This has been a very discussed topic in recent years. Many articles have appeared over the past 15 years or so but there were some way back in the early 60's.
Here is a bibliography of some of those papers:
W.G.V. Rosser. “What makes an electric current flow“, Am. J. Phys. 31 , 884-885 (1963)
Ian Michael Sefton, “Understanding Electricity and Circuits What the Texts Books Don’t Tell You”, Science Teachers Workshop, 2002, Sydney, Australia
J. D. Kraus, Electromagnetics, 2nd ed. (McGraw-Hill, 1973) p 416-418
J. D. Kraus, Electromagnetics, 4th ed. (McGraw-Hill, 1992) p 577-580
W. Beaty, “In a simple circuit, where does the energy flow?”, Science Hobbyist,
http://amasci.com/elect/poynt/poynt.html (12, 2000)
R. W. Chabay and B. A. Sherwood, Matter & Interactions, 4th ed. (Wiley,
New York, 2015).
R. W. Chabay and B. A. Sherwood, “A unified treatment of eletrostatics
and circuits” (2006).
3J. D. Jackson, “Surface charges on circuit wires and resistors play three
roles,” Am. J. Phys. 64, 855–870 (1996).
M. A. Heald, “Electric fields and charges in elementary circuits,” Am. J.
Phys. 52, 522–526 (1984).
N. W. Preyer, “Surface charges and fields of simple circuits,” Am. J. Phys.
68, 1002–1006 (2000).
I. Galili and E. Goihbarg, “Energy transfer in electrical circuits: A qualitative
account,” Am. J. Phys. 73, 141–144 (2005).
M. K. Harbola, “Energy flow from a battery to other circuit elements: Role
of surface charges,” Am. J. Phys. 78, 1203–1206 (2010).
A.K.T. Assis and J.A. Hernandes, The Electric Force of a Current, (C. Roy Keys, Inc. Montreal, Quebec) 2007 (ISBN: 978-0-9732911-5-5)
Rainer Muller, “A semiquantitative treatment of surface charges in DC circuits” Am. J. Phys. 80,
(9), Sept. 2012.