Enskog-Landau kinetic equation for multicomponent mixture. Analytical calculation of transport coefficients

The Enskog-Landau kinetic equation is considered to describe non-equilibrium processes of a mixture of charged hard spheres. This equation has been obtained in our previous papers by means of the non-equilibrium statistical operator method. The normal solution of this kinetic equation found in the first approximation using the standard Chapman-Enskog method is given. On the basis of the found solution the flows and transport coefficients have been calculated. All transport coefficients for multicomponent mixture of spherical Coulomb particles are presented analytically for the first time. Numerical calculations of thermal conductivity and thermal diffusion coefficient are performed for some specific mixtures of noble gases of high density. We compare the calculations with those ones for point-like neutral and charged particles.Comment: 5 LaTeX2e pages, 2 eps-figure

Novel probes for pH and dissolved oxygen measurements in cultivations from millilitre to benchtop scale

Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)pH value and the concentration of dissolved oxygen (DO) are key parameters to monitor and control cell growth in cultivation studies. Reliable, robust and accurate methods to measure these parameters in cultivation systems in real time guarantee high product yield and quality. This mini-review summarises the current state of the art of pH and DO sensors that are applied to bioprocesses from millilitre to benchtop scale by means of a short introduction on measuring principles and selected applications. Special emphasis is placed on single-use bioreactors, which have been increasingly employed in bioprocess development and production in recent years. Working principles, applications and the particular requirements of sensors in these cultivation systems are given. In such processes, optical sensors for pH and DO are often preferred to electrochemical probes, as they allow semi-invasive measurements and can be miniaturised to micrometre scale or lower. In addition, selected measuring principles of novel sensing technologies for pH and DO are discussed. These include solid-state sensors and miniaturised devices that are not yet commercially available, but show promising characteristics for possible use in bioprocesses in the near future

Nonequilibrium statistical operator method: Generalized transport equations of diffusion-reaction processes

Generalized transport equations for description of diffusion-reaction processes in chemically active mixtures are obtained. The nonequilibrium statistical operator method by Zubarev is used and both strong and weak nonequilibrium processes are analyzed. In the approximation of the second order in fluctuations we get generalized equations of chemical kinetics for bimolecular reactions with generalized rate constants. In the case of spatial uniformity the integro-differential equation for the matrix of partial scattering functions is received, which are related to partial dynamic structure factors of chemically reactive system by the time Fourier transformation