Volume 32, Issue 2

The production of modern pharma proteins is one of the most rapid growing fields in biotechnology. The overall development and production is a complex task ranging from strain development and cultivation to the purification and formulation of the drug. Downstream processing, however, still accounts for the major part of production costs. This is mainly due to the high demands on purity and thus safety of the final product and results in processes with a sequence of typically more than 10 unit operations. Consequently, even if each process step would operate at near optimal yield, a very significant amount of product would be lost. The majority of unit operations applied in downstream processing have a long history in the field of chemical and process engineering; nevertheless, mathematical descriptions of the respective processes and the economical large-scale production of modern pharmaceutical products are hampered by the complexity of the biological feedstock, especially the high molecular weight and limited stability of proteins. In order to develop new operational steps as well as a successful overall process, it is thus a necessary prerequisite to develop a deeper understanding of the thermodynamics and physics behind the applied processes as well as the implications for the product.

We are dealing with damage of brittle materials caused by growth of microcracks. In our model the cracks are penny-shaped. They can only enlarge but not heal. For a single crack a Rice–Griffith growth law is assumed: There is crack growth only if tension is applied normally to the crack surface, exceeding a critical value. Our aim is to investigate the effect of crack growth on macroscopic constitutive quantities. A possible approach taking into account such an internal structure within continuum mechanics is the mesoscopic theory. A distribution of crack lengths and crack orientations within the continuum element is introduced. Macroscopic quantities are calculated as averages with the distribution function. A macroscopic measure of the progressing damage, i.e., a damage parameter, is the average crack length. For this scalar damage parameter we derive an evolution equation. Due to the unilateral growth law for the single crack, it turns out that the form of this differential equation depends explicitly on the initial crack length distribution. In order to treat biaxial loading, it is necessary to introduce a tensorial damage parameter. We define a second-order tensor damage parameter in terms of the crack length and orientation distribution function.

A novel method for the calculation of friction factors through the computation of the irreversibility and rate of entropy production in two-phase flows has been developed. The model uses the momentum equation of the twophase fluid as well as appropriate closure equations to compute energy dissipation in a cylindrical pipeline system, which carries an air–solids mixture. Integral flow quantities, such as the total volumetric flow rate of the gas, the solids loadings, the pressure drop, and the friction factor of the flowing mixture may be readily computed from this model. The friction factors obtained via the entropy production method agree very well with experimental data and correlations derived in the past. The calculations also extend to the sources of irreversibility and the rate entropy production due to the friction of the flow as well as to the holdup of the two phases.

We propose an extension of the Galerkin–Eckhaus method in order to study thermoconvective instabilities not only in the weakly nonlinear régime, but also farther from the threshold. This extension consists in an appropriate choice of the basis functions used to expand the unknowns and in an increase of the number of amplitude equations taken into account. The rigid-free Rayleigh–Bénard problem with heat-conducting boundaries and the Marangoni–Bénard problem are considered in detail before generalizing to all thermoconvective instabilities. The validity of our approach is proven by comparing its results with a multiple scale method and with a finite element method. A very good agreement between all methods is found in the weakly nonlinear regime. Farther from the threshold, the agreement between our extended Galerkin–Eckhaus method and the finite element approach is also obtained with appropriate basis functions whose choice depends crucially on the value of the Prandtl number and also on the boundary conditions imposed at the top and bottom of the system.

There are two problematic items in García-Colín and Sandoval-Villalbazo's approach to “relativistic non-equilibrium thermodynamics” (L.S. García- Colín and A. Sandoval-Villalbazo, J. Non-Equilib. Thermodyn. 31, 2006, pp. 11–22). The paper does not follow the fundamentals of relativity theory; according to them, the energy-momentum tensor (EMT) has to include all energies of the considered system. Secondly, strange thermodynamic consequences result by using the presuppositions made by the authors. The paper is critically discussed and some shortcomings are elucidated.