= local shear stress at the wall Subscripts d = liquid drop g = gas properties i L = liquid properties rn 0 = stagnation point w = condition at wall 02 = free stream conditions = interface at liquidlgas boundary layers = maximum value for impingement on surface Superscripts I = derivative with respect to the independent variable 0 = degrees LITERATURE CITED

An approach is presented for modeling the effects of temperature and pH on the solubility of amino acids in water. The amino acids studied are alanine, amino-butyric acid, glycine, hydroxy-proline, proline, serine, threonine, and valine. The data employed are activity coefficients and solubilities of the amino acids in neutral water and the dissociation constants for the various amino-acid ionization reactions. Activity coefficients are correlated with the modified UNIFAC group contribution model and with new glycine and proline groups being introduced.A similar approach is presented for modeling the solubilities of certain antibiotics in mixed nonaqueous solvents. Fusion temperature data and solubilities of the antibiotics in pure organic solvents are used to deduce modified UNIFAC energy interaction parameters between new large antibiotic groups and the standard alkane (CH,), alcohol (OH), aromat (ACH), and ester (CCOO) groups. IntroductionIn a typical case, the cost involved in bioseparations may be as high as ninety percent of the total cost of manufacturing. Unfortunately, this area has not been given much research attention and bioseparation units are most often designed empirically rather than on the basis of rational information.The prediction of activity coefficients for amino acids has had only recent attention. Orella and Kirwan (1987), in their unpublished work, have made an attempt to predict solubilities of several amino acids (glycine, alanine, phenylalanine, valine, leucine, and iso-leucine). They considered the activitycoefficient to be made up of terms due to chemical interactions (from UNIFAC) and due to electrostatic interactions (from the extended Kirkwood theory).Nass (1988) has correlated amino acid activity coefficient and solubility data. She assumed that the activity coefficient is a product of terms due to chemical reaction equilibrium and due to physical interaction. Wilson's equation was used for the physical activity coefficient, with Bondi's volumes (Bondi, 1968) inserted for the pure-component liquid volume ratios. Activity coefficients for alanine, serine, and threonine in water, and solubilities of phenylalanine, tyrosine, and diiodotyrosine in water have been correlated. The correlations are in good agreement with the experimental data. The number of parameters regressed varied from three to ten. In this work, an attempt has been made to build a predictive model for the activity coefficients of amino acids. Amino acids in the study are alanine, amino-butyric acid, glycine, hydroxyproline, proline, serine, threonine, and valine. These are eight of the twenty most common amino acids. The effect of pH and temperature on amino acid solubility are considered.We have also explored the possibility of constructing a predictive model for the solubility in mixed solvents of six antibioticsanisomycin, carbomycin A, chloramphenicol, chloramphenicol palmitate, griseofulvin, and hygromycin A. The selection of these antibiotics is based on their commercial importance and the availability of so...

The basic assumptions of van der Waals theory are contained in two well-known concepts: excluded volume (repulsive forces) and a homogeneous, isotropic field potential (attractive forces). We have superimposed on these, one more well-known concept: the existence of dimers, trimers, etc., at chemical equilibrium. With Following the basic concepts of van der Waals, we postulate that when nT moles of fluid occupy volume V at temperature T, the pressure P can be expressed by P = Phs + Pa t [1] where subscript hs stands for hard sphere (repulsive forces) and subscript att stands for attractive forces.We rewrite the first contribution in terms of the compressibility factor Zhs Ph, = nTRTZhS/ V [2] where R is the gas constant. We introduce the reduced density t defined byThe attractive-force contribution to the pressure is rewritten in the form Patt = -(a/b2)7ratt(4) [4] where lratt is a function only of {. Xj+l.There is abundant experimental evidence which indicates that molecular clusters, as postulated, exist not only for polar and hydrogen-bonded molecules, but also for nonpolar molecules such as argon (7-9).Let .3 stand for the mole fraction of species i (monomer, dimer, etc.) [7] where a and b refer to the monomer.We also introduce the following reasonable simplifying assumptions bj= jb a1 = ja [3] [8] [9] where b is proportional to the volume of the hard-sphere molecules.The total number of moles nT is not a constant because, for an associating fluid, it depends on the density and the temperature. That is, the "pure" fluid is considered here to be a mixture of monomers, dimers, trimers, etc. Therefore, 1 depends on the "true" composition of the fluid. In the limit (all molecules are monomers) b = 7r NAV &3/6, where NAV is Avogadro's number and a is the collision diameter.where a and b refer to the monomer.Conservation of mass requires that the total number of moles nT is related to no (the number of moles that would exist if there were no association) by[10] nTEj&a = nOCombining Eq. 10 with Eqs. 6-9, we obtain a = (no/nT)2a and b = (nO/nT)b.[11] [12]

The modified Sanchez-Lacombe equation of state (MSL-EOS) is Neau's version of the Sanchez-Lacombe equation of state modified to include a Pe ´neloux-type volume translation. The purpose of this work is to report parameters for modeling the phase behavior of polyethylene solutions. The MSL equation is an empirical equation that contains four parameters to define each pure compound whether a solvent or a polydisperse polymer. The MSL equation uses conventional linear and quadratic mixing rules. A parametrization can be used to obtain the pure compound parameters from the molar mass, critical temperature, critical pressure, and acentric factor. These properties cannot be defined for polydisperse polymers, and parameters were determined from a combination of liquid density (PVT) data and polymer + solvent cloud point (xPT) data. Binary interaction parameters have been obtained for over 50 mixtures by correlating the fluid phase boundaries. Binary mixtures including ethylene, hexane, and/or cyclohexane are of particular interest to polyethylene production. A single binary interaction parameter is usually sufficient to represent vapor-liquid equilibrium, but temperature dependence is required to accurately represent liquid-liquid equilibrium. The MSL equation of state can be used to correlate the cloud points of polyethylene solutions at high pressures.

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