The pressure drop along rectangular microchannels containing bubbles

Abstract

This paper derives the difference in pressure between the beginning and the end of a rectangular microchannel through which a flowing liquid (water, with or without surfactant, and mixtures of water and glycerol) carries bubbles that contact all four walls of the channel. It uses an indirect method to derive the pressure in the channel. The pressure drop depends predominantly on the number of bubbles in the channel at both low and high concentrations of surfactant. At intermediate concentrations of surfactant, if the channel contains bubbles (of the same or different lengths), the total, aggregated length of the bubbles in the channel is the dominant contributor to the pressure drop. The difference between these two cases stems from increased flow of liquid through the ''gutters''-the regions of the system bounded by the curved body of the bubble and the corners of the channel-in the presence of intermediate concentrations of surfactant. This paper presents a systematic and quantitative investigation of the influence of surfactants on the flow of fluids in microchannels containing bubbles. It derives the contributions to the overall pressure drop from three regions of the channel: (i) the slugs of liquid between the bubbles (and separated from the bubbles), in which liquid flows as though no bubbles were present; (ii) the gutters along the corners of the microchannels; and (iii) the curved caps at the ends of the bubble.

Dynamics of microfluidic droplets

“…59 Nevertheless, the velocity difference should remain below 6% for typical capillary numbers 10 À6 < Ca d < 1. 60 Fuerstman et al 61 experimentally measured a difference of this magnitude between the droplet and outer fluid velocities. However, they also pointed out that the presence of surfactant can reduce the droplet velocity by up to 50%.…”

“…This path can be chosen across the droplet body, thus crossing the front and rear interfaces, 51,54 or directly from plug to plug through the gutters. 61 Here we adopt the first approach which will shed light on the effect of variable curvatures but the two formulations lead to the same result. 55 As sketched in Fig.…”

“…61 For this reason, simpler models have been proposed, based on empirical relationships, 63,69 or by considering simplified cases in fixed geometries, such as an inviscid dispersed phase (l ( 1) 60,61 or small droplets. 64 Nonetheless, these nonlinear pressure-flow rate relationships will play a major role in the transport of droplets when the single straight channel is replaced with a network of connected channels.…”

The role of feedback in microfluidic flow-focusing devices

“…These deviations are generally small for the bubble sizes considered in this work. Fuerstman et al (2007) found significant deviations for bubbles much longer than those considered here. (b) Observed bubble volume V b normalized by the channel volume V c plotted against gas pressure P normalized by the channel hydrodynamic pressure drop P c (defined in the text).…”

Optofluidic membrane interferometer: An imaging method for measuring microfluidic pressure and flow rate simultaneously on a chip

“…6 In addition, pressure measurement has been also used for the characterization of the mechanical properties in microfluidic systems, such as liquid viscosity, 7 red blood cell deformability, 8 and hydrodynamic resistance of a single confined moving droplet in microfluidic channels. 9 Most current pressure measurements still rely on external pressure transducers. 10,11 However, due to the pressure dissipation and delay in transmission, it is difficult to accurately measure the local pressure in a microfluidic system using an external pressure sensor.…”