Modeling of pressure and shear-driven flows in open rectangular microchannels

Tchikanda, Serge W.; Nilson, Robert H.; Griffiths, Stewart K.

doi:10.1016/j.ijheatmasstransfer.2003.03.001

Cited by 27 publications

(30 citation statements)

References 10 publications

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“…Compared to the study by Tchikanda et al (2004), the gutter in this work is more complex due to the following two aspects: (1) the cross section of the gutter in our work is not uniform due to the tip shape of the droplet end, while Tchikanda et al (2004) calculated the pressure drop for a uniform cross section and (2) They used a zero shear boundary condition at the free surface, which is not valid in our study because both the continuous and dispersed phase are viscous liquids. Our model considers these two factors.…”

Section: Determine L * Fillmentioning

confidence: 81%

“…Numerical simulations were performed to analyze the pressure drop through the gutter, which consists of three walls and the fourth being the interface between the dispersed phase and continuous phase. This model is built upon the study presented by Tchikanda et al (2004) for the pressure-driven flow in open rectangular channels, and its further improvement for droplet applications presented by Glawdel et al (2012b).…”

Section: Determine L * Fillmentioning

confidence: 99%

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Model of droplet generation in flow focusing generators operating in the squeezing regime

Chen

Glawdel

Cui

et al. 2014

Microfluid Nanofluid

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considers the influences of channel geometry (height-towidth ratio), viscosity contrast, flow rate ratio and capillary number with a wide variety. This model is validated by comparing predictions from the model with experimental results obtained through high-speed imaging. List of symbolsChannel height L eqv Equivalent droplet length of the uniform cross section L fill Droplet length that penetrates into the main channel at the end of the filling stage L gutter Length of the gutter at the end of the necking stage L pinch Distance between the two points of the V-shape at the end of the necking stage L pinch Variation of the V-shape in the droplet length direction during the necking stage N drop Number of the captured droplets in one video N frame Total number of frames in one video P 1 Pressure of the forming droplet at the end of the filling stage P 2 Pressure of the continuous phase at the cross at the end of the filling stage P 3Pressure of the continuous phase surrounding Abstract Flow focusing generators have been widely used to generate droplets for many applications which call for accurate physical models that describe the droplet formation process in such configurations for design and operation purposes. Most existing models are empirical correlations obtained based on extensive experimental results and thus very sensitive to their own data sets. A comprehensive model that involves less parameter fitting by incorporating more theoretical arguments and thus has an improved applicability is urgently needed to guide the design and operation of flow focusing generators. This work presents a 3D physical model describing the droplet formation process in microfluidic flow focusing generators that operate in the squeezing regime where droplet size is usually larger than the channel width. This model incorporates an accurate geometric description of the 3D droplet shape during the formation process, an estimation of the time period for the formation cycle based on the conservation of mass and a semi-analytical model predicting the pressure drop over the 3D corner gutter between the droplet curvature and channel walls, which allow an accurate determination of the droplet size, spacing and formation frequency. The model the tip of forming droplet at the end of the filling stage P 3D Pressure drop from the 3D numerical simulations P asy Pressure drop from the asymptotic model P neck Pressure of the continuous phase at the cross at the end of necking stage P tip Pressure of the continuous phase surrounding the tip of forming droplet at the end of the necking stage Q Flow ratē Q gutter Average flow rate through the gutter during the necking stage R neck Radius of the V-shape neck at the end of the necking stage s Spacing between two droplets T Droplet generation period t filling Filling period t necking Necking period u Fluid velocitȳ u g Average fluid velocity in the gutter V BF Volume of droplet at the beginning of the filling stage V BN Volume of the continuous phase in the V-shape at the beginning of the necking sta...

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Section: Determine L * Fillmentioning

confidence: 81%

Section: Determine L * Fillmentioning

confidence: 99%

Model of droplet generation in flow focusing generators operating in the squeezing regime

Chen

Glawdel

Cui

et al. 2014

Microfluid Nanofluid

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“…The first is a geometric description of the droplet shape and neck during the formation process in the transition regime. This was followed by an alternative force balance to calculate the initial fill volume that includes hydrodynamic resistance of the gap by incorporating the analytical approximations of Tchikanda et al [14]. Additional modifications to the resistance calculation were developed that account for the 3D shape of the droplet and the effect of the viscosity contrast between the two fluids.…”

Section: Discussionmentioning

confidence: 99%

“…Their intended application was the design of evaporative microfluidic cooling devices with parallel liquid-vapor flows [14]. The authors performed 2D numerical simulations to obtain the flow field for various gap shapes and then developed analytical solutions by blending asymptotic results for limits of channel aspect ratio and interface curvature.…”

Section: Pressure Drop Calculationmentioning

confidence: 99%

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Droplet formation in microfluidic T-junction generators operating in the transitional regime. II. Modeling

2012

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This is the second part of a two-part study on the generation of droplets at a microfluidic T-junction operating in the transition regime. In the preceding paper [Phys. Rev. E 85, 016322 (2012)], we presented our experimental observations of droplet formation and decomposed the process into three sequential stages defined as the lag, filling, and necking stages. Here we develop a model that describes the performance of microfluidic T-junction generators working in the squeezing to transition regimes where confinement of the droplet dominates the formation process. The model incorporates a detailed geometric description of the drop shape during the formation process combined with a force balance and necking criteria to define the droplet size, production rate, and spacing. The model inherently captures the influence of the intersection geometry, including the channel width ratio and height-to-width ratio, capillary number, and flow ratio, on the performance of the generator. The model is validated by comparing it to speed videos of the formation process for several T-junction geometries across a range of capillary numbers and viscosity ratios.

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Review of Nanoscale and Microscale Phenomena in Materials Processing

Iguchi

Ilegbusi

2010

Modeling Multiphase Materials Processes

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Modeling of pressure and shear-driven flows in open rectangular microchannels

Cited by 27 publications

References 10 publications

Model of droplet generation in flow focusing generators operating in the squeezing regime

Model of droplet generation in flow focusing generators operating in the squeezing regime

Droplet formation in microfluidic T-junction generators operating in the transitional regime. II. Modeling

Review of Nanoscale and Microscale Phenomena in Materials Processing

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