Collective coefficients

The equivalence of a and b is straightforward. By expanding the two factors in the numerator of Eq. (F.9) and collecting coefficients of the same.power of X, we obtain Eq. (F.IO). The equivalence of b and c is obtained by requiring that the two polynomials of degree t be identical (hence leading to the same BI). This is achieved by imposing the equalities... 

We obtain the general expression for S t) by expanding and collecting coefficients with the same powers of q u (note that r[Pg.325]

Now substitute Eq. (22.8) into Eqs. (22.1)-(22.3), collect coefficients of like powers, and rearrange the results to obtain the following wave equation in terms of pressure fluctuation ... 

Note that on the right side we also had to consider k as a variable because on the left k is part of the operand of the operator d. Since d(kxr) - kdxr + xrdk, we can use this relation and collect coefficients of the various dat and dxr. We obtain... 

The rate equation 8.51, written with collective coefficients, then becomes ... 

Table 8.3. Algebraic forms of rate equations and reactions orders for catalytic cycle 8.60 with different macs (collective coefficients ka etc. are defined differently in the different equations).

We now substitute these expansions for H, pk, and Wk into the wave equation 23-1, obtaining the result, after collecting coefficients of like powers of X,... 

Assuming for the time being that cloud droplets are stationary, then particles are captured by Brownian diffusion. The collection of particles by a falling drop will be discussed when we consider wet deposition in Chapter 20. The collection coefficient K Dp, x) can then be estimated by (12.57). Let us estimate this collection rate assuming that the cloud has a liquid water content of 0.5 g m and that all drops have diameters of 10 /im, resulting in a number concentration of Nj = 955 cm For such a monodisperse droplet population (15.95) simplifies to... 

When collecting coefficients with t" where n = 0,1,2..., we have... 

---