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<br />. <br /> <br />. <br /> <br />CHAPTER 3 <br /> <br />. <br /> <br />TIME - DEPENDENT EMPIRICAL EQUATIONS <br /> <br />. <br /> <br />As indicated in the last chapter, the most important variables in each of <br />the six previously described experimental studies are the growth time and the <br />ambient fog temperature. Empirical equations adequately describing the data <br />as a function of at least these two variables would therefore be useful. For <br />this reason development of time-dependent empirical equations for mass, a- <br />and c-axiallengths, and fall velocity for every degree of temperature in the <br />range of -4 and -20 oC will be carried out. The development of these <br />time - dependent equations in this chapter will involve theoretical and <br />experimental analyses. First, analysis of growth theories will help identify <br />their time - dependency. Then, experimental data will help calculate the <br />constants and other parameters involved in the time - dependent equations <br />and, in some cases, modify the theoretically derived equations in order to <br />adequately describe the data. The results will help verify theory and provide <br />empirical equations applicable to different regimes of growth. <br /> <br />. <br /> <br />. <br /> <br />. <br /> <br />. <br /> <br />Evaluation of Growth Theory <br /> <br />. <br /> <br />. <br /> <br />Mass and dimensions <br />The growth theory of Fukuta and Walter (1970) deals with a spherical ice <br />particle with a radius ~ 1 Ilm. Extending one mean free path for air molecules <br />from the surface is a resistance layer whose thickness is small compared with <br />the radius. The temperature difference between the particle surface and the <br /> <br />. <br />