Debenedetti condition

A mathematical condition for core softening was proposed by Debenedetti etal. [86] and requires that A [r/(r)j < Ofor Ar < 0, in some interval n < r < rz, together with u" r) > 0 for r < ri and r > rz- The above conditions are satisfied if, in the Interval (ri, r2), the product r/(r) (rather than just f(r)) reduces with decreasing interparticle separation. This requirement can be met also by a strictly convex potential, yielding a repulsive force that everywhere increases for decreasing r, provided that in a range of interparticle distances, the increasing rate of f(r) be sufficiently small. Debenedetti condition is satisfied by the YK potential whenever a < 2.3. 

The second value considered a = 3.3) is markedly greater than the threshold value beyond which Debenedetti condition holds no more. In this case, the YK potential monotonously increases for decreasing r together with its first and second... 

Mohamed, S. R. Debenedetti, P. G. Prud homme, R. K. Effects of Process Conditions on Crystals Obtained from Supercritical Mixtures. AIChE J. 1989b, 35, 325-328. 

Concentration overpotential arises due to external or internal mass transfer limitations. For typical cross-flow monoliths, Debenedetti (19) has shown that concentration overpotential is not important under conditions similar to those explored here. 

Case e is the result of precipitation under conditions above the ternary MCP and is the true supercritical antisolvent precipitation. The formation of very small particles indicates that characteristic times for surface tension disappearance are very short, droplets are not formed at the exit of the injector and the very small particles are released from the fluid phase. These aspects have been studied in the previously cited works of Werling and Debenedetti," which underline the interplay among the different consecutive or simultaneous process that characterize SAS, mainly mass transfer under sub-critical and supercritical conditions. The characteristic times... 

Several factors can affect this enhanced mass transfer. First, as Debenedetti and Reid ( pointed out, the very low kinematic viscosities in conjunction with very high buoyant forces serve to enhance natural convection at the same Reynolds number. This is accentuated by large density differences that can occur as naphthalene dissolves in the C02 It is possible to have very large, negative partial molar volumes (i.e., -2000 cc/mole) for a solute at conditions near the critical point (Eckert et al., (23)) which causes the fluid density to depend strongly on composition. At 35 0 and 100 atm, naphthalene s partial molar volume at infinite dilution is approximately -300 cc/mol. This can cause a significantly higher fluid... 

Weber, M. Russell, L.M. Debenedetti, P.G. Mathematical modeling of nucleation and growth of particles formed by the rapid expansion of a supercritical solution under subsonic conditions. J. Supercrit. Fluids 2002, 23, 65-80. 

Werling JO, Debenedetti PG. Numerical modeling of mass transfer in the supercritical antisolvent process miscible conditions. J Supercrit Fluids 2000 18 11-24. 

Mohamed RS, Debenedetti PG, Prud homme RK. Effects of process conditions on crystals obtained from supercritical mixtures. AIChE J 1989 35 325-332. 

NA Collins, PG Debenedetti, S Sundaresan. Disproportionation of toluene over ZSM-5 under near-critical conditions. AIChE J 34 1211-1214, 1988. 

The use of RESS in the processing of pharmaceuticals is driven, in large part, by the requirement for particles of a narrow size distribution. This requirement with regard to pharmaceutical particles is related to issues such as reproducibility and uniform solvation of drugs in the body. In the search for more favorable processing conditions through evaluations of various experimental parameters, organic materials such as polyaromatics are often used as models for pharmaceuticals. For example, Debenedetti and coworkers used naphthalene in supercritical CO2... 

In the same study, Debenedetti and coworkers evaluated the effect of naphthalene concentration on particle size (85). For two samples prepared under the same conditions, an increase in naphthalene mole fraction from 2.6% to 4.44% resulted in a decrease in particle size from 30-135 to 6-32 xm. The concentration effect was rationalized such that a higher naphthalene concentration should lead to a higher supersaturation ratio in the expansion jet and, therefore, a higher nucleation rate. Theoretically, the particle volume is inversely proportional to the... 

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