Peculiarities of unsteady mass transfer in flat channels with liquid and gel
Tóm tắt
The rate of the unsteady mass-transfer process in horizontal flat channels filled with viscous liquid (water) and in channels filled with gel has been measured experimentally. It has been established that the rate of propagation of a substance through a channel under the unsteady one-dimensional mass transfer conditions depends on its width and exceeds the value corresponding to the rate of diffusion. The measured mass transport rate in an open channel is less than in a closed channel. The reason for the increased mass-transfer rate with regard to the diffusion mechanism is the slow convective flow of liquid caused by the difference between the densities of a diffusing substance and water. The presence of the surface concentration gradient of liquid gives rise to the appearance of surface forces that significantly affect the mass transport rate. The similarity of the mass-transfer behavior in channels filled with pure liquid and gels is found experimentally, which allows one to talk about their presence, as well as of convective transport in them.
Tài liệu tham khảo
Gels: Structures, Properties, and Functions. Fundamentals and Applications, Progress of Colloid and Polymer Science, vol. 136, Tokita, M. and Nishinary, K., Eds., Berlin: Springer, 2009.
Scherer, G.W, Structure and properties of gels, Cem. Concr. Res., 1999, vol. 29, no. 8, pp. 1149–1157.
Mitchell, J.R, The rheology of gels, J. Texture Stud., 1980, vol. 11, no. 4, pp. 315–337.
Deryagin, B.V, The stability of colloid systems (theoretical aspect), Russ. Chem. Rev., 1979, vol. 48, no. 4, pp. 363–388.
Scherer, G.W, Aging and drying of gels, J. Non-Cryst. Solids, 1988, vol. 100, nos. 1–3, pp. 77–92.
Molecular Gels: Materials with Self-Assembled Fibrillar Networks, Weiss, R.G. and Terech, P., Eds., Dordrecht, Netherlands: Springer, 2006.
Raub, Ch.B., Suresh, V., Krasieva, T., Lyubovitsky, J., Mih, Ju.D., Putnam, A.J., Tromberg, B.J., and George, S.C, Noninvasive assessment of collagen gel microstructure and mechanics using multiphoton microscopy, Biophys. J., 2007, vol. 92, no. 6, pp. 2212–2222.
Deshpande, R., Pore Structure Evolution of Silica Gels and Microstructural Dependence of Its Properties, Albuquerque, N.M.: Univ. New Mexico, 1992.
Gels Handbook, Kajiwara, K. and Osada, Yo., Eds., Amsterdam: Elsevier, 2000, vols. 1–4.
Rivest, Ch., Morrison, D.W.G., Ni, B., Rubin, J., Yadav, V., Mahdavi, A., Karp, J.M., and Khademhosseini, A, Microscale hydrogels for medicine and biology: Synthesis, characteristics and applications, J. Mech. Mater. Struct., 2007, vol. 2, no. 6, pp. 1103–1119.
Arjmand, O., Ahmadi, M., and Hosseini, L, An overview of the polymer gel technique to improve the efficiency of water flooding into oil reservoirs (with introduction of a new polymer), Int. J. Chem. Pet. Sci., 2013, vol. 2, no. 1, pp. 1–9.
Westrin, B.A. and Axelsson, A, Diffusion in gels containing immobilized cells: A critical review, Biotechnol. Bioeng., 1991, vol. 38, no. 5, pp. 439–446.
Fang, H., Wan, R., Gong, X., Lu, H., and Li, S, Dynamics of single-file water chains inside nanoscale channels: Physics, biological significance and applications, J. Phys. D: Appl. Phys., 2008, vol. 41, no. 10, p. 103002.
Amsden, B, Solute diffusion within hydrogels: Mechanisms and models, Macromolecules, 1998, vol. 31, no. 23, pp. 8382–8395.
Pokusaev, B.G., Karlov, S.P., Vyazmin, A.V., and Nekrasov, D.A, Peculiarities of diffusion in gels, Thermophys. Aeromech., 2013, vol. 20, no. 6, pp. 749–756.
Lauffer, M, Theory of diffusion in gels, Biophys. J., 1961, vol. 1, no. 3, pp. 205–213.
Sukharev, Yu.I., Matveichuk, Yu.V., and Kurcheiko, C.B, Effect of periodic diffusion conductivity in silica gel, Izv. Chelyab. Nauch. Tsentra Ural. Otd. Ross. Akad. Nauk, 1999, no. 2, pp. 151–160.
Kutateladze, S.S., Fundamentals of Heat Transfer, New York: Hodder & Stoughton Educational, 1963.
Philibert, J, One and half century of diffusion: Fick, Einstein, before and beyond, Diffus. Fundam., 2006, vol. 4, pp. 611–619.
Pineda, I., Alvarez-Ramirez, J., and Dagdug, L, Diffusion in two-dimensional conical varying width channels: comparison of analytical and numerical results, J. Chem. Phys., 2012, vol. 137, no. 17, p. 174103.
