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<br />21 <br /> <br />Particulate Continuity Equations <br /> <br />The number continuity equation fo.. liquid water drops is: <br /> <br />"" <br /> <br />d f ~ f f;)(o V ) ,~f J <br />x x x X f1 x <br />-=-0N+V)T7-- +-K- <br />D t x (J Z P cl Z az p z <br /> <br />c~ <br /> <br />8 K <br />- -t fx +A fx +C1 - R1 +B1 +62 <br /> <br /> - F - a a (xf) (eq. 22) <br /> 1 x x <br />where f = the concentration density of drops of water mass x <br /> x <br /> W = updraft velocity <br /> V = terminal velocity of drop of mass x <br /> x <br /> p = air density <br /> K = eddy conductivity for particles <br /> p <br /> A = the dynamic entrainment term defined earl ier <br /> C1 = stochastic liquid-liquid coalescence term including <br /> <br />both the loss of drops of this mass (x) by coli ision <br />with any other drop and the gain of drops of this mass by <br />collision of two smaller drops to form one of this size <br /> <br />R1 = loss of liquid particles of this mass by their collision with <br />an ice particle of any mass to form a new ice particle <br />having a mass the sum of the masses of the two composite' <br />particles <br /> <br />a <br />