Adsorption mean residence time

Adsorption Isotherms. The adsorption isotherms were determined using the serum-replacement adsorption or desorption methods (7). For the adsorption method, the latex samples (50 or 100 cm 2% solids) containing varying amounts of PVA were equilibrated for 36 hours at 25°C, placed in the serum replacement cell equipped with a Nuclepore membrane of the appropriate pore size, and pressurized to separate a small sample of the serum from the latex. For the desorption method, the latex samples (250 cm 2.5% solids) were equilibrated for 36 hours at 25°C and subjected to serum replacement with DDI water at a constant 9-10 cm /hour. The exit stream was monitored using a differential refractometer. The mean residence time of the feed stream was ca. 25 hours. It was assumed that equilibrium between the adsorbed and solute PVA was maintained throughout the serum replacement. For both methods, the PVA concentration was determined using a An-C calibration curve. 

It is clear that, in the particular case illustrated, all material has a residence time of between to and t2 minutes and therefore the mean or average time spent in the system is between these two extremes. For a flow-mixing system in which no adsorption, reaction or change in volume flow rate occurs, this mean residence time is always equal to the volumetric holdup of the system divided by the constant flow rate through the system [1]. Thus, the mean residence time, t, equals V/Q and is seen to be identical... 

There are four unknown parameters in the theoretical impulse response for porous particles, h(t) the pellet diffusion time, tdif (which contains the effective diffusion coefficient of the pair T-C, Dtc, td.fs R p/D.f( , R is the radius of the pellet equivalent sphere), the mean residence time of the carrier-gas in the interparticle space, tc (tc = v/L with the carrier gas linear interstitial velocity, v, and column length, L), Peclet number, Pe (Pe = L.v/E, with E the effective axial dispersion coefficient) and the adsorption parameter, 5q (see below). Because matching with four unknown parameters would give highly correlated parameters, it is better to determine some parameters independently,... 

Figure 2.5a shows a snapshot from a Ru(0 001) surface with a small coverage of adsorbed O atoms at 300K. The O atoms are randomly distributed and move around like in a Brownian motion with a mean residence time (at 300K) of 60 ms at a certain adsorption site. However, due to the weak attraction between two adatoms with a minimum at a distance of 2flo ( o = lattice constant of the substrate), at higher coverages a separation into two phases, namely, a quasi-gaseous and a quasi-crystalline phase, takes place (Fig. 2.5b) [9]. Under present conditions, the two phases are in equilibrium with each other, a situation that is rationalized by the phase diagram depicted in Fig. 2.6a. In our case, the horizontal scale (composition) denotes the concentration of occupied sites (i.e., overall coverage 0). As long as 0 is small, we...

In the case of reversible adsorption, to is the vibrational period of the adsorbed particle perpendicular to the surface of the adsorbing solid it is typically of the order 10 to 10 s. In the case of reaction gas chromatography, ta depends essentially on the kinetics of the rate-determining associative desorption and the collision probability of water molecules with the adsorbed species. The mean residence time in the adsorbed state then becomes... 

Mean residence time of a nucleus at an adsorption site j... 

If one denotes by vj, pj and rj, respectively, the resonance frequency, the relative concentration and the mean residence time of a nucleus at an adsorption site , then the shape of the NMR spectrum for a system with two different sorts of adsorption sites j = a, b with pa + pb = 1 strongly depends on the quantity ... 

The linear chromatographic process is modeled as a composite Poisson process a chain of exponentially distributed fly times, followed by exponentially distributed adsorption times are generated. When adsorbed, the molecule is stationary the mean adsorption time is t . When desorbed, the molecule travels with the velocity of the mobile phase the mean fly time—residence time between a desorption and the subsequent adsorption—in the mobile phase is t. The elution time of the molecule is recorded when it reaches the end of the colxunn after n adsorption-desorption events on the average. The distribution of the single molecule elution times gives the band profile. 

Shown in Table 8.9 are chemical analyses of mean river water and seawater, along with residence times of the species and a comparison of relative concentrations in mean river water and the ocean. As in the discussion of the hydrologic cycle, the residence time of species in seawater, t, equals the amount of that species in the reservoir (the ocean), divided by its rate of input or output (which must be equal at steady state). The input is in streams and groundwaters discharging into the ocean. The output is through adsorption and/or precipitation in and on solids that end up in marine sediments. 

The velocity is chosen as a function of the molecule to be adsorbed and its inlet concentration. Commonly, the velocities range between 500 and 600 m h" i.e. 0.140 to 0.170 m s For well-adsorbed compounds, velocities reach 1,000 to 2,000 m h" (0.28 to 0.56 m s ). The bed depth is defined ftom the mean resid ice time (0) or from adsorption capacities, which depend on the cycle time. The residence time ranges between 0.1 to 5 s. 

Instantaneous adsorption. During the flow of polymer solutions through porous media, the hydrodynamic convection of macromolecules brings them into contact with solid surface in a mean time t which is of the order of a few seconds under our experimental conditions. Since the probability for a macromolecule to be adsorbed during the first contact with the pore surface free of adsorbed pol3mier is very high, the polymer adsorption can be considered as instantaneous. Indeed, this mean time is negligible compared to the residence time of macromolecules t inside the column. 

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