Electroosmotic flows are studied in wavy channels by expanding the solution into a double series in terms of the dimensionless amplitudes and of the dimensionless zeta potential for a binary dilute electrolyte. The expansion technique by means of formal calculations is described. Some examples are illustrated and discussed for two and three dimensional channels. The importance of the varicose or sinuous character of the channels as well as the role of high frequency roughness are demonstrated. These features may be used for practical purposes in order to amplify or diminish coupling effects in an algebraic way. (C) 2010 Elsevier Inc. All rights reserved.