Establishment Of Steady State Research Articles

Gas/particle partitioning of semi-volatile organic compounds in the atmosphere: Transition from unsteady to steady state

We derive differential equations to determine the kinetics of gas/particle partitioning of semi-volatile organic compounds (SVOCs). These equations model the transient states from initiation of sorption to particles (non-steady state) through the establishment of steady state. Two hypothetical scenarios are examined: (1) exchange of SVOCs between gas- and particle-phases alone; and (2) both gas/particle partitioning and wet and dry deposition of particles. The differential equations show that, under Scenario 1, a steady state is reached as an equilibrium between gas- and particle-phases, whereas under Scenario 2, the attained steady state is not in equilibrium. Our model shows that SVOCs in atmosphere where particle deposition is occurring reach a steady non-equilibrium state sooner than they would reach equilibrium under Scenario 1. We infer that SVOCs in the atmosphere will reach steady state instead of equilibrium between gaseous and particulate phases in circumstances where wet and dry deposition of particles cannot be neglected. In addition, our study indicates that the time for SVOCs to reach steady state in the atmosphere is fast, most likely within minutes or hours, suggesting that SVOCs are in steady or quasi-steady state in the atmosphere. Our analysis also reveals that gas/particle partitioning and particle deposition of SVOCs are dependent on each other.

Energy cost of walking: Solving the paradox of steady state in the presence of variable walking speed

Measurement of the energy cost of walking in children with cerebral palsy is used for baseline and outcome assessment. However, such testing relies on the establishment of steady state that is deemed present when oxygen consumption is stable. This is often assumed when walking speed is constant but in practice, speed can and does vary naturally. Whilst constant speed is achievable on a treadmill, this is often impractical clinically, thus rendering an energy cost test to an element of subjectivity. This paper attempts to address this issue by presenting a new method for calculating energy cost of walking that automatically applies a mathematically defined threshold for steady state within a (non-treadmill) walking trial and then strips out all of the non-steady state events within that trial. The method is compared with a generic approach that does not remove non-steady state data but rather uses an average value over a complete walking trial as is often used in the clinical environment. Both methods were applied to the calculation of several energy cost of walking parameters of self-selected walking speed in a cohort of unimpaired subjects and children with cerebral palsy. The results revealed that both methods were strongly correlated for each parameter but showed systematic significant differences. It is suggested that these differences are introduced by the rejection of non-steady state data that would otherwise have incorrectly been incorporated into the calculation of the energy cost of walking indices during self-selected walking with its inherent speed variation.

Modelling and Simulation Moisture Transfer in Wheat Stored in a Simulated Sealed Pit

A mathematical model, coupled to another one which was used to calculate the conductive heat transfer, was developed to predict the change of moisture distribution with time in the radial and axial directions in a simulated sealed cylindrical pit storing wheat. The finite difference method was used in the model to calculate the diffusive moisture transfer. The model predicts the grain moisture contents in the pit during the storage period using input data of initial grain temperature, initial grain moisture content, storage time and number of spatial elements in both radial and axial directions. Other input data include the finite difference spatial increment in both directions, the finite time increment, temperatures of soil surrounding the pit and the physical properties of grain, pit wall material and surrounding soil. To validate the model, predicted moisture contents were compared with measured data for wheat of Apollo variety being stored in a simulated sealed pit for a period of 70 days. The wheat was stored in a cylindrical mild steel tank with 0.6 m in both diameter and height. The initial uniform grain temperature was 15 °C and the initial uniform grain moisture content was 12.45% (w.b.). Both measured and predicted moisture contents show that the major change in wheat moisture content took place during the first week of the storage and an establishment of steady state under the storage conditions of the pit is unattainable i.e. moisture diffusion is a very slow process. At the end of the storage period, the grain moisture contents were increased by an average of 1.62% (w.b.) and the grain temperatures were decreased by an average of 2.63°C at the top layer of the pit. For the bottom layer of the pit, the grain moisture contents were decreased by an average of 0.50% (w.b.) and the grain temperatures increased by an average of 7.04°C. The diffusive moisture transfer model predicted the grain moisture contents with a standard error of estimate between measured and predicted of 0.18 -0.75% and of 0.18-0.74% (w.b.) using Chung's equation and modified Henderson's equation, respectively. There was no difference between the two sorption equations (Chung's and modified Henderson's equations) used in predicting grain moisture contents.

Evaluation of the reversible contribution to the reversing heat capacity in isotactic polystyrene

We report the results of time dependent analysis of the reversing heat capacity peaks in isotactic polystyrene (iPS). Solution grown crystals (SGCs) and bulk films of iPS were examined using quasi-isothermal temperature modulated differential scanning calorimetry (QI-TMDSC). Both types of iPS samples showed two reversing heat capacity peaks as reported before [H. Xu, P. Cebe, Macromolecules 37 (2004) 2797; H. Xu, P. Cebe, Macromolecules 38 (2005) 770], and the two peaks are associated with melting of different portions of crystal lamellae with different degree of thermal stability [T. Liu, J. Petermann, Polymer 42 (2001) 6453]. Here, the behavior of the reversing heat capacity is studied as a function of holding time from the establishment of steady state, until the end of the quasi-isothermal holding period. The reversing heat capacity decreases with time at each of the two peak positions. For both types of iPS (SGC and bulk film) the time dependence of each of the reversing heat capacity peaks is fitted using Cp(t)=Cp∞+A1exp(−t/τ1)+A2exp(−t/τ2). The fit parameters (equilibrium reversible heat capacity, Cp∞; prefactors, A1 and A2; relaxation times, τ1 and τ2) provide a means to compare the decay of the dual reversing heat capacity peaks of iPS solution grown crystals with bulk cold-crystallized film. Results show that iPS bulk films have longer relaxation times (τ1 and τ2) and smaller Cp∞ value than the iPS SGCs. Both results suggest that the iPS bulk films have higher degree of crystal perfection than SGCs.

