Speed of flow of individual droplets in microfluidic channels as a function of the capillary number, volume of droplets and contrast of viscosities

Abstract

Droplet microfluidic techniques offer an attractive compromise between the throughput (of i.e. reactions per second) and the number of input/output controls needed to control them. Reduction of the number of controls follows from the confinement to essentially one-dimensional flow of slugs in channels which—in turn—relies heavily on the speed of flow of droplets. This speed is a complicated function of numerous parameters, including the volume of droplets (or length L of slugs), their viscosity μ_d, viscosity μ_c and rate of flow of the continuous phase, interfacial tension and geometry of the cross-section of the channel. Systematic screens of the impact of these parameters on the speed of droplets remain an open challenge. Here we detail an automated system that screens the speeds of individual droplets at a rate of up to 2000 experiments per hour, with high precision and without human intervention. The results of measurements in channels of square cross-section (of width w = 360 μm) for four different values of the contrast of viscosities λ = μ_d/μ_c = 0.3, 1, 3, and 33, wide ranges of values of the capillary number Ca ∈ (10⁻⁴, 10⁻¹), and wide ranges of lengths of droplets l = L/w ∈ (0.8, 30) show that the speed of droplets depends significantly both on l and on λ. The dependence on Ca is very strong for λ > 1, while it is less important both for λ ≤ 1 and for λ ≫ 1.