kinetic equilibrium

kinetic equilibrium

[kə′ned·ik ‚ē·kwə′lib·rē·əm]
(mechanics)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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These are related to the physical conditions for the possible occurrence of the so-called property of macroscopic irreversibility (PMI) and the consequent one represented by the decay to kinetic equilibrium (DKE) which characterize the 1-body (kinetic) PDF in these N-body systems, i.e., when 1-body-factorized initial conditions are considered for the N-body Liouville equation [3].
In fact for the same equation it is not known in satisfactory generality whether smooth enough solutions of the same equation exist which satisfy the H-theorem inequality and decay asymptotically to kinetic equilibrium [23, 30].
(iv) MKI Prescription No.#4: fourth, in order to warrant the existence of DKE we shall require the functional [I.sub.M]([[rho].sup.(N).sub.1](t)) to be prescribed in such a way that at an arbitrary time t [member of] I, with t [??] [t.sub.o], the vanishing of both [I.sub.M]([[rho].sup.(N).sub.1](t)) and its time derivative ([partial derivative]/[partial derivative]t) [I.sub.M]([[rho].sup.(N).sub.1](t)) should occur if and only if the 1-body PDF solution of the Master kinetic equation coincides with kinetic equilibrium. As a consequence, for the functional [I.sub.M]([[rho].sup.(N).sub.1](t)) the following propositions should be equivalent:
with [[rho].sup.(N).sub.1M]([v.sub.1]) being a kinetic equilibrium PDF of the form (6).
(i) the time derivative inequality (18) and the conditions of existence of kinetic equilibrium (21);
Caption: Figure 2: Conventional kinetic equilibrium extraction of Clinacanthus nutans fresh and dried leaves (n = 3).
Caption: Figure 4: Peleg model kinetic equilibrium extraction of Clinacanthus nutans fresh and dried leaves (n = 3).
Caption: Figure 7: Peleg model kinetic equilibrium extraction of orientin and vitexin dried leaves extract (n = 3).
As it can be seen from Figure 1, the cassava husks powder presents a very rapid adsorption process, reaching kinetic equilibrium in less than 1 min.
The material reached kinetic equilibrium in less than 1 minute, and its optimum pH to perform Cd(II) uptake was found to be 5, what is very approximate to the material's point of zero charge (5.33).
Emphasis was laid on the estimation of kinetic equilibrium and thermodynamic parameters.

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