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<br />. <br /> <br />31 <br /> <br />. <br /> <br />vapor, T_ the ambient air temperature, p..., 5 a t the ambient saturation water <br />vapor density with respect to ice, p_ the ambient water vapor density, 0 the <br />diffusion coefficient of water vapor in air, p the atmospheric pressure, c v the <br />specific heat of air at constant volume, a the thermal accommodation <br />coefficient, "( the deposition coefficient and, Ra the specific gas constant for air. <br />From previous experimental studies, 1 = a > "( (Fukuta and Walter, <br />1970), which provides the basis for assuming that a = 1.0 for the <br />remainder of this thesis. <br />By letting m = 41t Pir 3/3 where P'i is the apparent density of the ice <br />crystal, performing the necessary arrangement and integration, and assuming <br />that r = 0 at t = 0, the relation between the radius and time becomes <br /> <br />. <br /> <br />. <br /> <br />. <br /> <br />C1r2 + C2r = t . <br /> <br />(3.6) <br /> <br />. <br /> <br />After solving for r by using the quadratic formula and choosing the proper <br />root, the relations between the mass, radius and time become <br /> <br />. <br /> <br />m ( t) = 41t P 'i r 3 ( t ) / 3 <br />= (2 1t p'i! 3) .. ( C 2/ C 1 /2) 3 .. [ ( 1 + 4 C 1 t / C 22 ) 1 /2 - 1 P <br />= m I 0 [ ( 1 + CD I( t ) 1 /2 - 1 P , (3.7) <br /> <br />. <br /> <br />where <br /> <br />. <br /> <br />m'o = 41tp'i( C2 / Cl )3 / 12 , (3.8) <br />CDK = 4Cl / C22 , (3.9) <br /> P'i ( L2 1 ), <br />Cl = 2 (5 i - 1) KR T2 + (3.10) <br />DP-,sat <br /> v _ <br /> <br />. <br /> <br />. <br />