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<br />. <br /> <br />32 <br /> <br />. <br /> <br />and <br /> <br />P'i L2la <br />C2 = S i-I ( 2 <br />KRvT _ <br /> <br />ly ) <br />+ . <br />Dp_,sat <br /> <br />(3.11) <br /> <br />. <br /> <br />. <br /> <br />If 2a is the diameter of the crystal, c the length and, H the axial ratio (= 2a/ c) <br />and nearly independent of time, then the relationships between time, mass <br />and a- and c-axiallengths of a hexagonal crystal become <br /> <br />. <br /> <br /> m (t) = mo[ ( 1 + COKt ) 1/2 - 1 p, (3.12) <br /> 2a(t) = ao [ ( 1 + CDKt ) 1/2 - 1 ] , (3.13) <br />and <br /> c( t) = Co [ ( 1 + CD K t ) 1/2 - 1 ] , (3.14) <br />where <br /> mo =9 ~ m'o / 41tH, (3.15) <br /> ao = C2 / Cl , (3.16) <br /> <br />. <br /> <br />. <br /> <br />. <br /> <br />and <br /> <br />Co = ao / H . <br /> <br />(3.17) <br /> <br />. <br /> <br />. <br /> <br />Of course, these relationships are valid only if the assumptions used to <br />derive the diffusion-kinetic equation for a spherical ice particle can also apply <br />to a nonspherical particle. However, these theoretical results give some <br />indication of the appropriate structure of the empirical equations and await <br />experimental verification later in this chapter. <br /> <br />. <br />