Volumetric behaviour

Lourdin, D., Colorma, P, and Ring, S.G. Volumetric behaviour of maltose-water, maltose-glycerol and starch-sorbitol-water systems mixtures in relation to structural relaxation, Carbohydr. Res., 338, 2883, 2003. 

Figure 5.3 presents the generic PVT relationship for a pure component in a 3D diagram. This representation captures both the temperature evolution of the phase boundaries at equilibrium, as well as their volumetric behaviour. The 2D representation for different cases is straightforward. 

The volumetric behaviour is given by equation 19. But in order to reproduce brittle behaviour at low confinement and ductility at high confinement, the dilatancy angle depends on the stress state according to equation 20. 

Whether these equations refer to enthalpy of mixing at constant pressure or energy of mixing at constant volume depends on the assumptions one makes about the volumetric behaviour of the system on mixing. 

Cracking is the most common distresses of rigid pavements. It is caused, to a great extent, not only by the concrete s volumetric behaviour under temperature variations but also by the repetitive loading caused by traffic and some other external factors. 

However, there are two effective stresses a and a", which is confusing. The situation will be optimum if we can assume either b = b, hence a = a", or matrix incompressibility which implies b = b = 1 and that a = a" = cr + pi. The last case is of particular importance and corresponds to the majority of cases in soils.The above flow rule is known as associative since the strain rate is normal to the yield surface, with the advantage that the nonnegativity of the dissipation is always satisfied. Geomateiials exhibit complex volumetric behaviours and sometimes call for non associative flow rules ... 

If an equation of state is available which accurately represents the volumetric behaviour of the phases in the system at the temperature of interest as functions of pressure and composition, Vi may be calculated as a function of the above variables. The fugacity of the component i can in principle be calculated by adding the integral of equation (7.2) to the starting condition given by equation (7.1). It is usual in these calculations to work in terms of the so-called fugacity coefficient fi,... 

Sadeghi R, Ziamajidi F (2007) Effect of aqueous solution of tri-potassium citrate on the volumetric behaviour of poly(propylene glycol) 400 at T—(288.15 to 313.15) K. J Chem Eng Data 52 1268-1272... 

Although the relative density as such is not a very useful parameter to describe the volumetric behaviour (and, subsequently, to quantify the friction angle) of a sand, it is still widely used in specifications of land reclamation projects because it can be determined through correlations with the cone resistance (also below the water table). These correlations have been established under controlled conditions in large calibration chambers, but their validity is almost exclusively limited to clean silica sand. 

An important series of reactions, which illustrates the diversity of behaviour to be expected, is the comproportionation of halates and halides. Bromides are oxidized quantitatively to bromine and iodides to iodine, this latter reaction being much used in volumetric analysis ... 

A binary suspension consists of equal masses of spherical particles of the same shape and density whose free falling velocities in the liquid are 1 mm/s and 2 mm/s, respectively. The system is initially well mixed and the total volumetric concentration of solids is 0.2. As sedimentation proceeds, a sharp interface forms between the clear liquid and suspension consisting only of small particles, and a second interface separates the suspension of fines from the mixed suspension. Using a suitable model for the behaviour of the system, estimate the falling rates of the two interfaces. It may be assumed that the sedimentation velocity uc in a concentrated suspension of voidage e is related to the free falling velocity u0 of the particles by ... 

A continuous fermenter with sterile feed is referred to as a chemostat. For constant volume operation, the inlet volumetric flow rate is equal to that at the output. With this model chemostat start-up, resultant steady state behaviour and cell washout phenomena are easily investigated by simulation. 

In equation 3.51, p is the density and n the power law flow behaviour index of the fluid. 51 and S2 are the cross-sectional areas of the smaller and larger pipes respectively and u the volumetric average velocity in the smaller pipe. 

In wet grinding the power consumption is generally about 30 per cent lower than that for dry grinding and, additionally, the continuous removal of product as it is formed is facilitated. The rheological properties of the slurry are important and the performance tends to improve as the apparent viscosity increases, reaching an optimum at about 0.2 Pa.s. At very high volumetric concentrations (ca. 50 volume per cent), the fluid may exhibit shear-thickening behaviour or have a yield stress, and the behaviour may then be adversely affected. 

Figure 5.24. Settling behaviour of a mixture consisting of equal volumes of polystyrene and ballotini at a volumetric concentrations exceeding 15 per cent...

Figure 2.11 The change in volumetric swelling behaviour due to (a) loss of cell wall material but not cell wall bulking agent, and (b) loss of cell wall cross-linking agent.

