Droplet-based microfluidics offers a promising tool in engineering and biomedicine such as drug delivery, biochemistry, sample handling in lab-on-a-chip devices, and tissue engineering. These systems provide the droplets manipulation that can be used as reactors without any contamination for medical purposes. Utilizing magnetic force and ferrofluid droplets can help to better control over the droplet formation and manipulation. Considering the importance of this issue and its rich underlying physics, in this dissertation, ferrofluid droplets formation under a time-dependent, non-uniform magnetic field is studied. A Pulse-Width-Modulation signal (PWM) is utilized to apply the time-dependent...