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As we have discussed in the Pre-analysis and Setup section, Stokes Number is the ratio of particle of particle response time to the flow characteristic time scale. Here, in the case of low Reynolds Number flow, particles response time is calculated using this formula:

{latex}
\large{
$$\tau_p = \frac{\rho D^2}{18 \mu}$$
}
{latex}

Here, we will use the inverse of the instability growth rate as the flow characteristic time scale:

{latex}
\large{
$$\tau_f = \frac{1}{\gamma} = \frac{1}{0.1751 s^{-1}}$$
}
{latex}

Thus combining the two equations above, we get:

{latex}
\large{
\begin{align*}
&St = \frac{\tau_p}{\tau_f} = \tau_p \gamma = \frac{\rho D^2}{18 \mu } \gamma \\
&\Rightarrow \rho = \frac{18 \mu \cdot St}{D^2 \gamma}
\end{align*}
}
{latex}

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