Hot-ball model

Bartle et al. [286] described a simple model for diffusion-limited extractions from spherical particles (the so-called hot-ball model). The model was extended to cover polymer films and a nonuniform distribution of the extractant [287]. Also the effect of solubility on extraction was incorporated [288] and the effects of pressure and flow-rate on extraction have been rationalised [289]. In this idealised scheme the matrix is supposed to contain small quantities of extractable materials, such that the extraction is not solubility limited. The model is that of diffusion out of a homogeneous spherical particle into a medium in which the extracted species is infinitely dilute. The ratio of mass remaining (m ) in the particle of radius r at time t to the initial amount (mo) is given by ... 

Figure 3.8 Ln(m/m0) vs. scaled time tt(= 7t2Dt/r2) for the hot-ball model, including the effect of particle shape. After Bartle et al. [286]. Reproduced from Journal of Supercritical Fluids, 3, K.D. Bartle et al., 143-149, Copyright (1990), with...

Steps (i) and (ii) are controlled by molecular diffusion. Higher operating temperatures can improve the kinetics of mass transfer in all three steps. Vandenburg et al. [37] described the kinetics of PFE extraction using the hot-ball model [286] derived for SFE extractions. 

Figure 3.19 Accelerated solvent extraction of Irganox 1010 from PP with 2-propanol at various temperatures. Points, experimental data solid lines, curve fitted using the hot-ball model. After Vandenburg et al. [37], Reprinted with permission from HJ. Vandenburg et al., Analytical Chemistry, 70, 1943-1948 (1998). Copyright (1998) American Chemical Society...

Figure 4.18 (a) STM image (39 x 23 nm) 02 molecules at Ag(l 10) at 65 K, illustrating the hot precursor mechanism at a coverage of 0.02. The inset shows an atomic resolution image of the silver surface and the 02 molecules as dark holes. Also shown (b) is a ball model with oxygen molecules (black) and surface silver atoms (white) and second layer silver atoms (grey). (Reproduced from Ref. 32). 

Models Based on a Desorption-Dissolution-Diffusion Mechanism in a Porous Sphere. The precursor of these models was the application by Bartle et. al [20] of the Pick s law of diflusion (or the heat conduction equation, i.e. the Fourier equation) to SFE of spherical particles. In doing so they had to assume an initial uniform distribution of the material extracted (in this specific case 1-8 cineole) from rosemary particles. Since Pick s law of difiusion from a sphere is analogous to a cooling hot ball (Crank [21] vs Carslaw and Jaeger [22]), this type of models have been considered to be analogous to heat transfer. This model was also used by Reverchon and his co-workers [23] and [24] to SFE of basil, rosemary and marjoram with some degree of success. 

How would you describe the differences between a cup of coffee and a cup of hot water What probably come to mind are the aroma, the dark color, and the taste of a good cup of coffee. Coffee s action as a stimulant is another obvious difference. These properties come from the chemical compounds that hot water dissolves from ground coffee beans. These compounds are molecules constructed from different atoms bound together in veiy specific arrangements. The molecule that makes coffee a stimulant is caffeine. Our background photo is a magnification of crystals of pure caffeine, and the inset is a ball-and-stick model of this molecule. 

The experimental test and model comparison have been carried out without bleed and hot bypass, but with a cold bypass valve opening of 40%. The use of the cold-air bypass valve (FV-170) allows compressor discharge to be directed into the turbine inlet, bypassing the heat exchangers, air plenum and fuel cell simulator. FV-170 is a nominal 15.4 cm ID Fisher-Rosemont V-150 Vee-Ball control valve with a full range slew rate of 1.5 seconds. 

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