Your question supposes a very linear version of the flow of stomach contents of:
In reality, it is not so linear. Firstly some background: The rumen and reticulum form the first two parts of the four, and are in fact a single chamber/organ (collectively known as the reticulorumen). They have different wall structures, and perform initial digestion of different particles (mostly heavier particles in the rumen such as grain and more digested hay). This reticulorumen chamber is where the initial microbial fermentation of the feed occurs. Matter passes from rumen to reticulum and back regularly by means of two distinct muscle contractions.
To aid in the breakdown of the feed, the cud is regularly regurgitated, chewed and then re-ingested. The re-ingested cud returns to the reticulorumen. From there, in order to advance down into the later stages of the digestive tract, it must pass through the reticulorumen orifice into the third compartment - the omasum. The orifice allows particles up to 4mm in size in cattle.
The omasum chamber removes water and some nutrients. The contractions of the omasum remove water and move solids through the system, and the contractions are speculated to filter out any larger particles and return them to the reticulorumen. Matter that has been processed by the omasum is passed along to the fourth chamber, the abomasum.
So to answer your question in brief, after mastication the cud returns to chambers one and two, potentially going round this loop several times until it is sufficiently broken down by chewing, saliva and bacterial action, and then it can proceed from there to the third chamber.
The "digesta circulation and reticulo rumen motility in the ruminent" paper (C. Poncet, C.H. Malbert, R. Baumont) has this to say:
The outflow of digesta, allowed by the opening of the ROO [reticulorumen orifice] during the second phase of the reticular contraction, is highly selective. The effluent does not contain particles greater than 2mm in sheep and 4mm in cattle. This is due to the buoyancy of the large particles in the reticulum, to the self filtration of the digesta during the passage through the ROO and perhaps to backflows from the omasum to the reticulum.
You may find it useful to get a copy of this collection of papers (quote from p.366): http://books.google.co.uk/books?id=Bcsa8Z4u-E4C&printsec=frontcover#v=onepage&q&f=false