Numerical study of laminar-turbulent transition in particle-laden channel flow.

We present direct numerical simulations of subcritical transition to turbulence in a particle-laden channel flow, with particles assumed rigid, spherical, and heavier than the fluid. The equations describing the fluid flow are solved with an Eulerian mesh, whereas those describing the particle dynamics are solved by Lagrangian tracking. Two-way coupling between fluid and particles is modeled with Stokes drag. The numerical code is first validated against previous results from linear stability: the nonmodal growth of streamwise vortices resulting in streamwise streaks is still the most efficient mechanism for linear disturbance amplification at subcritical conditions as for the case of a single phase fluid. To analyze the full nonlinear transition, we examine two scenarios well studied in the literature: (1) transition initiated by streamwise independent counter-rotating streamwise vortices and one three-dimensional mode and (2) oblique transition, initiated by the nonlinear interaction of two symmetric oblique waves. The threshold energy for transition is computed, and it is demonstrated that for both scenarios the transition may be facilitated by the presence of particles at low number density. This is due to the fact that particles may introduce in the system detrimental disturbances of length scales not initially present. At higher concentrations, conversely, we note an increase of the disturbance energy needed for transition. The threshold energy for the oblique scenario shows a more significant increase in the presence of particles, by a factor about four. Interestingly, for the streamwise-vortex scenario the time at which transition occurs increases with the particle volume fraction when considering disturbances of equal initial energy. These results are explained by considering the reduced amplification of oblique modes in the two-phase flow. The results from these two classical scenarios indicate that, although linear stability analysis shows hardly any effect on optimal growth, particles do influence secondary instabilities and streak breakdown. These effects can be responsible of the reduced drag observed in turbulent channel flow laden with heavy particles.

Determination of in vivo oxygen uptake and carbon dioxide evolution rates from off-gas measurements under highly dynamic conditions.

In vivo kinetics of Saccharomyces cerevisiae are studied, in a time window of 150 s, by analyzing the response of O(2) and CO(2) in the fermentor off-gas after perturbation of chemostat cultures by metabolite pulses. Here, a new mathematical method is presented for the estimation of the in vivo oxygen uptake rate (OUR) and carbon dioxide evolution rate (CER) directly from the off-gas data in such perturbation experiments. The mathematical construction allows effective elimination of delay and distortion in the off-gas measurement signal under highly dynamic conditions. A black box model for the fermentor off-gas system is first obtained by system identification, followed by the construction of an optimal linear filter, based on the identified off-gas model. The method is applied to glucose and ethanol pulses performed on chemostat cultures of S. cerevisiae. The estimated OUR is shown to be consistent with the independent dissolved oxygen measurement. The estimated in vivo OUR and CER provide valuable insights into the complex dynamic behavior of yeast and are essential for the establishment and validation of in vivo kinetic models of primary metabolism.

Characterization of null mutants of the glyoxylate cycle and gluconeogenic enzymes in S. cerevisiae through metabolic network modeling verified by chemostat cultivation.

Biomass yields for several null mutants in Saccharomyces cerevisiae were successfully predicted with a metabolic network model. Energetic parameters of the model were obtained from growth data in C-limited aerobic chemostat cultures of the corresponding wild-type strain, which exhibited a P/O ratio of 1.46, a non-growth-related maintenance of 56 mmol ATP/C-mol biomass/h, and a growth-related requirement of 655 mmol ATP/C-mol biomass. Biomass yields and carbon uptake rates were modeled for different mutants incapacitated in their glyoxylate cycle and their gluconeogenesis. Biomass yields were calculated for different feed ratios of glucose to ethanol, and decreases for higher ethanol fractions were correctly predicted for mutants with deletions of the malate synthase, the isocitrate lyase, or the phosphoenolpyruvate carboxykinase. The growth of the fructose- 1,6-bisphosphatase deletion mutant was anticipated less accurate, but the tendency was modeled correctly.

Improved rapid sampling for in vivo kinetics of intracellular metabolites in Saccharomyces cerevisiae.

An integrated approach is used to develop a rapid sampling strategy for the quantitative analysis of in vivo kinetic behavior based on measured concentrations of intracellular metabolites in Saccharomyces cerevisiae. Emphasis is laid on small sample sizes during sampling and analysis. Subsecond residence times are accomplished by minimizing the dead volume of the sterile sampling system and by maximizing flow rates through application of vacuum to the sampling tubes in addition to the overpressure in the fermenter. A specially designed sample tube adapter facilitates sampling intervals of 4 to 5 s for various test tube types. Statistical analysis of the results obtained from enzymatic and liquid chromatography mass spectrometry (LC-MSMS) analysis of the metabolite concentrations was used to optimize the sampling protocol. The most notable improvement is reached through the introduction of vacuum drying of the cell extract. The presented system is capable of reliably dealing with fermenter samples as small as 1-g with a variation of less than 3%, and is thus ideally suited for intracellular measurements on small, lab-scale fermenters.

Statistical reconciliation of the elemental and molecular biomass composition of Saccharomyces cerevisiae.

A systematic mathematical procedure capable of detecting the presence of a gross error in the measurements and of reconciling connected data sets by using the maximum likelihood principle is applied to the biomass composition data of yeast. The biomass composition of Saccharomyces cerevisiae grown in a chemostat under glucose limitation was analyzed for its elemental and for its molecular composition. Both descriptions initially resulted in conflicting results concerning the elemental composition, molecular weight, and degrees of reduction. The application of the statistical reconciliation method, based on elemental balances and equality relations, is used to obtain a consistent biomass composition. Simultaneously, the error margins of the data sets are significantly reduced in the reconciliation process. On the basis of statistical analysis it was found that inclusion of about 4% water in the list of biomass constituents is essential to adequately describe the dry biomass and match both set of measurements. The reconciled carbon content of the biomass varied 4% from the ones obtained from the molecular analysis. The proposed method increases the accuracy of biomass composition data of its elements and its molecules by providing a best estimate based on all available data and thus provides an improved and consistent basis for metabolic flux analysis as well as black box modeling approaches.