A
dynamic in-silico model captures the kinetics of 1-d gravity driven instabilities,
in gravity or centrifuge, of fluid-infiltrated poroelastic media in a partial
differential equation (pde). The pde yields the porosity profile over height and
time for the given initial and boundary conditions, during slow compaction in
counter-current fluid drainage. Processes captured are amongst others
sedimentation, creaming and subsidence. The most important limiting
prerequisite is that the incompressible dispersed medium is sufficiently
structured and/or concentrated that it compacts during slow drainage, without
segregation in sizes or in components. For Unilever, modeling of gravitational instability of products is important to
quantify or extrapolate long time behavior during shelf life or use centrifuge data to quickly predict long term shelf
performance of products.
References
[1]
Mow, V.C. and Lai, W.M. (1979) Mechanics of Animal Joints. Annual Review of Fluid Mechanics, 11, 247-288. https://doi.org/10.1146/annurev.fl.11.010179.001335
[2]
Bowen, R.M. (1980) Incompressible Porous Media Models by Use of the Theory of Mixtures. International Journal of Engineering Science, 18, 1129-1148. https://doi.org/10.1016/0020-7225(80)90114-7
[3]
Holmes, M.H. (1986) Finite Deformation of Soft Tissue: Analysis of a Mixture Model in Uniaxial Compression. Journal of Biomechanical Engineering, 108, 372-381. https://doi.org/10.1115/1.3138633
[4]
Barry, S.I. and Mercer, G.B. (1999) Flow and Deformation in Poroelasticity: I Unusual Exact Solutions. Mathematical and Computer Modelling, 30, 23-29. https://doi.org/10.1016/S0895-7177(99)00177-6
[5]
Barry, S.I. and Holmes (2001) Asymptotic Behaviour of Thin Poroelastic Layers, IMA. Journal of Applied Mathematics, 66, 175-194. https://doi.org/10.1093/imamat/66.2.175
[6]
Henderson, N., Brêttas, J.C. and Sacco, W.F. (2010) A Three-Parameter Kozeny–Carman Generalized Equation for Fractal Porous Media. Chemical Engineering Science, 65, 4432–4442. https://doi.org/10.1016/j.ces.2010.04.006
[7]
Hossain, Z. and Cohen, A.J. (2012) Relationship among Porosity, Permeability, Electrical and Elastic Properties. SEG Las Vegas 2012 Annual Meeting. https://doi.org/10.1190/segam2012-1496.1
[8]
Van Wyk, C.M. (1946) Note on the Compressibility of Wool. The Journal of The Textile Institute, 37, T285. https://doi.org/10.1080/19447024608659279
[9]
Taylor, P.M. and Pollet, D.M. (2002) Static Low-Load Lateral Compression of Fabrics. Textile Research Journal, 72, 983-990. https://doi.org/10.1177/004051750207201109
[10]
Toll, S. (1998) Packing of Fiber Reinforcements. Polymer Engineering & Science, 38, 1337-1350. https://doi.org/10.1002/pen.10304
[11]
Zohuri, B. (2015) Dimensional Analysis and Self-Similarity Methods for Engineers and Scientists. Chapter 2, Springer, Berlin. https://doi.org/10.1007/978-3-319-13476-5
[12]
Martin, J., Rskotomalala, N. and Salin, D. (1994) Hydrodynamic Dispersion Broadening of a Sedimentation Front. Physics of Fluids, 6, 3215-3217. https://doi.org/10.1063/1.868051
[13]
Hutter, E.M., Kuijk, A., Veen S.J., van der Weg, P.B., Weg, P. and Velikov, K.P. (In Preparation) Gravity-Driven Instabilities in Multiphase Emulsion-in-Fibrillar Colloidal Gels Systems.
[14]
Romanoff, A.L. and Romanoff, A.J. (1949) The Avian Egg.
[15]
Kuentz, M. and Roethlisberger, D. (2003) Rapid Assessment of Sedimentation Stability in Dispersions Using Near Infrared Transmission Measurements during Centrifugation and Oscillatory Rheology. European Journal of Pharmaceutics and Biopharmaceutics, 56, 355-361. https://doi.org/10.1016/S0939-6411(03)00108-5
[16]
https://www.lum-gmbh.com/step-technology_en.html
[17]
Doornhof, D., et al. (2006) Compaction and Subsidence—Schlumberger. Oilfield Review, 18, 50-68.
[18]
Zeng, X. and Decker, M. (2009) Improving the Numerical Solution of Soil Moisture-Based Richards Equation for Land Models with a Deep or Shallow Water Table. Journal of Hydrometeorology, 10, 308-319. https://doi.org/10.1175/2008JHM1011.1
[19]
Kynch, G.J. (1952) A Theory of Sedimentation. Transactions of the Faraday Society, 48, 166-176. https://doi.org/10.1039/tf9524800166
[20]
Tory, E. (1996) Sedimentation of Small Particles in a Viscous Fluid. Computational Mechanics Publications, Southampton.
[21]
Bürger, R. and Concha, F. (1998) Mathematical Model and Numerical Simulation of the Settling of Flocculated Suspensions. International Journal of Multiphase Flow, 24, 1005-1023. https://doi.org/10.1016/S0301-9322(98)00026-3
[22]
Concha, F. and Bürger, R. (2002) A Century of Research in Sedimentation and Thickening. KONA No. 20.
