Professor Brodkey worked for Esso Standard Oil Company (now Exxon) as a research chemical engineer. His work involved the development and design of modifications for a synthetic lubricating oil additives plant involving alkylation, sulfurization, and neutralization. He also worked for E.I. DuPont de Nemours and Co. as a chemical engineer doing research on the nature of drying synthetic polymers and pilot plant production. At Ohio State, his work has been primarily in the field of fluid mechanics with specialization in the areas of fundamental turbulent fluid flow (~40 publications), mixing (~25 publications), rheology (~15 publications), two phase flow (~10 publications), as well as other fields (~20 publications), and 10 patents. Recently he has been involved in the application of image processing and analysis to problems in fluid mechanics (~10 publications). He is well known for his graduate text, The Phenomena of Fluid Motions, which has been republished by Dover. His newest text, Transport Phenomena: A Unified Approach, (with H.C.Hershey) was published in 1988 by McGraw-Hill as part of their prestigious Chemical Engineering Series and is now available in paper back form.

Professor Brodkey received a "Senior U.S. Scientist Award" (1975) from the Alexander von Humboldt Foundation, a "Senior Fellowship in Science" (1972) from NATO, and the "Outstanding Paper of the Year Award"(1970) from the Canadian Society for Chemical Engineering. For the Fall of 1978, he received the Visiting Professorship award from the Japan Society for the Promotion of Science. More recently he was selected to receive The Ohio State University's Distinguished Senior Research Award (1983 )and a Senior Research Award (1983) from the College of Engineering of The Ohio State University. This latter award, which can be given every three years for work based on the preceding three years, was awarded again to Prof. Brodkey in 1986. During the summer of 1983 he was once again invited to visit Germany under the von Humboldt Senior U.S. Scientist Program. In 1985, he was awarded the Senior Research Award of the American Society of Engineering Education and elected a Fellow of the AIChE. In 1986, he received the Chemical Engineering Lectureship Award sponsored by 3M and given by ASEE. In 1987 he was elected a Fellow of the American Physical Society. He has also been made a fellow o f the American Association for the Advancement of Science (1954) and of the American Institute of Chemists. In 1994, he held the W.W. Clyde Chair of Engineering at the University of Utah, received the 1994 North American Mixing Forum's award for Outstanding Research, and had two sessions at the San Francisco Annual AIChE meeting held in his honor for his 65th birthday. In 1998, at the Miami Annual AIChE meeting, he has another session in honor of his 70th birthday.  In 2002, at UNCTAM-14 in Blacksburg a symposium "Turbulence in Chemical Processing"is in his honor.  In 2002 he was elected a Fellow of The American Academy of Mechanics. Professor Brodkey is still active in research, teaching, and Departmental affairs, even though he has been appointed as an Emeritus Professor.