Efficient Lagrangian scalar tracking method for reactive local mass transport simulation through porous media

International Journal for Numerical Methods in Fluids

Volumn 67, Issue 4, 2011, Pages 501-517

  Voronov, Roman S ^a   van Gordon, Samuel B ^a   Sikavitsas, Vassilios I ^a   Papavassiliou, Dimitrios V ^a  

^a University of Oklahoma   (United States)

Author keywords

Lagrangian methods; Lattice Boltzmann simulations; Reactive flows; Transport in porous media

Indexed keywords

BONE TISSUE ENGINEERING; COLLISION FREQUENCY; COMPLICATED BOUNDARY CONDITIONS; EFFECTIVE DIFFUSIVITIES; FIRST-ORDER; FLOW PERFUSION; FLOWS THROUGH POROUS MEDIA; HETEROGENEOUS REACTIONS; IRREVERSIBLE REACTIONS; LAGRANGIAN; LAGRANGIAN METHODS; LATTICE BOLTZMANN SIMULATIONS; LATTICE-BOLTZMANN METHOD; REACTION RATE COEFFICIENTS; REACTIVE FLOW; SCHMIDT NUMBERS; SINGLE SOLVENTS; TRACKING METHOD; TRANSPORT IN POROUS MEDIA; TRANSPORT SIMULATION; VELOCITY FIELD;

BROWNIAN MOVEMENT; FLOW SIMULATION; POROUS MATERIALS; REACTION RATES; SCAFFOLDS (BIOLOGY); SOLUTE TRANSPORT; TISSUE; VELOCITY;

LAGRANGE MULTIPLIERS;

EID: 79956212377     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.2369     Document Type: Article

References (44)

