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Biofilm is a layer of syntrophic microorganisms stick to each other and to the surface. The importance of biofilms is enormous in various industrial applications and human everyday life. The effects of biofilm could be either positive or negative. Positive effects are encountered in industrial processes, bioremediation, and wastewater treatment. Negative effects are more common with the marine industry being one of the sectors, which confronts severe corrosion problems caused by biofouling on the surfaces of equipment and infrastructures. In space industry, microbial contamination and biofouling adversely affect both crew health and mission-related equipment, the latter including hardware, water systems, piping, and electrical tools. The capacity of biofilms to grow in space environment was confirmed already in 1991. One of the most important surface properties of biofilms is wettability, which dictates not only how a liquid spreads over the uneven external surface of biofilms but also how it penetrates into their porous and morphologically complex structure. To investigate wetting and spreading onto biofilms, model materials are often used to simulate different morphological and functional features of biofilms in a controlled way, for example, soft, deformable, soluble, structured, porous materials. Here, we review recent advances in wetting and spreading on porous and soft deformable surface together with biofilms wetting properties and its importance in space industry. We conclude with a discussion of the main directions for future research efforts regarding biofilm wetting.

The cell cycle is the biological process used by cells to replicate their genetic material and give birth to new cells that are in turn eligible to proliferate. It is highly regulated by the timed expression of proteins which trigger cell cycle events such as the start of DNA replication or the commencement of mitosis (when the cell physically divides into two daughter cells). Mathematical models of the cell cycle have been widely developed both at the intracellular (protein kinetics) and macroscopic (cell duplication) levels. Due to the cell cycle specificity of most chemother-apeutic drugs, these models are increasingly being used for the study and simulation of cellular kinetics in the area of cancer treatment. In this work, we present a population balance model (PBM) of the cell cycle in leukemia that uses intracellular protein expression as state variable to represent phase progress. Global sensitivity analysis highlighted cell cycle phase durations as the most significant parameters; experiments were performed to extract them and the model was validated. Our model was then tested against other differential cell cycle models (ODEs, delay differential equations (DDEs)) in their ability to fit experimental data and oscillatory behavior. We subsequently coupled each of them with a pharmacokinetic/pharmacodynamic model of chemotherapy delivery that was previously developed by our group. Our results suggest that the particular cell cycle model chosen highly affects the outcome of the simulated treatment, given the same steady-state kinetic parameters and drug dosage/scheduling, with our PBM appearing to be the most sensitive under the same dose.

The cell cycle is a biologically timed process by which cells duplicate. It consists of 4 phases, during which cells undergo different mandatory transformations. Modelling the cell cycle therefore requires capturing the evolution of those processes inside of each phase. A specific three stage biologically supported population balance model employed to simulate evolution of several cell cultures is studied here in detail. The three governing equations of this model are composed by growth and transition terms. A one equation analogue of the multistage model is formulated and it is solved analytically in the self-similarity domain. The effect of initial conditions at the system evolution is studied numerically. The three model equations are then considered by using asymptotic and numerical techniques. It is shown that in the case of sharp interstage transition the discontinuities of the initial conditions are preserved during cell growth leading to eternal oscillations whereas for distributed transition the cell distribution converges to a self-similar (long time asymptote) shape. It is also illustrated that the closer the initial condition to the self similar distribution the faster the convergence to self-similarity and the smaller the oscillations of the total cell number. Exact results are given for the growth parameters of the population balance and lumped models.

Sectional (zero order) methods constitute a very important class of methods for the solution of the population balance equation offering distinct advantages compared to their competitors, namely, higher order and moment methods. For the last ten years a particular sectional method, the so called fixed pivot technique (Kumar et al, 1996) has been the one most extensively used in the scientific community for the solution of the coagulation and breakage equations because it offers arbitrary grid choice and conservation of two moments of the particle size distribution. More recently, a new method (called cell average technique; Kumar et al, 2006; Kostoglou, 2007) has been developed which gives more accurate results than the fixed point technique. In the present work, the extension of this new method in order to conserve three moments is attempted. A stable algorithm for the solution of the coagulation and breakage equation is developed. The new method allows improved computation of moments of practical interest.

