Exercise $10\mathrm{.}11$: Particle agglomeration and breakage

Particle agglomeration between particles of sizes $n$ and $m$ is modeled by the event

$P_n+P_m{k}_{nm}{P}_{n+m},r_{nm}=k_{nm}{f}_n{f}_m$

Particle breakage is modeled by the event

$P_n{k}_{nm}^{\text{'}}{P}_m+P_{n-m},r_{nm}=k_{nm}^{\text{'}}{f}_n$

in which a particle of size $n$ breaks into two particles of sizes $m$ and $n-m.$ Here we

assume that size reflects a quantity, such as particle mass, that is conserved during the

agglomeration or breakage process.

For which of these processes is the mean of the stochastic model at low particle

number equal to the deterministic population balance? Justify your answer. Compare

your answer to that in $[13]$; see the last paragraph before the conclusions. Compare

also to the later version $[14,$ pp$.305,311].$

$6.)$ The CSTR

Figure $620$: Steady$-$state comversion vertwas residence time $-log$

scale.

$6\mathrm{.}3$ The CSTR

Figure $6\mathrm{.}28$: Comversion and temperature vs$.$ time for $T=30$min.