Osmotic model

Neural networks have also been used in Slovenia, to model the release characteristics of diclofenac [52] in China, to study release of nifedipine and nomodipine [53] and in Yugoslavia to model the release of aspirin [54], More recently, work in this area has been extended to model osmotic pumps in China [55] and enteric coated tablets in Ireland [56],... 

Figure A2.3.16. Theoretical HNC osmotic coefTicients for a range of ion size parameters in the primitive model compared with experimental data for the osmotic coefficients of several 1-1 electrolytes at 25°C. The curves are labelled according to the assumed value of a+- = r+ + r-...

Figure A2.3.17 Theoretical (HNC) calculations of the osmotic coefficients for the square well model of an electrolyte compared with experimental data for aqueous solutions at 25°C. The parameters for this model are a = r (Pauling)+ r (Pauling), d = d = 0 and d as indicated in the figure.

In principle, simulation teclmiques can be used, and Monte Carlo simulations of the primitive model of electrolyte solutions have appeared since the 1960s. Results for the osmotic coefficients are given for comparison in table A2.4.4 together with results from the MSA, PY and HNC approaches. The primitive model is clearly deficient for values of r. close to the closest distance of approach of the ions. Many years ago, Gurney [H] noted that when two ions are close enough together for their solvation sheaths to overlap, some solvent molecules become freed from ionic attraction and are effectively returned to the bulk [12]. 

In Chap. 8 we discuss the thermodynamics of polymer solutions, specifically with respect to phase separation and osmotic pressure. We shall devote considerable attention to statistical models to describe both the entropy and the enthalpy of mixtures. Of particular interest is the idea that the thermodynamic... 

Osmotic pressure experiments provide absolute values for Neither a model nor independent calibration is required to use this method. Experimental errors can arise, of course, and we note particularly the effect of impurities. Polymers which dissociate into ions can also be confusing. We shall return to this topic in Sec. 8.13 for now we assume that the polymers under consideration are nonelectrolytes. 

For many years, it was thought that the macro solute forms a new phase near the membrane—that of a gel or gel-like layer. The model provided good correlations of experimental data and has been widely used. It does not fit known experimental facts. An explanation that fits the known data well is based on osmotic pressure. The van t Hoff equation [Eq. (22-75)] is hopelessly inadequate to predict the osmotic pressure of a macromolecular solution. Using the empirical expression... 

A. Milchev, K. Binder. Osmotic pressure, atomic pressure and the virial equation of state of polymer solutions Monte Carlo simulations of a bead-spring model. Macromol Theory Simul 5 915-929, 1994. 

The subject of this chapter is single-phase heat transfer in micro-channels. Several aspects of the problem are considered in the frame of a continuum model, corresponding to small Knudsen number. A number of special problems of the theory of heat transfer in micro-channels, such as the effect of viscous energy dissipation, axial heat conduction, heat transfer characteristics of gaseous flows in microchannels, and electro-osmotic heat transfer in micro-channels, are also discussed in this chapter. 

This application is designed to model the influence of various concentrations of a solute near one edge of the membrane, on the diffusion of water through the membrane. Specifically we are interested in determining whether the model reveals a difference in the flow of water out of one compartment relative to the other. It is well known that if a semipermeable membrane is impervious to a solute on one side of a membrane, a greater flow of water from the other side will occur. This is a model of the osmotic effect, the flow of water through the... 

Using cellular automata we have an opportunity to model the flow of water from each compartment into the membrane, when a solute is present on one side of the membrane. By design, the membrane in our model is composed of 31% empty cells. At iteration zero, in our dynamics, the membrane contains no water. After several iterations, there will be flows of water from the two compartments into the membrane. If we monitor the early stages of this process, we may detect a possible preference for water to flow from one of the compartments. Such a condition would model the early stages of the osmotic effect. 

K = Debye screening length 4 = model parameter n = osmotic pressure p = density T = tortuosity factor <1> = swelling ratios... 

There have been recent studies on the importance of NO in modulating skin blood flow in both normal animals and in inflammatory models. Khan etiU. (1993), using laser-Doppler techniques, showed that the NOS inhibitor L-NAME inhibited rabbit ear blood flow. It was possible to do this chronically for up to 2 weeks using implanted osmotic pumps. Pons et id. (1993) also used laser Doppler to show that the vasodilator eflFect of LPS in rabbit skin, which mimics the efiect of Gram-negative bacteria, was likely to involve both i-NOS and IL-1. We have already discussed the damaging eflPects of neutrophils... 

In accordance with observed data, this model shows that water flux increases linearly with applied pressure AP, decreases with higher salt concentration through its impact on osmotic pressure Jt, increases with a smaller membrane thickness I, and increases with temperature through the temperature dependence of the water permeability P . The model also demonstrates that the solute or salt flux J, increases linearly with applied pressure AP, increases with higher salt concentration c , increases with a smaller membrane thickness I, and increases with temperature through the temperature dependence of the solute permeability Pj. Polarization, as described early in this section, causes the wall concentration c to exceed the bulk concentration ci,. 

Equation (20-80) requires a mass transfer coefficient k to calculate Cu, and a relation between protein concentration and osmotic pressure. Pure water flux obtained from a plot of flux versus pressure is used to calculate membrane resistance (t ically small). The LMH/psi slope is referred to as the NWP (normal water permeability). The membrane plus fouling resistances are determined after removing the reversible polarization layer through a buffer flush. To illustrate the components of the osmotic flux model. Fig. 20-63 shows flux versus TMP curves corresponding to just the membrane in buffer (Rfouimg = 0, = 0),... 

Osmotic coefficient data measured by Park (Park and Englezos, 1998 Park, 1999) are used for the estimation of the model parameters. There are 16 osmotic coefficient data available for the Na2Si03 aqueous solution. The data are given in Table 15.1. Based on these measurements the following parameters in Pitzer s... 

Estimate Pitzer s electrolyte activity coefficient model by minimizing the objective function given by Equation 15.1 and using the following osmotic coefficient data from Rard (1992) given in Table 15.5. First, use the data for molalities less than 3 mol/kg and then all the data together. Compare your estimated values with those reported by Rard (1992). Use a constant value for in Equation 15.1. 

Park, H., and P. Englezos, "Osmotic Coefficient Data for Na2Si03 and Na2Si03-NaOH by an Isopiestic Method and Modelling Using Pitzer s Model", Fluid Phase Equilibria, 153, 87-104 (1998). 

Water status of the seedlings was determined each afternoon by obtaining leaf diffusive resistance, water potential, and osmotic potential. Diffusive resistance was measured on both the adaxial and abaxial surfaces of the youngest fully expanded leaf for six randomly selected plants in each treatment using a Lambda Model LI-60 meter and a narrow aperture sensor. Total leaf resistance (R) was calculated from the component resistances (r) as follows ... 

Leaf water potential and osmotic potential were measured using a Wescor Dewpoint Microvoltmeter (Model HR-33) coupled with C-51 and C-52 sample chambers. Two plants from each group were sampled each day by taking two 7-mm diameter leaf disks from each plant, one for water potential and one for osmotic potential. Plants from which leaf disks were obtained were discarded. The water potential of a leaf disk was read following a 2-hr equilibration period in a sample... 

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