A Laplace pressure gradient between a droplet and a liquid meniscus was utilized to create an on-demand constant flow rate capillary pump. Electrowetting on dielectric was implemented to induce the pressure gradient in the microchannel. For an initial droplet volume of 0.3 μL and a power of 12 nW a constant flow rate of 0.02 μL s(-1) was demonstrated. The effects of the wetting line energy on the static contact angle and the wetting line velocity on the dynamic contact angle in the pump operation were studied. Sample loading on-demand could be achieved by regulating an electric potential.