Mathematical modeling of drop mixing in a slit-type microchannel

Handique, Kalyan; Burns, Mark A.

doi:10.1088/0960-1317/11/5/316

Cited by 110 publications

(134 citation statements)

References 20 publications

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“…3D. Mixing between the sequentially injected inlet fluids is also facilitated through the interlayering that occurs because of parabolic flow (37). This dynamic flow control process and a more rigorous analysis of mixing using both laminar and mixer algorithms can be seen in Movie 1, which is published as supporting information on the PNAS web site.…”

Section: Resultsmentioning

confidence: 99%

Computerized microfluidic cell culture using elastomeric channels and Braille displays

Zhu

Futai

et al. 2004

Proc. Natl. Acad. Sci. U.S.A.

372

312

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Computer-controlled microfluidics would advance many types of cellular assays and microscale tissue engineering studies wherever spatiotemporal changes in fluidics need to be defined. However, this goal has been elusive because of the limited availability of integrated, programmable pumps and valves. This paper demonstrates how a refreshable Braille display, with its grid of 320 vertically moving pins, can power integrated pumps and valves through localized deformations of channel networks within elastic silicone rubber. The resulting computerized fluidic control is able to switch among: (i) rapid and efficient mixing between streams, (ii) multiple laminar flows with minimal mixing between streams, and (iii) segmented plug-flow of immiscible fluids within the same channel architecture. The same control method is used to precisely seed cells, compartmentalize them into distinct subpopulations through channel reconfiguration, and culture each cell subpopulation for up to 3 weeks under perfusion. These reliable microscale cell cultures showed gradients of cellular behavior from C2C12 myoblasts along channel lengths, as well as differences in cell density of undifferentiated myoblasts and differentiation patterns, both programmable through different flow rates of serumcontaining media. This technology will allow future microscale tissue or cell studies to be more accessible, especially for highthroughput, complex, and long-term experiments. The microfluidic actuation method described is versatile and computer programmable, yet simple, well packaged, and portable enough for personal use.pump ͉ valve ͉ bioreactor ͉ mixer ͉ perfusion A dvanced microfluidic cellular assays (1-6) and microscale tissue engineering studies (7-10) would benefit from robust and convenient methods to computer-control accurate spatiotemporal patterns of microfluidic flows in arrays of fluidic networks. In the past, fluidic control included syringe pumps (11), hydrogel valves (12), gravity-driven pumps (13), evaporation-based pumps (14, 15), acoustic pumps (16), gas-generationbased pumps (17, 18), and centrifugal force in CD chips (19). Electrokinetic flow (20-22), thermopneumatic (23, 24), pneumatic͞hydraulic (25), or mechanical (26, 27) valves and pumps have a high degree of control, but require external connection lines to larger equipment for actuation. A few fully integrated and self-packaged systems (23, 28) have been developed, but lack the reconfigurability inherent with numerous active valves and pumps.Here, we report a method to precisely control fluid flow inside elastomeric capillary networks by using multiple (tens to hundreds) computer-controlled, piezoelectric, movable pins. These pins are positioned as a grid on a refreshable Braille display (e.g., F. H. Papenmeier, Schwerte, Germany), which is a tactile device used by the visually impaired to read computer text. Each pin can act as a valve and be shifted upward to push against channels contained in silicone rubber and completely shut the channel. Three sequential valves of this...

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Section: Resultsmentioning

confidence: 99%

Computerized microfluidic cell culture using elastomeric channels and Braille displays

Zhu

Futai

et al. 2004

Proc. Natl. Acad. Sci. U.S.A.

372

312

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“…There are two vortices of flow in a plug moving through a straight microchannel, one in the upper half of the plug and another in the lower half (as viewed in Fig. 4) [23]. In principle, these vortices can enhance mixing by reducing stl.…”

Section: Mixing In Plugs Of Solutions With Viscosity Higher Than Watermentioning

confidence: 99%

Effects of viscosity on droplet formation and mixing in microfluidic channels

Tice

Lyon

Ismagilov

2004

Analytica Chimica Acta

324

254

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This paper characterizes the conditions required to form nanoliter-sized droplets (plugs) of viscous aqueous reagents in flows of immiscible carrier fluid within microfluidic channels. For both non-viscous (viscosity of 2.0 mPa s) and viscous (viscosity of 18 mPa s) aqueous solutions, plugs formed reliably in a flow of water-immiscible carrier fluid for Capillary number less than 0.01, although plugs were able to form at higher Capillary numbers at lower ratios of the aqueous phase flow rate to the flow rate of the carrier fluid (in all the experiments performed, the Reynolds number was less than 1). The paper also shows that combining viscous and non-viscous reagents can enhance mixing in droplets moving through straight microchannels by providing a nearly ideal initial distribution of reagents within each droplet. The study should facilitate the use of this droplet-based microfluidic platform for investigation of protein crystallization, kinetics, and assays.

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“…Without moving parts in the devices, these methods are usually robust and reliable. Various passive mixing techniques have been reported such as multilamination [14,15], injection [16], hydrodynamic focusing [17], and droplet mixing [18][19][20][21][22]. Droplet mixing utilizes the internal recirculating vortices in moving droplets to promote mixing.…”

Section: Introductionmentioning

confidence: 99%

“…The first model simplifies a parabolic velocity profile in the droplets [19]. Therefore, the model is valid only when the droplet is sufficiently long, because the transverse flow at the front and the rear of the droplet is not considered.…”

Section: Introductionmentioning

confidence: 99%

Analysis of chaotic mixing in plugs moving in meandering microchannels

2011

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Droplets moving in meandering microchannels can serve as a passive and robust strategy to produce chaotic mixing of species in droplet-based microfluidics. In this paper, a simplified theoretical model is proposed for plug-shaped droplets moving in meandering microchannels at Stokes flow. With this model to provide the velocity field, particle tracking, which requires a large computation time, is performed directly and easily without interpolation. With this convenience, a broad survey of the parameter space is carried out to investigate chaotic mixing in plugs, including the channel curvature, the Peclet number, the viscosity ratio, and the plug length. The results show that in order to achieve rapid mixing in plugs in meandering microchannels, a large curvature, a small Peclet number, a moderate viscosity ratio, and a moderate plug length are preferred.

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Mathematical modeling of drop mixing in a slit-type microchannel

Cited by 110 publications

References 20 publications

Computerized microfluidic cell culture using elastomeric channels and Braille displays

Computerized microfluidic cell culture using elastomeric channels and Braille displays

Effects of viscosity on droplet formation and mixing in microfluidic channels

Analysis of chaotic mixing in plugs moving in meandering microchannels

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