. Here we show that unlike capillarity-driven insoluble wicking (exhibiting diffusive growth of wetting distance with time), the wicking distance in soluble porous media grows linearly with time as dominated by liquid viscosity rather than surface tension. Such soluble wicking is highly sensitive to flow orientation relative to fibre alignment, so that it arises only in the crosswise direction while being strongly inhibited in the lengthwise direction. We present a theoretical model to explain the experimentally measured wicking rates in soluble porous media.

Type
JFM Papers
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Abd El-Hady, A. & Abd El-Rehim, H.A. 2004 Production of prednisolone by pseudomonas oleovorans cells incorporated into pvp/peo radiation crosslinked hydrogels. Biomed Res. Intl 2004 (4), 219226.Google ScholarPubMed
Barnes, A.C., Bieze, T.W.N., Enderby, J.E. & Layte, J.C. 1994 Dynamics of water in the poly(ethylene oxide) hydration shell: a quasi elastic neutron-scattering study. J. Phys. Chem. 98, 1152711532.CrossRefGoogle Scholar
Baver, L.D. 1949 Retension and movement of soil moisture. In Hydrology (ed. O.E. Meinzer), pp. 364–384. Dover Publications.Google Scholar
Bayramli, E. & Powell, R.L. 1990 The normal (transverse) impregnation of liquids into axially oriented fiber bundles. J. Colloid Interface Sci. 138, 346353.CrossRefGoogle Scholar
Bear, J. 1972 Dynamics of Fluid in Porous Media, pp. 161176. Elsevier.Google Scholar
Brielles, N., et al. 2007 Imbibition and dissolution of a porous medium. Ind. Engng Chem. Res. 46, 57855793.CrossRefGoogle Scholar
Burgess, I.B., Mishchenko, L., Hatton, B.D., Kolle, M., Loncar, M. & Aizenberg, J. 2011 Encoding complex wettability patterns in chemically functionalized 3D photonic crystals. J. Am. Chem. Soc. 133, 1243012432.CrossRefGoogle ScholarPubMed
Buckingham, E. 1914 On physically similar systems; illustrations of the use of dimensional equations. Phys. Rev. 4 (4), 345376.CrossRefGoogle Scholar
Cai, J. & Yu, B. 2011 A discussion of the effect of tortuosity on the capillary imbibition in porous media. Transp. Porous Med. 89 (2), 251263.CrossRefGoogle Scholar
Carman, P.C. 1941 Capillary rise and capillary movement of moisture in fine sands. Soil Sci. 52 (1), 114.CrossRefGoogle Scholar
Colombo, P., Bettini, R., Santi, P., de Ascentiis, A. & Peppas, N.A. 1996 Analysis of the swelling and release mechanisms from drug delivery systems with emphasis on drug solubility and water transport. J. Control. Release 39, 231237.CrossRefGoogle Scholar
Cornell, D. & Katz, D.L. 1953 Flow of gases through consolidated porous media. Ind. Engng Chem. 45 (10), 21452152.CrossRefGoogle Scholar
Couper, A. & Stepto, R.F.T. 1969 Diffusion of low-molecular weight poly (ethylene oxide) in water. T. Faraday Soc. 65, 24862496.CrossRefGoogle Scholar
Daccord, G. 1987 Chemical dissolution of a porous medium by a reactive fluid. Phys. Rev. Lett. 58, 479.CrossRefGoogle ScholarPubMed
Darcy, H. 1856 Les Fontaines publiques de la ville de Dijon. Victor Dalmont.Google Scholar
Doi, M. & Edwards, S.F. 1988 The Theory of Polymer Dynamics, pp. 222236. Oxford University Press.Google Scholar
Dupuit, J.È.J. 1863 Ètudes thèoriques et pratiques sur le mouvement des eaux dans les canaux dècouverts et à travers les terrains permèables. Dunod.Google Scholar
Ebagninin, K.W., Benchabane, A. & Bekkour, K. 2009 Rheological characterization of poly (ethylene oxide) solutions of different molecular weights. J. Colloid Interface Sci. 336, 360367.CrossRefGoogle ScholarPubMed
Forchheimer, P. 1986 Uber die ergiebigkeit von brummen-anlagen und sickerschlitzen. Z. Arch. Ing.-Ver. Hannover. 32, 539563.Google Scholar
de Gennes, P.-G. 1979 Scaling Concepts in Polymer Physics, pp. 165200. Cornell University Press.Google Scholar
de Gennes, P.-G., Brochard-Wyart, F. & Quéré, D. 2004 Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves. Springer-Verlag.CrossRefGoogle Scholar
Griffiths, J.C. 1952 Grain-size distribution and reservoir-rock characteristics. Bull. Am. Assoc. Petrol. Geol. 36 (2), 205229.Google Scholar
