Double divergence of stress tensor for migration flux I am looking to calculate migration as a function of time using equation in Image 1. SigmaP is the total particle stress tensor in the cylindrical coordinates (r, theta, z). I am only interested in migration taking place in the z direction.  Is the divergence of stress tensor in z direction shown in Image 2 correct? What do I have to do next to get the double divergence computed?
Thanks


 A: You can look at wikipedia, there is a useful list of almost all the vector calculus formulae :
https://en.wikipedia.org/wiki/Del_in_cylindrical_and_spherical_coordinates
In cylindrical coordinates : $(\nabla.\sigma)_z=(\partial_r \sigma_{rz}+\frac{1}{r}\partial_{\theta}\sigma_{\theta z}+\partial_z \sigma_{zz}+\frac{\sigma_{rz}}{r})\hat{\mathbf{z}}$
I'm not sure what you mean with "I am only interested in migration taking place in the z direction". Is it that $(\nabla.\sigma)_r=(\nabla.\sigma)_{\theta}=0 $ ?
If so, when you get to the second divergence : 
$\nabla.(\frac{2 a^2}{9 \eta_0}f(\phi)\nabla.\sigma)=\frac{2 a^2}{9 \eta_0} \Big(\nabla f(\phi) \nabla.\sigma + f(\phi)\nabla(\nabla.\sigma)\Big)$ 
with $\nabla f(\phi) \nabla.\sigma=\partial_z f(\phi)(\partial_r \sigma_{rz}+\frac{1}{r}\partial_{\theta}\sigma_{\theta z}+\partial_z \sigma_{zz}+\frac{\sigma_{rz}}{r})$ 
and $\nabla(\nabla.\sigma)=\partial_z(\partial_r \sigma_{rz}+\frac{1}{r}\partial_{\theta}\sigma_{\theta z}+\partial_z \sigma_{zz}+\frac{\sigma_{rz}}{r})$
PS: you can use latex to write on stackexchange your equations and mathematical symbols
