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Abstract:
While shear emulsification is a well understood industrial process, geometrical confinement in microfluidic systems introduces fascinating complexity, so far prohibiting complete understanding of droplet formation. The size of confined droplets is controlled by the ratio between shear and capillary forces when both are of the same order, in a regime known as jetting, while being surprisingly insensitive to this ratio when shear is orders of magnitude smaller than capillary forces, in a regime known as squeezing. Here, we reveal that further reduction of—already negligibly small—shear unexpectedly re-introduces the dependence of droplet size on shear/capillary-force ratio. For the first time we formally account for the flow around forming droplets, to predict and discover experimentally an additional regime—leaking. Our model predicts droplet size and characterizes the transitions from leaking into squeezing and from squeezing into jetting, unifying the description for confined droplet generation, and offering a practical guide for applications.

Abstract:
The adsorption of carboxymethylcellulose polymers on molybdenite was studied using spectroscopic ellipsometry and atomic force microscopy imaging with two polymers of differing degrees of carboxyl group substitution and at three different electrolyte conditions: 1 × 10–2 M KCl, 2.76 × 10–2 M KCl, and simulated flotation process water of multicomponent electrolyte content, with an ionic strength close to 2.76 × 10–2 M. A higher degree of carboxyl substitution in the adsorbing polymer resulted in adsorbed layers that were thinner and with more patchy coverage; increasing the ionic strength of the electrolyte resulted in increased polymer layer thickness and coverage. The use of simulated process water resulted in the largest layer thickness and coverage for both polymers. The effect of the adsorbed polymer layer on bubble–particle attachment was studied with single bubble–surface collision experiments recorded with high-speed video capture and image processing and also with single mineral molybdenite flotation tests. The carboxymethylcellulose polymer with a lower degree of substitution resulted in almost complete prevention of wetting film rupture at the molybdenite surface under all electrolyte conditions. The polymer with a higher degree of substitution prevented rupture only when adsorbed from simulated process water. Molecular kinetic theory was used to quantify the effect of the polymer on the dewetting dynamics for collisions that resulted in wetting film rupture. Flotation experiments confirmed that adsorbed polymer layer properties, through their effect on the dynamics of bubble–particle attachment, are critical to predicting the effectiveness of polymers used to prevent mineral recovery in flotation.

Keywords:
flotation, bubble, adsorption