Ha, J., Kim, J., Jung, Y., Yun, G., Kim, D.-N. & Kim, H.-Y. 2018 Poro-elasto-capillary wicking of cellulose sponges. Sci. Adv. 4, eaao7051.CrossRefGoogle ScholarPubMed
Jacob, C.E. 1946 Radial flow in a leaky artesian aquifer. Trans. Am. Geophys. Un. 27 (2), 198208.CrossRefGoogle Scholar
Kozeny, J. 1927 Uber kapillare leitung der wasser in boden. S.-Ber. Wiener Akad., Abt. 136, 271306.Google Scholar
Kim, J., Ha, J. & Kim, H.-Y. 2017 Capillary rise of non-aqueous liquids in cellulose sponges. J. Fluid Mech. 818, R2.CrossRefGoogle Scholar
Kim, J., Moon, M.-W., Lee, K.-R., Mahadevan, L. & Kim, H.-Y. 2011 Hydrodynamics of writing with ink. Phys. Rev. Lett. 107, 264501.CrossRefGoogle ScholarPubMed
Kim, S.J., Choi, J.W., Moon, M.W., Lee, K.R., Chang, Y.S., Lee, D.Y. & Kim, H.-Y. 2015 Wicking and flooding of liquids on vertical porous sheets. Phys. Fluids 27, 032105.CrossRefGoogle Scholar
Landeryou, M., Eames, I. & Cottenden, A. 2005 Infiltration into inclined fibrous sheets. J. Fluid Mech. 529, 173193.CrossRefGoogle Scholar
Mao, N. & Russell, S.J. 2008 Capillary pressure and liquid wicking in three-dimensional nonwoven materials. J. Appl. Phys. 104, 034911.CrossRefGoogle Scholar
Nelson, W.R. & Baver, L.D. 1940 Movement of water through soils in relation to the nature of the pores. Proc. Soil. Sci. Soc. Am. 5, 6076.Google Scholar
Purcell, W.R. 1949 Capillary pressures-their measurement using mercury and the calculation of permeability therefrom. J. Petrol. Tech. 1 (02), 3948.CrossRefGoogle Scholar
Raux, R.S., Cockenpot, H., Ramaioli, M., Quéré, D. & Clanet, C. 2013 Wicking in a powder. Langmuir 29, 36363644.CrossRefGoogle ScholarPubMed
Rodriguez, E., Giacomelli, F. & Vazquez, A. 2004 Permeability-porosity relationship in rtm for different fiberglass and natural reinforcements. J. Compos. Mater. 38, 259268.CrossRefGoogle Scholar
Rose, W. & Witherspoon, P.A. 1956 Studies of Waterflood Performance. Division of the Ill. State Geol. Survey.Google Scholar
Scheidegger, A.E. 1960 The Physics of Flow Through Porous Media, pp. 124151. University of Toronto Press.Google Scholar
Shin, B., Ha, J., Lee, M., Park, K., Park, G.H., Choi, T.H., Cho, K.-J. & Kim, H.-Y. 2018 Hygrobot: a self-locomotive ratcheted actuator powered by environmental humidity. Sci. Robot. 3, eaar2629.CrossRefGoogle ScholarPubMed
Singh, B.N. & Kim, K.H. 2000 Floating drug delivery systems: an approach to oral controlled drug delivery via gastric retention. J. Control. Release 63, 235259.CrossRefGoogle ScholarPubMed
Szymczak, P. & Ladd, A.J. 2011 Instabilities in the dissolution of a porous matrix. Geophys. Res. Lett. 38, L07403.CrossRefGoogle Scholar
Thomas, S.W., Chiechi, R.C., LaFratta, C.N., Webb, M.R., Lee, A., Wiley, B.J., Zakin, M.R., Walt, D.R. & Whitesides, G.M. 2009 Infochemistry and infofuses for the chemical storage and transmission of coded information. Proc. Natl Acad. Sci. USA 106, 91479150.CrossRefGoogle ScholarPubMed
Twist, J.N. & Zatz, J.L. 1988 Membrane–solvent–solute interaction in a model permeation system. J. Pharm. Sci. 77, 536540.CrossRefGoogle Scholar
Vrentas, J.S. & Duda, J.L. 1979 Molecular diffusion in polymer solutions. AIChE J. 25, 124.CrossRefGoogle Scholar
Washburn, E.W. 1921 The dynamics of capillary flow. Phys. Rev. 17, 273.CrossRefGoogle Scholar
Werzer, O., Warr, G.G. & Atkin, R. 2011 Compact poly (ethylene oxide) structures adsorbed at the ethylammonium nitrate-silica interface. Langmuir 27, 35413549.CrossRefGoogle ScholarPubMed
Xia, D. & Brueck, S.R.J. 2008 Strongly anisotropic wetting on one-dimensional nanopatterned surfaces. Nano Lett. 8, 28192824.CrossRefGoogle ScholarPubMed
Yang, G.-Z., et al. 2018 The grand challenges of science robotics. Sci. Robot. 3, eaar7650.CrossRefGoogle ScholarPubMed
Yoon, J., Cai, S., Suo, Z. & Hayward, R.C. 2010 Poroelastic swelling kinetics of thin hydrogel layers: comparison of theory and experiment. Soft Matt. 6, 60046012.CrossRefGoogle Scholar
Yuasa, H., Takashima, Y. & Kanaya, Y. 1996 Studies on the development of intragastric floating and sustained release preparation. I. Application of calcium silicate as a floating carrier. Chem. Pharm. Bull. 44, 13611366.CrossRefGoogle Scholar