His research at Brown was on the effects on diffusion of temperature gradients. He came up with a set of equations  in 1929 now called Onsager reciprocal relations. The importance of these equations in statistical mechanics was not realized for many years. However by 1968 they were considered important for Onsager to win the Nobel Prize in Chemistry. In 1933, after leaving Browns, Onsager traveled to Austria to visit electrochemist Hans Falkenhagen. He met Falkenhagen's sister-in-law, Margrethe Arledter. They were married on September 7, 1933, and had three sons and a daughter.