The use of walnut oil in paint can be traced back even further than that of linseed. When 15th century artists began to add oil to their tempera colours it was walnut oil that seemed the obvious choice. Jan van Eyck in Flanders and Antonello da Messina in Italy both knew of its handling properties.
Walnut oil dries at the same rate as linseed oil, but it does not yellow as much. Michael Harding use it as the binder for their lead whites, but it is not widely used as it is around three times the price of linseed oil. Use it to thin whites and to bring out the brightness in other colours.