COLLEGE OF ARTS AND SCIENCES Department of Mathematics and Statistics

# Lynn Schreyer

##### Associate Professor
Office: Neill Hall Room 225
Phone: (509) 335-3152
Fax: (509) 335-1188
Email:Lynn.Schreyer@wsu.edu

##### Teaching - Courses
MATH 440/540 Applied Math I: Partial Differential Equations

##### Research Interests
I am interested in mathematically modeling porous media - any material consisting of a solid and one or more other phases. In particular I enjoy modeling swelling porous materials (materials that swell due to the addition of more material, changing the concentration of ions, or the unloading of a pressure load), and porous materials with more than one fluid phase. Examples of swelling porous media include clays (expansive soils), polymers (such as drug-delivery polymers and bio-polymers), and cell membranes. To develop models I use a combination of averaging theory and thermodynamics (exploitation of the second law and manipulating independent variables to relate theory with what is measurable). PhD students have worked on modeling drug-delivery systems involving swelling polymers such as Aleve ( Tessa Weinstein and Keith Wojciechowski), the movement of cilia in lungs (Kannanut Chamsri), and transport of water through multiphase fluid porous media ( Eric Sullivan). I have also contributed in collaborative settings to modeling forest fires, upscaled reactive transport, laminar to turbulent transition of fluid flow, and refugee movement.
##### Publications
1. T.R. Ginn, L. G. Schreyer, and K. Zamani, Phase Exposure-Dependent Exchange Water Resources Research, 53, 619-632, 2017.
2. M. Addassi, L. Schreyer, B. Johannesson, and H. Lin, Pore-Scale Modeling of Vapor Transport in Partially Saturated Capillary Tube with Variable Area Using Chemical Potential, Water Resources Research, 52(9), pp. 7023-7035, 2016.
3. L. Schreyer, Note on Coussy's Thermodynamical Definition of Fluid Pressure for Deformable Porous Media, Transport in Porous Media, 114(3), pp. 815-821, 2016.
4. K. Chamsri and L. Schreyer-Bennethum, Permeability of Fluid Flow Through a Periodic Array of Cylinders, Applied Mathematical Modeling, 39(1), pp. 244-254, 2015.
5. K.J. Wojciechowski, J. Chen, L. Schreyer-Bennethum, and K. Sandberg Well-posedness and Numerical Solution of a Nonlinear Volterra Partial Integro-Differential Equation Modeling a Swelling Porous Media, Journal of Porous Media, 17(9), pp 763-784, 2014.
6. L. Schreyer-Bennethum, Effective Stress for Saturated and Unsaturated Porous Media - A Differential Approach, Vadose Zone Journal, 13(5), 2014.
7. L. Schreyer-Bennethum, Macroscopic Flow Potentials in Swelling Porous Media, Transport in Porous Media 94(1), pp. 47-68, 2012.
8. L. Schreyer-Bennethum and L. Albright, Evaluating the Incorporation of Technology and Application Projects in the Higher Education Mathematics Classroom, International Journal of Mathematical Education in Science and Technology 42(1), pp. 53-63, 2011.
9. J. Mandel, L.S. Bennethum, J.D. Beezley, J.L. Coen, C.C. Douglas, L.P. Franca, M. Kim, and A. Vodacek, A Wildland Fire Model with Data Assimilation Mathematics and Computers in Simulation 79, pp. 584-606, 2008.
10. T.F. Weinstein, L.S. Bennethum, J.H. Cushman, Multiscale, Three-Phase Theory for Swelling Drug Delivery Systems. Part I: Constitutive Theory. Journal of Pharmaceutical Sciences, 97(5), pp. 1878-1903, 2008.
11. T.F. Weinstein, L.S. Bennethum, J.H. Cushman, Multiscale, Three-Phase Theory for Swelling Drug Delivery Systems. Part II: Flow and Transport Models. Journal of Pharmaceutical Sciences, 97(5), pp. 1904-1915, 2008.
12. Lynn Schreyer-Bennethum. Theory of Flow and Deformation of Swelling Porous Materials at the Macroscale. Computers and Geotechnics, 34, pp. 267-278, 2007.
13. T. Weinstein and L. S. Bennethum. On the Derivation of the Transport Equation for Swelling Porous Materials with Finite Deformation. International Journal of Engineering Science, 44(18-19), pp. 1408-1422, 2006.
