$9\mathrm{.}3$ Batch Crystallizer with Constant Rate of Diluent Addition

For a solute being

crystallized by batch crystallization with a constant rate of change of diluent concentra$-$

tion, predict the effect on the crystal size at any given time for each of the changes in

the variables given. Justify your answers based on an expression for the crystal size as

a function of these variables.

$($a$)$ An increase in the nucleation rate

$($b$)$ An increase in the growth rate

$($c$)$ An increase in the supersaturation, for $b[$Equation $(9\mathrm{.}2\mathrm{.}2)]$ greater than $g[$Equation

$(9\mathrm{.}2\mathrm{.}3)]$

$($d$)$ An increase in $k_m$ in the equation $d\frac{c_d}{d}t=k_m,$ where $c_d$ is the diluent concentration

$($e$)$ An increase in $k_p[$Equation $(9\mathrm{.}3\mathrm{.}1)]9\mathrm{.}3$ Batch Crystallizer with Constant Rate of Diluent Addition For a solute being

crystallized by batch crystallization with a constant rate of change of diluent concentra$-$

tion, predict the effect on the crystal size at any given time for each of the changes in

the variables given. Justify your answers based on an expression for the crystal size as

a function of these variables.

$($a$)$ An increase in the nucleation rate

$($b$)$ An increase in the growth rate

$($c$)$ An increase in the supersaturation, for $b[$Equation $(9\mathrm{.}2\mathrm{.}2)]$ greater than $g[$Equation

$(9\mathrm{.}2\mathrm{.}3)]$

$($d$)$ An increase in $k_m$ in the equation $d\frac{c_d}{d}t=k_m,$ where $c_d$ is the diluent concentration

$($e$)$ An increase in $k_p[$Equation $(9\mathrm{.}3\mathrm{.}1)]$

$(9\mathrm{.}2\mathrm{.}1)B=\frac{dN}{dt}=k_n(c-c^{**}{)}^n$

$(9\mathrm{.}2\mathrm{.}2)B=\frac{dN}{dt}=k_1{M}_T^j(c-c^{**}{)}^b$

$(9\mathrm{.}2\mathrm{.}3)R=\frac{1}{A}\frac{dW}{dt}=k_G(c-c^{**}{)}^g$