Dimensionless model for impedimetric sensing of particle laden droplets in digital microfluidic devices

Microfluidic lab-on-a-chip (LOC) devices miniaturize and automate biological protocols while reducing labor and equipment costs. An automated LOC can be used by operators with little training, provided the device incorporates real-time autonomous feedback to the user. Digital microfluidic (DMF) devices are a LOC platform that can create, move, merge, and mix discrete droplets of fluid through the application of asymmetric electric fields. The geometry of DMF devices also allows for integration of real-time impedimetric feedback without integration of additional sensing components. This investigation presents an analytical model for impedimetric sensing of particle laden droplets in DMF devices. The proposed model is based on an equivalent circuit that contains particles of a general size and vertical distribution. Since the proposed model provides an analytical formulation, it can be used to identify dimensionless parameters that govern the impedimetric response of the system. These parameters include: measurement frequency, local area fraction, dimensionless particle size, and the ratios of electrical properties of the particles and the surrounding fluid. The model was used to predict impedimetric response of particle laden droplets in DMF devices. Impedance increased monotonically with volume fraction regardless of particle orientation. This increase was more rapid for horizontally distributed particles than vertically distributed particles. The model also predicts that particle concentration and measurement frequency can be used to independently control sensitivity and saturation of the impedance measurements to changes in electrical properties of the fluid that may occur due to chemical reactions in the droplet.