Short- and long-term dynamic modelling of pressure-driven flow for droplet microfluidic applications

Microfluidic devices are commonly driven by syringe or pressure pumps. Syringe pumps cause persistent flow oscillations and have slow response times. Comparatively, pressure pumps typically offer stable output and a fast response time. However, the compressed air provided by the pressure pump must be interfaced with the liquid samples at the so-called reservoir holder. The multi-phase system introduces short- and long-term dynamics. Long-term dynamics are of interest for passive microfluidic systems while active microfluidic systems benefit from modelling short-term dynamics for consideration in the controller design. The lack of quantified analysis limits the performance of these systems. The model herein proposed starts from the fundamental principles (conservation of mass, conservation of energy). Key assumptions enable the formulation of a system of differential equations describing the short- and long-term dynamics. Both a passive and an active system are considered as case studies with varying parameters such as reservoir volume and shape, and microfluidic chip resistance. The analysis allows better-informed decisions when designing a microfluidic system as well as uncertainty estimation for experimental data collection.