There are some high-priority refer unit trains from the west to east costs. UP calls it the "Ice-Cold Express". BNSF knows it as the "Sallad Shooter" (or maybe it's the other way around).

Yes we do. It goes up to New York I think to a distribution center.

There's the Tesco express in the UK run by DRS. Not officially known as that, more a term rail enthusiasts have give it. It conveys intermixed traffic for the supermarket chain Tesco.

In 1931, the St Louis Southwestern (better known as the Cotton Belt) started a fast freight train, called the Blue Streak Merchandise. It offered overnight service from St Louis to Little Rock, Texarkana and Memphis, plus second day service to Houston or Dallas. The Train has since been expanded, with three trains a day from St Louis and one train originating in Memphis. All four now go all the way to the Los Angeles area. One of the Blue Streak Merchandisers is devoted to auto parts, only.

Like the Juice Train, are there other branded unit trains out there?

And do we really drink that much orange juice to warrant a train!? (ok ok, yes, I drink A LOT of orange juice)

Tropicana Juice And Other Famous Unit Trains?