The role of physical stability on the establishment of steady states in the phytoplankton community of two Maritime Antarctic lakes

The role of physical stability on the establishment of steady states in the phytoplankton community of two Maritime Antarctic lakes

Temporal relaxation of plasma electrons acted upon by direct current electric and magnetic fields

On the basis of the time-dependent electron Boltzmann equation the temporal relaxation of the electrons in the presence of electric and magnetic fields in weakly ionized, collision dominated plasmas has been studied. The relaxation process is treated by using a strict time-dependent two-term approximation of the velocity distribution function expansion in spherical harmonics. A new technique for solving the time-dependent electron kinetic equation in this two-term approximation for arbitrary angles between the electric and magnetic fields has been developed and the main aspects of the efficient solution method are presented. Using this new approach and starting from steady-state plasmas under the action of time-independent electric fields only, the impact of superimposed DC magnetic fields on the electron relaxation is analyzed with regard to the control of a neon plasma. The investigations reveal an important effect of the magnetic field on the temporal relaxation process. In particular, it has been found that the relaxation time of the electron component with respect to the establishment of steady-state can be enlarged by some orders of magnitude when increasing the magnetic field strength.

A probabilistic view on steady-state enzyme reactions

A new theoretical description of steady-state enzyme reactions is proposed. The description is based on the concepts of the probability theory instead of the conventional formalism of chemical kinetics. A general steady-state rate equation is obtained using a probabilistic model of the catalytic act. As a result, the classical problems of enzyme kinetics can be formulated and considered in a different aspect. It is shown that the new theory presents a clearer treatment of some commonly obscure questions, such as the steady-state establishment. The theory also gives additional possibilities in the interpretation of the experimental results of traditional methods and proposes certain new ways in experimental investigations of enzymes.

The effect of automatic ph maintenance on steady state cultivation regimes and their stability. A theoretical study of the case of a perfect ph controller and perfect stirring

AbstractThe dynamics of pH‐controlled chemostat and pH‐auxostat is considered. The medium flow governed by pH‐controller is calculated using the ionic (mass‐charge) balance equations. The generalized equations of pH‐controlled continuous fermentation are developed for the case of two variables: cell biomass and residual substrate concentrations. The study of steady state solutions has shown a substantial dependence of the variable patterns on a concentration of alkali (or acid) in titrant medium flow. The generalized analytical expressions for eigenvalues (reciprocals of transient characteristic times) of the culture dynamics have been obtained. The rates of transients during the steady state establishment are considered using these eigenvalues.

A static-sims study on preferential sputtering on copper-nickel alloy surface

Preferential sputtering on homogeneous copper-nickel alloy surface has been studied with static-SIMS, and the overall ionization probability ratio of sputtered atoms has been estimated. The measurement of preferential sputtering was made on a range of all alloy compositions with Ar + ion impacts of 700 eV. Sample alloy surfaces were prepared by abrasion in running water in order to avoid surface segregation. After 10 min bombardment of Ar + ions in each measurement, the static-SIMS peak ratio of copper and nickel comes to a steady state. The nickel surface concentration derived from the peak ratio, was compared with AES results previously reported, and found to be higher than those in the range of lower nickel concentrations. The difference can be explained with the measurement mechanism of SIMS and AES concerning the “altered layer”. It is reasonable to consider that AES investigates the “altered layer”, while static-SIMS investigation after establishment of steady state is independent of the “altered layer” and gives information just below the “altered layer”.

Nitrification Studies at Non-limiting Substrate Concentrations

Theoretical models of nitrification were tested using an experimental model consisting of a column of glass beads inoculated with nitrifying bacteria, through which was passed a constant flow of substrate at non-limiting concentration. Effluent was analysed for conversion products. Both zero-order and first-order rate constants for substrate conversion decreased by 1·4% for each 1 ml h−1 decrease in flow rate presumably because of the development of oxygen limitation. Logistic growth kinetics described growth adequately and bacteria were distributed evenly throughout the column after establishment of steady states. Bacterial concentrations of 1·4 × 109 ml−1 and conversion rates of 5·62 × 10−9 p.p.m. N as NO2 − h−1 organism−1 were obtained for Nitrobacter and 6·47 × 106 ml−1 and 3·75 × 10−7 p.p.m. N as NH4 + h−1 organism−1 for Nitrosomonas. During periods of oxygen starvation a lag was observed following increases in flow rate producing undershoots in product concentrations before establishment of new steady states.