  Resonance processes are common phenomena in multiscale (slow-fast) systems.
In the present paper we consider capture into resonance and scattering on
resonance in 3-D volume-preserving slow-fast systems. We propose a general
theory of those processes and apply it to a class of viscous Taylor-Couette
flows between two counter-rotating cylinders. We describe the phenomena during
a single passage through resonance and show that multiple passages lead to the
chaotic advection and mixing. We calculate the width of the mixing domain and
estimate a characteristic time of mixing. We show that the resulting mixing can
be described using a diffusion equation with a diffusion coefficient depending
on the averaged effect of the passages through resonances.
