  Mixing in fluids is a rapidly developing field of fluid mechanics
\cite{Sreen,Shr,War}, being an important industrial and environmental problem.
The mixing of liquids at low Reynolds numbers is usually quite weak in simple
flows, and it requires special devices to be efficient. Recently, the problem
of mixing was solved analytically for a simple case of random flow, known as
the Batchelor regime \cite{Bat,Kraich,Fal,Sig,Fouxon}. Here we demonstrate
experimentally that very viscous liquids at low Reynolds number, $Re$. Here we
show that very viscous liquids containing a small amount of high molecular
weight polymers can be mixed quite efficiently at very low Reynolds numbers,
for a simple flow in a curved channel. A polymer concentration of only 0.001%
suffices. The presence of the polymers leads to an elastic instability
\cite{LMS} and to irregular flow \cite{Ours}, with velocity spectra
corresponding to the Batchelor regime \cite{Bat,Kraich,Fal,Sig,Fouxon}. Our
detailed observations of the mixing in this regime enable us to confirm sevearl
important theoretical predictions: the probability distributions of the
concentration exhibit exponential tails \cite{Fal,Fouxon}, moments of the
distribution decay exponentially along the flow \cite{Fouxon}, and the spatial
correlation function of concentration decays logarithmically.
