George E. Kapellos

Theoretical modeling of fluid flow in cellular biological media: An overview

Fluid-structure interactions strongly affect, in multiple ways, the structure and function of cellular biological media, such as tissues, biofilms, and cell-entrapping gels. Mathematical models and computer simulation are important tools in advancing our understanding of these interactions, interpreting experimental observations, and designing novel processes and biomaterials. In this paper, we present a comprehensive survey and highlight promising directions of future research on theoretical modeling of momentum transport in cellular biological media with focus on the formulation of governing equations and the calculation of material properties both theoretically and experimentally. With regard to the governing equations, significant work has been done with single-scale approaches (e.g. mixture theory), whereas traditional upscaling methods (e.g. homogenization, volume averaging) or multiscale equation-free approaches have received limited attention. The underlying concepts, strengths, and limitations of each approach, as well as examples of use in the field of biomaterials are presented. The current status of knowledge regarding the dependence of macroscopic material properties on the volume fractions, geometry, and intrinsic material properties of the constituent phases (cells, extracellular matrix and fluid) is also presented. The observation of conformational changes that occur at finer levels of the structural hierarchy during momentum transport, the correlation of macro-properties with geometrical and topological features of materials with heterogeneous and anisotropic microstructure, as well as the determination of dynamic material properties are among important challenges for future research.

Modeling Momentum and Mass Transport in Cellular Biological Media: From the Molecular to the Tissue Scale

Cellular biological media, such as tissues and biofilms, are multiphase complex systems with dynamically evolving and highly organized hierarchical structures. The objective of this chapter is to present a comprehensive review of the theoretical modeling of momentum and mass transport in cellular biological media. In the spirit of a bottom-up approach, the chapter begins with a concise exposition of the state of the art in the mechanics of individual biomacromolecules, subcellular structures (e.g., cytoskeleton, membrane) and biological cells that build up the cellular biological medium. Thereafter, the main part is focused on the formulation of balance laws and constitutive equations, as well as on the experimental and theoretical calculation of constitutive parameters. The conceptual framework and the mathematical foundation is presented for various theoretical approaches, including single-scale–single-phase models, the theory of interacting continua, upscaling methods (e.g., spatial averaging, homogenization) and multiscale equation-free approaches.

Plane Couette-Poiseuille flow past a homogeneous poroelastic layer

An analytical solution is presented for the problem of fully developed plane Couette-Poiseuille flow past a homogeneous, permeable poroelastic layer. Main novel feature of this work is that the compressibility, which is related to the action of the free-fluid pressure on the poroelastic layer, is taken into account. Therefore, the solid stress problem is two-dimensional, although the fluid flow problem remains one-dimensional in the limit of infinitesimal strain. The pressure-related compressibility affects strongly the distribution of the von Mises stress in the poroelastic layer by shifting the local maximum towards the high-pressure region of the channel. Furthermore, the established analytical solution is used to investigate some aspects of the mechanotransducing role of the endothelial surface layer. A compressible surface layer might serve as a “bumper’’ by reducing the magnitude of the overall shearing force (viscous and elastic) acting on endothelial cells, as compared to the magnitude of the flui...

Microbial Strategies for Oil Biodegradation

Abstract The current understanding of the fundamental microscale mechanisms that underlie the biodegradation of oily substrates by microbial communities is concisely reviewed in this chapter. Depending on a microbes affinity for the oily phase and its ability to proliferate in multicellular structures, three fundamental growth modes are identified: suspended interfacial (flatlanders), and biofilm. Each growth mode might involve one, or more, substrate uptake tactics depending on the microbes preference for the physical state of the oil compound, which might be dissolved in the aqueous phase, complexed with surfactant in micelles and emulsified oil droplets, or in the oily phase. A minimal continuum-based formulation for the mathematical description of biofilm formation over deformable oil–water interfaces is also presented.

Chapter 8 – Fluid-Biofilm Interactions in Porous Media

Improved understanding and quantification of fluid-biofilm interactions are of essential importance in unraveling the mechanisms of biofilm formation and migration in porous materials. In this chapter, the development of microbial biofilms in porous media is reviewed in depth, with emphasis on the processes occurring at the pore-scale and by including both experimental and modeling aspects. Furthermore, a computer-aided simulator is presented for the prediction of the pattern of evolution and the rate of growth of heterogeneous biofilms within the pore space of porous materials. The simulator combines continuum-based descriptions of fluid flow and solute transport with particle-based descriptions of biofilm growth and detachment. As a case study, the interactions between fluid flow and growing biofilms are examined in the context of biological clogging of various porous structures (single pore, granular 2D core, consolidated 3D core) and under different flow regimes (constant flow rate versus constant pressure drop).

Hierarchical Simulation of the Spatiotemporal Evolution of Heterogeneous Biofilms and their Impact on the Flow Pattern and Mass Transport in 3-D Porous Media

A computer-aided simulator has been developed for the prediction of the pattern of evolution and the rate of growth of heterogeneous biofilms within the pore space of 3-D virtual porous media (core-scale). The biofilm itself is considered as a heterogeneous porous material that exhibits a hierarchy of length scales. A recently developed theoretical model, which takes into account fundamental geometric and physicochemical properties of the biofilm at the cell- and molecular-scales, is used to calculate the values of the local hydraulic permeability and diffusion coefficient within it. Modified Navier-Stokes-Brinkman equations are solved numerically to determine the velocity and pressure fields within the pore space, which is occupied partly by free fluid and partly by biofilms. Under the action of large fluid shear stresses biofilm fragments detach and re-enter into the free fluid stream. A Lagrangian-type simulation is used to determine the trajectories of the detached fragments until they exit from the system or re-attach to downstream grain or biofilm surfaces. Furthermore, the spatiotemporal distributions of nutrients and soluble cellular products are determined from the numerical solution of the governing convection-diffusion-reaction equations. The simulator incorporates growth and apoptosis kinetics for the bacterial cells and production and lysis kinetics for the extracellular polymeric substances that compose the biofilm. Growth-induced deformation of the biofilms is implemented by using a cellular automaton approach. Transient changes in the pore geometry caused by biofilm proliferation intensify the formation of preferential flowpaths within the porous medium. The decrease of permeability caused by clogging of the porous medium is calculated and is found to be in qualitative agreement with published experimental results.