Abstract
Hydrodynamic lift forces offer a convenient way to manipulate particles in microfluidic applications, but there is little quantitative information on how non-inertial lift mechanisms act and compete with each other in the confined space of microfluidic channels. This paper reports measurements of lift forces on nearly spherical drops and bubbles, with diameters from one quarter to one half of the width of the channel, flowing in microfluidic channels, under flow conditions characterized by particle capillary numbers Ca(P) = 0.0003-0.3 and particle Reynolds numbers Re(P) = 0.0001-0.1. For Ca(P) < 0.01 and Re(P) < 0.01 the measured lift forces were much larger than predictions of deformation-induced and inertial lift forces found in the literature, probably due to physicochemical hydrodynamic effects at the interface of drops and bubbles, such as the presence of surfactants. The measured forces could be fit with good accuracy using an empirical formula given herein. The empirical formula describes the power-law dependence of the lift force on hydrodynamic parameters (velocity and viscosity of the carrier phase; sizes of channel and drop or bubble), and includes a numerical lift coefficient that depends on the fluids used. The empirical formula using an average lift coefficient of ~500 predicted, within one order of magnitude, all lift force measurements in channels with cross-sectional dimensions below 1 mm.
Highlights
Manipulation of solid particles, liquid drops, gas bubbles, and cells is an important subfield of microfluidics.[1,2,3] Immersion in a continuous liquid phase enables the processing, using microfluidic flows, of systems that either cannot flow such as solid particles, or coalesce if brought in contact, such as drops and bubbles
We chose the pairs of dispersed and continuous phase fluids that we investigated according to the following criteria: (i) they were relatively common and commonly used in microfluidic applications, (ii) they were chemically compatible with the materials of the microfluidic channels, e.g. polydimethylsiloxane (PDMS), poly(methyl methacrylate) (PMMA), glass, (iii) they had viscosities larger than ~5 mPa·s, because for the flow conditions we used, bubbles and drops often did not experience a centering lift force in carriers with lower viscosities, and (iv) the difference in densities between the continuous and dispersed phases were on the order of 1 g/cm[3], because the changes in the steadystate position caused by lower density differences were too small to resolve optically
The combination of fluids we chose for this measurement—water as the dispersed phase, and a fluorocarbon liquid (PFPHP) containing water-insoluble surfactant (THPFO) as the continuous phase—is typical for microfluidic applications in which drops are used as chemical microreactors.[7]
Summary
Manipulation of solid particles, liquid drops, gas bubbles, and cells is an important subfield of microfluidics.[1,2,3] Immersion in a continuous liquid phase enables the processing, using microfluidic flows, of systems that either cannot flow such as solid particles, or coalesce if brought in contact, such as drops and bubbles. We are interested in one particular case of lift forces: those that act on nearly spherical bubbles and drops that have dimensions smaller than but comparable to the cross-section of the channel, and are carried by a liquid inside microchannels, i.e., channels with crosssectional dimensions smaller than ~1 mm. Such systems are encountered in applications that screen and sort drops at high throughput,[16] and in applications that require the mechanical isolation of drops from the walls of channels, for example in nucleation studies.[17]. Eqn (5) is accurate as long as the drop or bubble is not too close to the walls, e.g. the separation between the drop and the wall is larger than the diameter of the drop or bubble
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