Semi-steady state flow

As part of the "DECOVALEX" project, we were asked to predict the total water flow rate to the excavated tunnel over the last 17.40 meters of FEBEX tunnel section (between 54.00 and 71.40 m). A purely-hydraulic computation, using the previous calibration, yields an estimated steady-state flow of between 6 and 7.6 ml/min. This size scale is to be compared with total water inflow estimated from a semi-quantitative hydrogeological map of the FEBEX tunnel 7.8 ml/min (with an estimation of about 27% of inflow water coming through the matrix). In comparison with the continuous prediction (Alonso et al, 2001), this estimation is rather good and the discontinuous approach allows localizing water output with greater precision. (This kind of comparison was not included within the "DECOVALEX" task.)... 

Pro 4 Very rapid irreversible sorption occurs on initial addition of high concentrations of phenolic acids to soil subsequently, however, sorption is very slow for cinnamic acid derivatives and almost non-existent for benzoic acid derivatives. For soil systems with continuous production of phenolic acids a semi-steady state will occur and irreversible sorption will thus be very small. That phenolic acids and soils can potentially reach a steady state has been demonstrated in the continuous-flow system. 

The steady-state stagnation-flow equations represent a boundary-value problem. The momentum, energy, and species equations are second order while the continuity equation is first order. Although the details of boundary-condition specification depend in the particular problem, there are some common characteristics. The second-order equations demand some independent information about V,W,T and Yk at both ends of the z domain. The first-order continuity equation requires information about u on one boundary. As developed in the following sections, we consider both finite and semi-infinite domains. In the case of a semi-infinite domain, the pressure term kr can be determined from an outer potential flow. In the case of a finite domain where u is known on both boundaries, Ar is determined as an eigenvalue of the problem. 

The steady state method is often used in continuous-flow operation with reaction, which is often the case in full-scale applications. In laboratory-scale investigations, the steady state method can be used with a semi-batch set-up (gas phase continuous) with reaction or a continuous-flow set-up (both gas and liquid phases continuous) with or without reaction. 

Semi-batch only the continuous phase flows at steady state, while particles are circulated inside the device. 

Before discussing theoretical approaches let us review some experimental results on the influence of flow on the phase behavior of polymer solutions and blends. Pioneering work on shear-induced phase changes in polymer solutions was carried out by Silberberg and Kuhn [108] on a polymer mixture of polystyrene (PS) and ethyl cellulose dissolved in benzene a system which displays UCST behavior. They observed shear-dependent depressions of the critical point of as much as 13 K under steady-state shear at rates up to 270 s Similar results on shear-induced homogenization were reported on a 50/50 blend solution of PS and poly(butadiene) (PB) with dioctyl phthalate (DOP) as a solvent under steady-state Couette flow [109, 110], A semi-dilute solution of the mixture containing 3 wt% of total polymer was prepared. The quiescent... 

Steady-state dialysis - The equihbrium dialysis technique is accelerated by having buffer flow at a constant rate on one side of the semi-permeable membrane and by stirring both sides in order to minimize the concentration gradients [36]. Diafiltration - A type of dialysis equihbrium in which pressure is used to force the ligand-containing solution from one chamber into the protein-containing chamber [37]. 

Nonisothermal reactor design requires the simultaneous solution of the appropriate energy balance and the species material balances. For the batch, semi-batch, and steady-state plug-flow reactors, these balances are sets of initial-value ODEs that must be solved numerically, in very limited situations (constant thermodynamic properties, single... 

Mathematical formalism has been developed using semi-empirical considerations [36, 37]. Computer simulation smdies show that resulting equation predicts oscillations. Attempt has been made to provide justification on the bases of Navier-Stokes equation but it is open to question. Dimensional analysis has recently been employed for investigating the phenomena [31]. Flow dynamics and stability in a density oscillator have been examined by Steinbock and co-workers [38], They have related it to Rayleigh-Taylor instability of two different dense viscous liquids. A theoretical description has been presented which is based on a one-fluid model and a steady state approximation for a two-dimensional flow using Navier-Stokes equation. However, the treatment is quite complex and cannot explain the generation of electric potential oscillations. 

Consider a semi-infinite expanse of an initially uniform gas bounded by its plane condensed phase. Depending on the conditions of the gas and the condensed phase, condensation or evaporation will take place on the condensed phase the disturbance induced by their interaction will propagate in the gas and after a long time a steady condensation or evaporation flow will be established. The senior author (Y. S.) considered the problem on the basis of kinetic theory in Ref. 1 when condensation takes place. In Ref. 1 the behavior of the gas is analyzed numerically by a finite difference method for a large number of initial situations, from which the transient behavior to a final steady state is classified and the steady behavior, especially the relation satisfied among the parameters at infinity and on the condensed phase in a condensation flow, is clarified. 

The computer display then shows the steady-state values for characteristics such as the thermal conductivity k [W/(mK)], thermal resistance R [m K/W] and thickness of the sample s [mm], but also the transient (non-stationary) parameters like thermal diffusivity and so called thermal absorptivity b [Ws1/2/(jti2K)], Thus it characterizes the warm-cool feeling of textile fabrics during the first short contact of human skin with a fabric. It is defined by the equation b = (Xpc)l, however, this parameter is depicted under some simplifying conditions of the level of heat flow q [ W/m2] which passes between the human skin of infinite thermal capacity and temperature T The textile fabric contact is idealized to a semi-infinite body of the finite thermal capacity and initial temperature, T, using the equation, = b (Tj - To)/(n, ... 

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