Abstract: For low Reynolds number flow in a micro-fluidic device, thecapillary and viscous stresses are more important than the inertialforces, as ischaracteristic of the micro-fluidic devices. Based on the free energyfunction, a phase-field method is applied for thetwo-phase flow in a micro-fluidic device and the interaction of the fluidcomponents with a wall. The transportequations of dimensionless form for the two-phase flow are obtained. Tosolve the transport equationsfor a micro-fluidic square pipe, a numerical method is proposed using thefinite difference method. The numerical simulation of the flow and thedeformation of a droplet in a cubic pipe is carried out, and the effects of thecapillary number and the drop radius on the deformation and the additionalpressure drop ahead of and behind the droplet are studied. Thesimulations show that the additional pressure drop increases with thedroplet size, and decreases with the capillary number.