Publisher Summary The linear breakage equation is a partial integrodifferential equation belongs to a more general class of population. This equation balances and describes the evolution of a particle size distribution (PSD) of a particle population undergoing breakage. The limited breakage excludes the possibility of self-similar solution and leads to a static steady-state PSD (compare to dynamic steady-state PSD of selfsimilarity). The reason of the considerable development of the limited breakage theory is that the corresponding inverse problem (estimation of breakage kernel from PSD shape) is much simpler than that of self-similarity theory. The extension of the breakage equation to spatial dimensions including phenomena such as convection and diffusion has been studied and several analytical solutions were found. These terms can be of phenomenological nature (e.g. modelling the actual mixing situation in grinding equipment or can refer to the actual processes. Breakage equations with more than one internal variable have been studied in the physics literature mainly with regard to large time asymptotic and scaling behavior.

As diesel emissions regulations are becoming more stringent, diesel particulate filters (DPFs) have become possibly the most important and complex diesel emission control device. A traditional design of experiments approach becomes very time consuming and costly if one wants to address DPF design, system integration, regeneration control strategy optimization and ash ageing assessment, due to the very large number of tests needed. The application of simulation tools provides a promising alternative and hence simulation is increasingly being used for the design of exhaust emission control systems. In a DPF many coupled physico-chemical phenomena occur over widely disparate spatial and temporal scales and the simulation approach should account for and exploit these features. This becomes possible with the introduction of certain defensible assumptions and/or simplifications to arrive at an accurate but computationally tractable DPF simulation approach, for the needs of industrial users. The present chapter summarizes the current state of the science and technology of DPF simulation, from the Aerosol & Particle Technology Laboratory (APTL), addressing consistent and rigorous refinements in a number of areas including: the aerodynamics at the filter and channel inlet, flow, filtration and reaction phenomena at the DPF material microstructure scale, and in coupling/interfacing DPF simulation with three-dimensional (3D) Computational Fluid Dynamics (CFD) codes. Experimental results are cited where appropriate, to re-enforce/validate the points brought forward by the simulation approach.

Sectional (zero order) methods constitute a very important class of methods for the solution of the population balance equation offering distinct advantages compared to their competitors, namely, higher order and moment methods. For the last ten years a particular sectional method, the so called fixed pivot technique [1] has been the most extensively used in the scientific community for the solution of the coagulation equation because it offers arbitrary grid choice and conservation of two moments of the particle size distribution. Very recently, a new method (called cell average technique [2]) has been developed which gives more accurate results than the fixed point technique. In the present work, the extension of this new method in order to conserve three moments is attempted. A stable algorithm for the solution of the coagulation equation is developed. The new method allows improved computation of moments of practical interest.

Publisher Summary This chapter presents a novel optimization approach to achieve desired release rates in drug-delivery devices using laminated layers. A mathematical model is presented to describe the drug release among successive layers laminated together to form matrices with different initial concentrations, drug diffusivities, and thickness of each layer. An analytical-based optimization approach is performed and results compared with relevant work and a formal optimal control approach is employed to determine the optimal initial concentration in the layers, along with their thickness and diffusivities, to achieve a drug release profile as close to required profile (e.g., constants release) as possible for all times. The proposed optimization approach can be extended to cases where the initial drug is greater than its solubility limit in the release medium and in a different geometry (e.g., polymeric hemispheres).

Embryonic stem cells (ESCs) are capable of differentiation into a wide variety of cell types. Their use for cell therapy and regenerative medicine applications necessitates the expansion of cell numbers in bioreactors. Herein, we compare an ordinary differential equation (ODE) model of ESC expansion in a batch bioreactor with a novel mathematical model using population balance equations (PBM). Even though both models similarly describe cell expansion during the undifferentiated culture phase, the PBM captures fine oscillations in the total cell population introduced by the initiation of the differentiation process.