Vapour and gas sorption measurements can be performed with static or dynamic methods, either of which can provide information on equilibrium behaviour. Furthermore, the measurements can be performed using gravimetric or volumetric based instrumentation. The most common flow methods are inverse gas chromatography (IGC) [1] for volumetric studies and dynamic gravimetric instrumentation [2]. 

Two tanks in series. Consider the two tanks shown in Fig. 7.16. In this system neither the rate of flow through tank 1 nor the level in tank 1 is affected by what occurs in tank 2. Thus the two processes (or capacity systems) are non-interacting and we can model their dynamic behaviours individually. To establish the relationship between the level in tank 2 and the volumetric flowrate entering tank 1 at any instant of time, we need only to determine the individual transfer functions between Q0 and Q, and between 2, and z2. 

A detailed model of the pilot-plant MVC was derived and validated against experimental data in a previous study (Barolo et al., 1998 and also see Chapter 4). The model consists of material and energy balances, vapour liquid equilibrium on trays (with Murphree tray efficiency to account for tray nonideal behaviour), liquid hydraulics based on the real tray geometry, reflux subcooling, heat losses, and control-law calculations based on volumetric flows. The model provides a very accurate representation of the real process behaviour, but is computationally expensive for direct use within an optimisation routine. Greaves et al. (2003) used this model as a substitute of the process. 

In particular, minima in plots of AV against x2 are not necessarily due to the trend in the initial state quantity, and volumetric data can provide some indication of the details of reaction mechanism. Thus for the hydrolysis of p-chlorobenzyl chloride (Sn2), a shallow minimum in 5mAF for reaction in aqueous ethyl alcohol stems from a more intense maximum in 8m than for 5mF. At the other end of the scale, a sharp minimum in 8mAF for t-butyl chloride solvolysis (SnI) results from a sharp minimum in SmF, 5m V3 changing only gradually as x2 is increased. The behaviour of the volumetric properties for the benzyl... 

The volumetric expansion of the liquid when it is contacted with the SCF plays the key role in the process. The behaviour reported by Yeo et al. [10] and by Kordikowski et al. [11] for the dymethylsulfoxide (DMSO)-CC>2 system at two temperatures shows that CO2 produces a remarkable volumetric expansion of DMSO near the mixture critical point. The increase of antisolvent amount in the mixed solvent and the evaporation of the organic liquid into the SCF eventually cause the precipitation of the solute. A cleaning step, carried out with pure antisolvent, is necessary after the precipitation, in order to remove completely the liquid solvent from the solid particles the antisolvent pushes the liquid out of the vessel, then it has to extract the residual solvent from the solid and the dry solid particles can be collected. 

The behaviour of foamed emulsions changes considerably when the oil volume reaches about 70%. The properties of a foamed emulsion at such a volumetric ratio are similar to those of a concentrated emulsion. Table 7.7 presents the results from the determination of the stability of foamed emulsions obtained from 10% Volgonate and OP-10 at equal initial gas content and different volumetric content of the organic phase (80-91%). 

Pressure Swing Adsorption (PSA) unit is a dynamic separation process. In order to create a precise model of the process and thus an accurate design, it is necessary to have a good knowledge of the mixture s adsorption behaviour. Consequently, the dilAision rates in the adsorbent particles and the mixture isotherms are extremely vital data. This article intends to present a new approach to study the adsorption behaviour of isomer mixtures on zeolites. In a combined simulation and experimental project we set out to assess the sorption properties of a series of zeolites. The simulations are based on the configurational-bias Monte Carlo technique. The sorption data are measured in a volumetric set-up coupled with an online Near Infra-Red (NIR) spectroscopy, to monitor the bulk composition. Single component isotherms of butane and iso-butane were measured to validate the equipment, and transient volumetric up-take experiments were also performed to access the adsorption kinetics. 

As far as the adsorption and skeletal isomerization of cyclopropane and the product propene are concerned, results mainly obtained by infrared spectroscopy, volumetric adsorption experiments and kinetic studies [1-4], revealed that (i) both cyclopropane and propene are adsorbed in front of the exchangeable cations of the zeolite (ii) adsorption of propene proved to be reversible accompanied by cation-dependent red shift of the C=C stretching frequency (iii) a "face-on" sorption complex between the cyclopropane and the cation is formed (iv) the rate of cyclopropane isomerization is affected by the cation type (v) a reactant shape selectivity is observed for the cyclopropane/NaA system (vi) a peculiar catalytic behaviour is found for LiA (vii) only Co ions located in the large cavity act as active sites in cyclopropane isomerization. On the other hand, only few theoretical investigations dealing with the quantitative description of adsorption process have been carried out. 

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