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xxvi Nomenclature

Xm mole fraction of functional group m in y mole fraction in vapor phase; distance; mass UNIFAC method fraction in extract; mass fraction in overflow x mole fraction in liquid phase; mole fraction in y vector of mole fractions in vapor phase any phase; distance; mass fraction in raffinate; Z compressibility factor = Pv/RT; total mass; mass fraction in underflow; mass fraction of height particles Z froth height on a tray C f  = / x normalized mole fraction xi xj 1 ZL length of liquid flow path across a tray j=1 Z¯ lattice coordination number in UNIQUAC and x vector of mole fractions in liquid phase UNIFAC equations xn fraction of crystals of size smaller than L z mole fraction in any phase; overall mole frac- Y mole or mass ratio; mass ratio of soluble mate- tion in combined phases; distance; overall mole rial to solvent in overflow; pressure-drop fraction in feed; dimensionless crystal size; factor for packed columns defined by (6-102); length of liquid flow path across tray concentration of solute in solvent; parameter z vector of mole fractions in overall mixture in (9-34)

Greek Letters

thermal diffusivity, k/CP ; relative volatility; ij binary interaction parameter in Wilson equation surface area per adsorbed molecule mV/L; radiation wavelength ∗ ideal separation factor for a membrane +, − limiting ionic conductances of cation and ij relative volatility of component i with respect anion, respectively to component j for vapor-liquid equilibria; ij energy of interaction in Wilson equation parameter in NRTL equation chemical potential or partial molar Gibbs free , energy-balance parameters defined by j j j energy; viscosity (10-23) to (10-26) momentum diffusivity (kinematic viscosity), relative selectivity of component i with respect ij /; wave frequency; stoichiometric coefficient to component j for liquid–liquid equilibria v(i) number of functional groups of kind k in mole- film flow rate/unit width of film; k cule i in UNIFAC method thermodynamic function defined by (12-37) fractional current efficiency; dimensionless dis- k residual activity coefficient of functional group tance in adsorption defined by (15-115); dimen- k in UNIFAC equation sionless warped time in (11-2) specific heat ratio; activity coefficient osmotic pressure; product of ionic concentra- − change (final initial) tions solubility parameter; film thickness; velocity mass density boundary layer thickness; thickness of the lam- inar sublayer in the Prandtl analogy b bulk density crystal density c concentration boundary layer thickness M ij Kronecker delta p particle density exponent parameter in (3-40); fractional poros- s true (crystalline) solid density ity; allowable error; tolerance in (10-31) surface tension; interfacial tension; Stefan- = × −8 2 · 4 b bed porosity (external void fraction) Boltzmann constant 5.671 10 W/m K D eddy diffusivity for diffusion (mass transfer) I interfacial tension

H eddy diffusivity for heat transfer s, L interfacial tension between crystal and solution

M eddy diffusivity for momentum transfer tortuosity; shear stress; dimensionless time in adsorption defined by (15-116); retention time p particle porosity (internal void fraction) of mother liquor in crystallizer; convergence Murphreevapor-phaseplateefficiencyin(10-73) criterion in (10-32) area fraction in UNIQUAC and UNIFAC equa- ij binary interaction parameter in NRTL equation tions; dimensionless concentration change de- fined in (3-80); correction factor in Edmister w shear stress at wall group method; cut equal to permeate flow rate v number of ions per molecule to feed flow rate for a membrane; contact  , volume fraction; parameter in Underwood angle; fractional coverage in Langmuir equa- equations (9-24) and (9-25) tion; solids residence time in a dryer; root of ¯ the Underwood equation, (9-28) local volume fraction in the Wilson equation { } L average liquid residence time on a tray t probabilityfunctioninthesurfacerenewaltheory Maxwell-Stefan mass-transfer coefficient in a pure-species fugacity coefficient; association binary mixture factor in the Wilke-Chang equation; recovery Seader_44460_fm.qxd 8/30/05 5:15 PM Page xxvii

Nomenclature xxvii

factor in absorption and stripping; volume frac- equilibria calculations for single-stage extrac- tion; concentration ratio defined by (15-125) tion; sphericity defined before Example 15.7 ¯ partial fugacity coefficient o dry-packing resistance coefficient given by (6-113) df froth density fractional entrainment; loading ratio defined by e effective relative density of froth defined by (6-48) (15-126); sphericity acentric factor defined by (2-45); segment frac- s particle sphericity tion in UNIFAC method segment fraction in UNIQUAC equation; V/F in flash calculations; E/F in liquid–liquid

Subscripts

A solute L liquid phase; leaching stage a,ads adsorption LM log mean of two values, A and B = (A − B)/ avg average ln(A/B) B bottoms LP low pressure b bulk conditions; buoyancy M mass transfer; mixing-point condition; mixture m bubble bubble-point condition mixture; maximum max maximum C condenser; carrier; continuous phase min minimum c critical; convection; constant-rate period N stage cum cumulative n stage D distillate, dispersed phase; displacement O overall d drag; desorption o,0 reference condition; initial condition d,db dry bulb out leaving des desorption OV overhead vapor dew dew-point condition P permeate ds dry solid R reboiler; rectification section; retentate E enriching (absorption) section r reduced; reference component; radiation e effective; element res residence time eff effective S solid; stripping section; sidestream; solvent; F feed stage; salt f flooding; feed; falling-rate period s source or sink; surface condition; solute; satu- G gas phase ration GM geometric mean of two values, A and B = T total square root of A times B t turbulent contribution g gravity V vapor gi gas in W batch still go gas out w wet solid-gas interface H,h heat transfer w,wb wet bulb I, I interface condition ws wet solid i particular species or component X exhausting (stripping) section in entering x,y,z directions irr irreversible at the edge of the laminar sublayer j stage number 0 surroundings; initial k particular separator; key component ∞ infinite dilution; pinch-point zone

Superscripts

E excess; extract phase LF liquid feed F feed o pure species; standard state; reference ID ideal mixture condition (k) iteration index p particular phase