14. L. S. Bennethum. Compressibility Moduli for Porous Materials Incorporating Volume Fraction, Journal of Engineering Mechanics, 132(11), pp. 1205-1215, 2006.
15. L. S. Bennethum. Flow and Deformation: Understanding the Assumptions and Thermodynamics, in Proceedings of the XVth International Conference on Computational Methods in Water Resources (CMWR XV), June 13-17, 2004, Chapel Hill, NC, Volume 1, pp. 349-357, 2004.
16. J. H. Cushman, L. S. Bennethum, and P. P. Singh. Toward Rational Design of Drug Delivery Substrates: I. Mixture Theory for Two-Scale Biocompatible Polymers, Multiscale Modeling and Simulation, 2(2), pp. 302-334, 2004.
17. J. H. Cushman, P. P. Singh, and L. S. Bennethum. Toward Rational Design of Drug Delivery Substrates: II. Mixture Theory for Three-Scale Biocompatible Polymers and a Compuational Example, Multiscale Modeling and Simulation, 2(2), pp. 335-357, 2004.
18. L. S. Bennethum and T. Weinstein. Three Pressures in Porous Media, Transport in Porous Media, 54(1), pp. 1-34, 2004.
19. P. P. Singh, J. H. Cushman, L. S. Bennethum, and D. E. Maier. Thermomechanics of Swelling Biopolymeric Systems, Transport in Porous Media, 53, pp. 1-24, 2003.
20. J. H. Cushman, L. S. Bennethum, and B. X. Hu. A Primer on Upscaling Tools for Porous Media, Advances in Water Resources, 25 (8-12), pp. 1043 - 1067, 2002.
21. L. S. Bennethum and J. H. Cushman. Multicomponent, Multiphase Thermodynamics of Swelling Porous Media with Electroquasistatics:  I. Macroscale Field Equations, Transport in Porous Media, 47(3), pp. 309-336, 2002.
22. L. S. Bennethum and J. H. Cushman. Multicomponent, Multiphase Thermodynamics of Swelling Porous Media with Electroquasistatics: II. Constitutive Theory, Transport in Porous Media, 47(3), pp. 337-362, 2002.
23. L. S. Bennethum, M.M. Murad, and J. H. Cushman. Macroscale Thermodynamics and the Chemical Potential for Swelling Porous Media, Transport in Porous Media, 39(2), pp. 187-225, 2000.
24. L. S. Bennethum and J. H. Cushman. Coupled Solvent and Heat Transport of a Mixture of Swelling Porous Particles and Fluids:  Single Time-Scale Problem, Transport in Porous Media, 36(2), pp. 211-244, 1999.
25. L. S. Bennethum, M. A. Murad, and J. H. Cushman. Modified Darcy's Law, Fick's Law, and Terzaghi's Effective Stress Principle for Swelling Clay Soils Computers and Geotechnics, 20(3/4), pp. 245-266, 1997.
26. L. S. Bennethum and T. Giorgi. Generalized Forchheimer Law for Two-Phase Flow Based on Hybrid Mixture Theory, Transport in Porous Media, 26(3), pp. 261-275, 1997.
27. X. Feng and L. S. Bennethum. A Domain Decomposition Method for Solving a Helmholtz-like Problem In Elasticity using a Wilson Nonconforming Element , Mathematical Modelling and Numerical Analysis, 31(1), pp. 1-25, 1997.
28. L. S. Bennethum, M. A. Murad, and J. H. Cushman. Clarifying Mixture Theory and the Macroscale Chemical Potential, International Journal of Engineering Science, 34(14), pp. 1611-1621, 1996.
29. L. S. Bennethum and J. H. Cushman. Multiphase, Multicomponent Theory for Multiscale Swelling Systems with Interfaces. Part I: Balance Laws, International Journal of Engineering Science, 34(2), pp. 125-145, 1996.
30. L. S. Bennethum and J. H. Cushman. Multiphase, Multicomponent Theory for Multiscale Swelling Systems with Interfaces. Part II: Constitutive Theory, International Journal of Engineering Science, 34(2), pp. 147-169, 1996.
31. M. A. Murad, L. S. Bennethum, and J. H. Cushman. A Multi-Scale Theory of Swelling Porous Media: I. Application to One-Dimensional Consolidation, Transport in Porous Media, 19, pp. 93-122, 1995.
32. J. Douglas, Jr., J. Santos, D. Sheen, and L. S. Bennethum. Frequency Domain Treatment of One-Dimensional Scalar Waves, Mathematical Models and Methods in Applied Sciences, 3, pp. 171-194, 1993.