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28 Physical and Thermal Technologies <br /> Q = the external concentration of the substance <br /> k = the absorption constant �� �, -9 y-wy <br /> Ifatt =0, x =0, then: <br /> x =Q(1-e k') (2) <br /> The constant k is found to be: <br /> k=dx/dt (3) <br /> Q-x i <br /> By multiplying both numerator.and denominator by V, the volume of the bubble, <br /> we obtain: V <br /> k=Vdx/dt (4) <br /> V(Q-X) <br /> which is the ratio between the amount of substance entering the given volume per <br /> unit time and quantity V(Q-x) needed to reach the asymptotic value. By <br /> analyzing the concentration change within the fine bubbles sent through a <br /> saturated (water-filled) porous matrix interacting with a catalytic matrix (iron <br /> silicate), the kinetic rates of reaction can be characterized. <br /> The rate at which the substance quantity kjQV flows in one unit of time <br /> from aqueous solution into the bubble is proportional to Henry's Constant. The <br /> second rate of decomposition within the bubble can be considered as k2, a second <br /> rate of reaction (-k2x), where: <br /> dx =k,Q-k2x (5) <br /> dt <br /> At equilibirum, as dx/dt= 0: <br /> kl <br /> X =---- Q (h) <br /> k2 <br /> However, if the reaction to decompose is very rapid; so —k2x goes to zero, <br /> the rate of reaction would maximize k1Q, i.e., be proportional to Henry's Constant <br /> and maximize the rate of extraction since VOC saturation is not occurring within <br /> the bubbles. <br /> PROCESS DESCRIPTION <br /> The concentration of HVOC expected in the bubble is a consequence of <br /> rate of invasion and rate of removal. In practice, the ozone concentration is <br />