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This paper reports on analytical and experimental studies of transient effects in electroosmotic (EO) micropumps, focusing on an EO micropump operational paradigm of practical importance: the use of variable-duty-cycle square wave driving voltages. Models of transient effects in EO micropumps are evaluated and developed, and load inertia as well as thermal and diffusion effects are considered. Detailed models, based on solutions for electroosmotic flow between infinite parallel plates, are presented for slit capillary array EO micropumps with slit half-width on the order of one micron. Driving typical microfluidic system loads, analysis by analogy to Stokes' second problem predicts pseudosteady electroosmotic flow in these micropumps for input frequencies up to 100 Hz, with attenuation of high-frequency components of square-wave inputs due to load inertial effects. In experiments with slit capillary array electroosmotic micropumps driven by 10 Hz square waves, micropump output is observed to be generally nonlinear with duty cycle, with significant flow rate enhancement relative to constant-voltage operation at duty cycles above 40%. Lateral diffusion during temporary zero-field conditions may lead to a slight increase in time-averaged zeta potential for square-wave-driven EO micropumps.