Bosi, L., Ghosh, P.K., and Marchesoni, F, Analytical estimates of free Brownian diffusion times in corrugated narrow channels, J. Chem. Phys., 2012, vol. 137, no. 17, p. 174110.
Makhnovskii, Yu.A., Zitserman, V.Yu., and Antipov, A.E, Directed transport of a Brownian particle in a periodically tapered tube, J. Exp. Theor. Phys., 2012, vol. 115, no. 3, pp. 535–549.
Polyanin, A.D., Kutepov, A.M., Vyazmin, A.V., and Kazenin, D.A, Hydrodynamics, Mass and Heat Transfer in Chemical Engineering, London: Taylor and Francis, 2002.
Polyanin, A.D. and Vyaz’min, A.V, Differential-difference heat-conduction and diffusion models and equations with a finite relaxation time, Theor. Found. Chem. Eng., 2013, vol. 47, no. 3, pp. 217–225.
Deryagin, B.V., Churaev, N.V., and Muller, V.M., Poverkhnostnye sily (Surface Forces), Moscow: Nauka, 1985.
Muhr, A.H. and Blanshard, J.-M.V., Diffusion in gels, Polymer, 1982, vol. 23, Suppl., pp. 1012–1026.
Yankov, D, Diffusion of glucose and maltose in polyacrylamide gel, Enzyme Microb. Technol., 2004, vol. 34, no. 6, pp. 603–610.
Neuman, S.P. and Tartakovsky, D.M, Perspective on theories of non-Fickian transport in heterogeneous media, Adv. Water Resour., 2009, vol. 32, no. 5, pp. 670–680.
Pokusaev, B.G., Kazenin, D.A., and Karlov, S.P, Immersion tomographic study of the motion of bubbles in a flooded granular bed, Theor. Found. Chem. Technol., 2004, vol. 38, no. 6, pp. 561–568.
Pokusaev, B.G., Karlov, S.P., Nekrasov, D.A., and Zakharov, N.S, Onset of convective flows in a nearwall granular layer during nonstationary liquid boiling, Tech. Phys. Lett., 2014, vol. 40, no. 8, pp. 680–683.
Vitovskii, O.V., Kuznetsov, V.V., and Nakoryakov, V.E, Stability of the displacement front and development of “fingering” in a porous medium, Fluid Dynam., 1989, vol. 24, no. 5, pp. 739–745.
Kutepov, A.M., Pokusaev, B.G., Kazenin, D.A., Karlov, S.P., and Vyaz’min, A.V, Interfacial mass transfer in the liquid–gas system: An optical study, Theor. Found. Chem. Eng., 2001, vol. 35, no. 3, pp. 213–216.
Karlov, S.P., Kazenin, D.A., and Vyazmin, A.V, The time evolution of chemo-gravitational convection on a brim meniscus of wetting, Physica A, 2002, vol. 315, nos. 1–2, p. 236–242.
Lee, S., Lee, H.-Y., Lee, I.-F., and Tseng, C.-Y., Ink diffusion in water, Eur. J. Phys., 2004, vol. 25, no. 2, pp. 331–336.
Malkin, A.Ya. and Chalykh, A.E., Diffuziya i vyazkost' polimerov: Metody izmereniya (Diffusion and Viscosity of Polymers: Measurement Methods), Moscow: Khimiya, 1979.
Helseth, L.E, A simple experiment for visualizing diffusion, Eur. J. Phys., 2011, vol. 32, p. 1193–1197.
Kazenin, D.A., Karlov, S.P., Nekrasov, D.A., and Pokusaev, B.G, Rapid analysis of the diffusion properties of gels for organizing filtration flows in soil, Ekolog. Prom–st. Rossii, 2011, no. 1, pp. 13–15.
Michelman-Ribeiro, A., Horkay, F., Nossal, R., and Boukari, H, Probe diffusion in aqueous poly(vinyl alcohol) solutions studied by fluorescence correlation spectroscopy, Biomacromolecules, 2007, vol. 8, no. 5, pp. 1595–1600.
Liu, J., Chen, L., Li, L., Hu, X., and Cai, Y, Steadystate fluorescence study on release of camptothecin from agar hydrogel, Int. J. Pharm., 2004, vol. 287, nos. 1–2, pp. 13–19.
Polyanin, A.D. and Zaitsev, V.F., Spravochnik po nelineinym uravneniyam matematicheskoi fiziki: Tochnye resheniya (Handbook of Nonlinear Equations of Mathematical Physics: Exact Solutions), Moscow: Fizmatlit, 2002.
Polyanin, A.D, Exact generalized separable solutions to nonlinear delay reaction–diffusion equations, Theor. Found. Chem. Eng., 2015, vol. 49, no. 1, pp. 107–114.