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Droplet Formation by Confined Liquid Threads Inside Microchannels Cees J. M. van Rijn, and Willem G.N. van Heugten Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b01668 • Publication Date (Web): 04 Sep 2017 Downloaded from http://pubs.acs.org on September 4, 2017
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Droplet Formation by Confined Liquid Threads Inside Microchannels Cees J.M. van Rijn*, and Willem G.N. van Heugten, Microfluidics and Nanotechnology, Laboratory of Organic Chemistry, Wageningen University, Stippeneng 4, 6708 WE Wageningen, The Netherlands *Corresponding author: Cees J.M. van Rijn, E-mail:
[email protected], Phone: +31 317482370; Fax: +31 848823204 Key words: droplet formation, microchannel ABSTRACT A confined liquid thread can form monodisperse droplets near the exit of a microchannel provided the continuous phase is able to enter the microchannel. A general model that accurately predicts droplet size including breakup position inside the microchannel is presented and is verified with experimental observations; breakup happens as long as the capillary number (Ca) of the liquid thread is below a critical capillary number (Cacr); for cylindrical microchannels it is derived that Cacr=1/16. Below Cacr formed droplets at the exit of the microchannel have a diameter approximately two times the diameter of the liquid thread; around and above Cacr the liquid thread remains stable and formed droplets grow infinitely large. The presented controlled droplet generation method is a useful tool for producing monodisperse emulsions and has great potential for food and pharmaceutical industry.
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INTRODUCTION In recent years, microfluidic devices1-3 are progressively used to transform both free surface and confined liquid threads in more or less monodisperse droplets with techniques based on cross-flow4-7 or co-flowing8-10 fluids such as in flow focusing systems.11-12 In these devices, a liquid thread is actively contacted with a second immiscible fluid near a breakup region where formation of droplets is initiated. The droplet size is directly dependent on the flow rate of the continuous phase that applies shear on the liquid thread or applies drag on the forming droplet.9,10 Methods in microfluidics in which the flow of the continuous phase plays an insignificant role in the breakup process are: terrace-based microchannel emulsification13-18 and long microchannels with a rectangular cross section.19-21 Microchannel emulsification can be scaled up by using membranes22-25 having many thousands of separate parallel microchannels on a square centimeter of membrane area. The instability and ultimate breakup of the confined liquid thread in microchannels is driven by a mismatch between the Laplace pressure of the growing droplet at the exit of the microchannel and of the liquid thread inside the microchannel.13,17,18,21 Sometimes breakup is hampered by external forces, such as buoyancy, leading to non-uniform droplet sizes. An analytical model to describe the physics behind breakup inside a microchannel, in particular the location where the breakup is happening is still lacking.26 By neglecting the pressure gradient within the dispersed phase, a model to predict droplet sizes in a quasi-static regime has been described.20,21 Also it was observed that droplets grow larger at higher flow rates, and eventually grow indefinitely at very high flow rates.20,21 Here, we report a model to describe the instability and breakup of a confined viscous liquid thread inside a microchannel based on a circular cross section, which can be extended to microchannels with other geometries.
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Such a model that provides insight in which parameters determine the breakup of the droplet and predicts the size of the corresponding droplets and the location inside the microchannel where the breakup occurs has not been presented before. This paper describes for the first time the exact relation between droplet size and microchannel diameter (Eq. 7), and describes the transition between making droplets with a finite diameter and making droplets with an infinite diameter (Eq. 9). In addition, the location of breakup inside the microchannel (Eq.14) is predicted by considering in detail the pressure gradient of the dispersed phase inside the microchannel. Moreover, all presented relations are solely determined by the following physical observables: interfacial tension (γ), viscosity of the disperse phase (η), velocity of the dispersed phase (v), droplet radius (Rd), microchannel radius (Rc), and place of breakup inside the microchannel (H). The model is experimentally verified by studying the breakup inside a microchannel in which corrugations are introduced to enable passive inflow of continuous phase to initiate the breakup process (Figure 1). Due to interfacial tension, the liquid thread will have a cylindrical shape with radius Rc comparable with the radius of the microchannel. This corrugated microchannel together with a fully controlled experimental setup allowed us to study in details the growth of the droplets. Our findings provide new insight in the breakup process and will bring understanding of droplet formation to a next level.
Figure 1. (a) Schematic representation of the microfluidic setup. (b) Cross section of a star shaped corrugated round microchannel with nine corrugations.
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MATERIALS AND METHODS Silicone oil DC 200 fluid 350 Cs (Dow Corning) and silicone oil AS100 (Fluka) were used as dispersed phase. Demineralized water containing surfactant Tween–20 (Merck) (1 and 5 w/v %) or sodium dodecyl sulfate (SDS) (Fluka) (1 w/v %) were used as continuous phase. Viscosities were measured using rheometer (Paar Physica MCR 300). Interfacial tensions have been measured using the pendant drop method from droplet profile analysis. Viscosities and interfacial tensions are listed in Table 1.
Table 1. Physical properties of dispersed and continuous phase: interfacial tension γ and viscosity η.
γ (mN/m)
η (mPa s)
Oil type
η (mPa s)
dispersed phase
dispersed phase 1% tween20
5% tween20
continuous phase
Silicone oil 100
110
4.0
3.5
0.9
Silicone oil 350
370
5.0
4.5
0.9
The velocity of the continuous phase outside the microchannel was set lower than 1 mm/s to prevent premature breakup of the liquid thread by viscous drag of the continuous phase exerted on the forming droplet. After breakup of the liquid thread, formed droplets at the exit of the microchannel were carried away to clear the view on the droplet formation process. A microfluidic setup (Figure 1a) was placed under an optical microscope (Olympus BH2) connected to a Motic MC 2000 camera (about 15 frames per second (fps)). Data analysis was performed with computer software ImageJ (NIH) and Matlab (MathWorks). The dispersed phase was pressed through the microchannel using a pressurized nitrogen controlled Wallace & Tierman device. The dispersed phase flowrate was generated by a constant pressure without any pulsations to prevent premature breakup. Typical Reynolds numbers for a laminar flow
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