I DEBRIS DISPERSAL COMPUTATIONS J. R. Banister Presiding (A) The Fall of Small Particles or Heavy Molecules Through the Upper Atmosphere H. L. Davis* and J. R. Banister Sandia Laboratory We have computed the vertical transport of small particles or heavy molecules through a one-dimensional model of the upper atmosphere by considering these small particles to be an impurity of small concentration, Both the effects of diffusion and the earth's gravitational field have been considered in the computation. In the model it has been assumed that the atmosphere is stagnant, isothermal, and has a decreasing exponential dependence of density upon the height; however, it should be relatively easy, if the need would arise, to use in the calculations the actual temperature and density of the atmosphere as a function of the height. Also, some simple models of turbulence could be taken into account, and more about turbulence will be mentioned after treating the model which has been described. For the model, the flow rate, I’, of the impurity across a horizontal surface is given by K K p p ax where x is the height above the earth, c is the concentration of the impurity at x, and p is the density of the atmosphere at x. The second term in equation (1) is the flow rate caused by the diffusion of the impurity into the surrounding atmosphere, with K, 2 being given by 1/2 1+ Ko : a 1/2 (= (a + A) ™m . (2) This is the usual diffusion coefficient for one type of spherically symmetrical particle diffusing into another. equation (2), m is the average mass of the air particles, M is the mass of the impurity particles, In a is the average radius of the air particles, A is the radius of the impurity particles, k is Boltzmann's constant, and T is the absolute temperature of the atmosphere. The first term of equation (1) is the flow rate caused by the earth's gravitational field, i.e., the drop rate through a viscous fluid. To obtain an expression for K> the equilibrium situation is considered, gardless of the concentration or cencentration gradient, the flow rate equation will apply. That is, re- So if a concentration profile is injected into our model of the atmosphere, the time development of the concentration profile is completely governed by the flow rate equation. place across a horizontal surface. But eventually an equilibrium will occur such that no flow will take For this equilibrium the effects of diffusion and the earth's gravitational field are still present; however, they counterbalance each other such that the net flow across any horizontal *Speaker presenting the paper. 17