Seader_44460_fm.qxd 8/30/05 5:15 PM Page xxvi 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.