Concepts and methods for describing critical phenomena in fluids

The predictions of theoretical models for a critical-point phase transistion in fluids, namely the classical equation with third-degree critical isotherm, that with fifth-degree critical isotherm, and the lattice gas, are reviewed. The renormalization group theory of critical phenomena and the hypothesis of universality of critical behavior supported by this theory are discussed as well as the nature of gravity effects and how they affect cricital-region experimentation in fluids. The behavior of the thermodynamic properties and the correlation function is formulated in terms of scaling laws. The predictions of these scaling laws and of the hypothesis of universality of critical behavior are compared with experimental data for one-component fluids and it is indicated how the methods can be extended to describe critical phenomena in fluid mixtures

The thermal conductivity of steam in the zero density limit as a function of temperature

An equation for the thermal conductivity of steam at pressures of 1 atmosphere and below is presented. Sources of the experimental data and the actual data used in the analysis are presented. Also included is low density data below 100 C

Three-particle collisions in a gas of hard spheres

Three particle collisions in gas of hard sphere

Modeling the development of tissue engineered cartilage

The limited healing capacity of articular cartilage forms a major clinical problem. In general, current treatments of cartilage damage temporarily reliefs symptoms, but fail in the long term. Tissue engineering (TE) has been proposed as a more permanent repair strategy. Cartilage TE aims at cultivating suitable implant material for cartilage repair. This has to be achieved by providing a favorable environment for cartilage regeneration in vitro (Chapter 1). The following phases can be distinguished: First, cells are isolated from the patient and expanded in culture to obtain sufficient numbers. Then the cells are seeded in a scaffold, i.e. a biodegradable three-dimensional structure that provides support for the cells. Subsequently, during culture in a bioreactor, the cells are conditioned to synthesize extracellular matrix components, resulting in neo-cartilage formation. Eventually, the newly formed cartilage construct has to acquire adequate mechanical properties, in order to be reimplanted into the patient. However, in general the mechanical properties of TE cartilage do not meet these functional requirements. In addition there is a definite lack of control over the functional development of tissue engineered cartilage. Current research is mainly characterized by a strong experimental basis. The use of computational methods is relatively limited, while modeling can potentially provide an important contribution to the optimization of bioreactors and culture protocols. In addition, modeling can prove useful in the reduction of the number of experiments and the interpretation of the results. In the present thesis, a computational approach is proposed that enables the modeling of the functional development of tissue engineered cartilage. The computational method is applied to establish relationships between mechanical stimulation of cartilage constructs by dynamic compression and transport of solutes, for example nutrients, within these constructs (Chapter 2). It is shown that compression-induced fluid flow can affect the transport of large solutes but not that of small solutes. This has implications for matrix synthesis. A microstructural homogenization approach is used to determine how the synthesis of extracellular matrix at the cellular level, translates in the evolving mechanical properties of the newly formed cartilage as a whole (Chapter 3). The results indicate that the matrix distribution at the cellular level may be of less importance than its molecular organization. With respect to the kinetics of cartilage formation, it is known that cellular energy metabolism is closely associated with the synthesis of extracellular matrix. Therefore, using the model, the cellular uptake of glucose and oxygen and the production of lactate is characterized on the basis of experimental data (Chapter 4). It is shown that cellular uptake in the experiments was influenced by both the initial glucose concentration in the culture medium and the cell density in the construct. Matrix synthesis and proliferation can be stimulated in an uncoupled manner, by applying different time intervals of dynamic compression. In order to interpret and predict cell behavior, models are developed for the temporal regulation of chondrocyte proliferation and biosynthesis, in response to varying dynamic compression regimens (Chapter 5). These models are able to provide a reasonable overall representation of experimental results for different loading regimens. However, for specific loading cases the predictive value is limited. Subsequently, cellular uptake data is used to predict, numerically, the nutrient supply in different bioreactor setups and to evaluate the effect of mixing, perfusion and geometry (Chapter 6). The results indicate that transport limitations are not insurmountable, providing that the bioreactor environment is well homogenized and oxygenated. It can be concluded that the proposed modeling approach can provide a valuable contribution in determining optimal culture conditions for cartilage tissue engineering (Chapter 7). At the present stage, additional identification and quantification of chondrocyte behavior is necessary, with respect to utilization, biosynthesis and mechanotransduction. In addition, criteria with respect to matrix synthesis have to be established