1. Succi S. The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Oxford University Press: Oxford, New York, 2001.
2. Sukop MC, Thorne DT. NetLibrary Inc. Lattice Boltzmann Modeling an Introduction for Geoscientists and Engineers. Springer: Berlin, New York, 2006; 117-144.
3. Chen S, Doolen GD. Lattice Boltzmann method for fluid flows. Annual Review of Fluid Mechanics 1998; 30:329-364.
4. Kang QJ, Lichtner PC, Zhang DX. An improved Lattice Boltzmann model for multicomponent reactive transport in porous media at the pore scale. Water Resources Research 2007; 43:W12S14.1-W12S14.12.
5. Van Leemput P, Vandekerckhove C, Vanroose W et al. Accuracy of hybrid Lattice Boltzmann/finite difference schemes for reaction-diffusion systems. Multiscale Modeling and Simulation 2007; 6:838-857.
6. Papavassiliou DV. Turbulent transport from continuous sources at the wall of a channel. International Journal of Heat and Mass Transfer 2002; 45:3571-3583.
7. Papavassiliou DV, Hanratty TJ. The use of Lagrangian-methods to describe turbulent transport of heat from a wall. Industrial and Engineering Chemistry Research 1995; 34:3359-3367.
8. Thummala N. Convective heat transfer in microfluidics using Lagrangian methods and Lattice Boltzmann simulations. M.S. Thesis, School of Chemical, Biological and Materials Engineering, University of Oklahoma, Norman, 2004.
9. Papavassiliou DV. Understanding macroscopic heat/mass transfer using meso- and macro-scale simulations. In Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena. Gorban AN, Kazantzis N, Kevrekidis YG et al. (eds). Springer: Berlin, New York, 2006; 489-515.
10. Bhattacharya A, Usta OB, Yashin VV et al. Self-sustained motion of a train of haptotactic microcapsules. Langmuir 2009; 25:9644-9647.
11. Wang JY, Zhang XX, Bengough AG et al. Domain-decomposition method for parallel lattice Boltzmann simulation of incompressible flow in porous media. Physical Review E 2005; 72(1). Article No. 016702.
12. Kandhai D, Koponen A, Hoekstra AG et al. Lattice-Boltzmann hydrodynamics on parallel systems. Computer Physics Communications 1998; 111:14-26.
13. Cosgrove JA, Buick JM, Tonge SJ et al. Application of the lattice Boltzmann method to transition in oscillatory channel flow. Journal of Physics A-Mathematical and General 2003; 36:2609-2620.
14. Boyd J, Buick J, Green S. A second-order accurate Lattice Boltzmann non-Newtonian flow model. Journal of Physics A--Mathematical and General 2006; 39:14241-14247.
15. Yoshino A, Hotta Y, Hirozane T et al. A numerical method for incompressible non-Newtonian fluid flows based on the Lattice Boltzmann method. Journal of Non-Newtonian Fluid Mechanics 2007; 147:69-78.
16. Gabbanelli S, Drazer G, Koplik J. Lattice Boltzmann method for non-Newtonian (power-law) fluids. Physical Review E 2005; 72(4). Article No. 046312.
17. Swift MR, Orlandini E, Osborn WR et al. Lattice Boltzmann simulations of liquid-gas and binary fluid systems. Physical Review E 1996; 54:5041-5052.
18. Chen HD, Chen SY, Matthaeus WH. Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method. Physical Review A 1992; 45:R5339-R5342.
19. Frisch U, Hasslacher B, Pomeau Y. Lattice-gas automata for the Navier-Stokes equation. Physical Review Letters 1986; 56:1505-1508.
20. Qian YH, Dhumieres D, Lallemand P. Lattice BGK models for Navier-Stokes equation. Europhysics Letters 1992; 17:479-484.
21. McNamara GR, Zanetti G. Use of the Boltzmann-equation to simulate lattice-gas automata. Physical Review Letters 1988; 61:2332-2335.
22. Voronov RS, VanGordon S, Sikavitsas VI et al. Computational modeling of flow induced shear stresses within 3D salt-leached porous scaffolds imaged via micro-CT. Journal of Biomechanics 2010; 43:1279-1286.
23. Bhatnagar PL, Gross EP, Krook M. A model for collision processes in gases. 1. Small amplitude processes in charged and neutral one-component systems. Physical Review 1954; 94:511-525.
24. Bird RB, Stewart WE, Lightfoot EN. Transport Phenomena. Wiley: New York, 2002.
25. Einstein A. The motion of elements suspended in static liquids as claimed in the molecular kinetic theory of heat. Annalen Der Physik 1905; 17:549-560.
26. Mitrovic BM, Papavassiliou DV. Effects of a first-order chemical reaction on turbulent mass transfer. International Journal of Heat and Mass Transfer 2004; 47:43-61.
27. Nguyen KT, Papavassiliou DV. Effects of a reacting channel wall on turbulent mass transfer. International Journal of Heat and Mass Transfer 2008; 51:2940-2949.
28. Nguyen KT, Papavassiliou DV. Flow effects on the kinetics of a second-order reaction. Chemical Engineering Journal 2008; 140:370-380.
29. Tomadakis MM, Rupani D. Diffusion controlled reaction rate, survival probability, and molecular trajectory characteristics in the bulk, transition and Knudsen regime. Chemical Engineering Journal 2007; 128:1-10.
30. Kretlow JD, Mikos AG. From material to tissue: biomaterial development, scaffold fabrication, and tissue engineering. AIChE Journal 2008; 54:3048-3067.
31. Tuan RS, Boland G, Tuli R. Adult mesenchymal stem cells and cell-based tissue engineering. Arthritis Research and Therapy 2003; 5:32-45.
32. Jaiswal N, Haynesworth SE, Caplan AI et al. Osteogenic differentiation of purified, culture-expanded human mesenchymal stem cells in vitro. Journal of Cellular Biochemistry 1997; 64:295-312.
33. Sikavitsas VI, Bancroft GN, Holtorf HL et al. Mineralized matrix deposition by marrow stromal osteoblasts in 3D perfusion culture increases with increasing fluid shear forces. Proceedings of the National Academy of Sciences of the United States of America 2003; 100:14683-14688.
34. Holtorf HL, Jansen JA, Mikos AG. Flow perfusion culture induces the osteoblastic differentiation of marrow stromal cell-scaffold constructs in the absence of dexamethasone. Journal of Biomedical Materials Research Part A 2005; 72A:326-334.
35. Sikavitsas VI, Temenoff JS, Mikos AG. Biomaterials and bone mechanotransduction. Biomaterials 2001; 22:2581-2593.
36. Allori AC, Sailon AM, Pan JH et al. Biological basis of bone formation, remodeling, and repair-Part III: Biomechanical forces. Tissue Engineering Part B-Reviews 2008; 14:285-293.
37. Mikos AG, Thorsen AJ, Czerwonka LA et al. Preparation and characterization of poly( L-lactic acid) foams. Polymer 1994; 35:1068-1077.
38. Hou QP, Grijpma DW, Feijen J. Porous polymeric structures for tissue engineering prepared by a coagulation, compression moulding and salt leaching technique. Biomaterials 2003; 24:1937-1947.
39. Lakhotia S, Papoutsakis ET. Agitation induced cell injury in microcarrier cultures-protective effect of viscosity is agitation intensity dependent-experiments and modeling. Biotechnology and Bioengineering 1992; 39:95-107.
40. Sikavitsas VI, Bancroft GN, Lemoine JJ et al. Flow perfusion enhances the calcified matrix deposition of marrow stromal cells in biodegradable nonwoven fiber mesh scaffolds. Annals of Biomedical Engineering 2005; 33:63-70.
41. Porter B, Zauel R, Stockman H et al. 3-D computational modeling of media flow through scaffolds in a perfusion bioreactor. Journal of Biomechanics 2005; 38:543-549.
42. Alvarez-Barreto JF, Linehan SM, Shambaugh RL et al. Flow perfusion improves seeding of tissue engineering scaffolds with different architectures. Annals of Biomedical Engineering 2007; 35:429-442.
43. Weinbaum S, Cowin SC, Zeng Y. A model for the excitation of osteocytes by mechanical loading-induced bone fluid shear stresses. Journal of Biomechanics 1994; 27:339-360.
44. Matsumoto M, Nishimura T. Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Transactions on Modeling and Computer Simulation (TOMACS) 1998; 8:3-30.