A Simplified Model for Determining Interfacial Position in Convergent Microchannel Flows

Hitt, Darren L.; Macken, Nelson A.

doi:10.1115/1.1792272

Cited by 10 publications

(24 citation statements)

References 13 publications

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“…3d). The relation between Q* and β observed in the experiments is approximately described by the analytical equation derived by Hitt and Macken 68 for describing the planar surface position formed between converging flows of two substreams of one identical liquid in a Fig. 7 The measured total frictional pressure drop (ΔP tot,exp ) under the three-phase slug flow in the chip versus the model predictions (ΔP tot,model ) given by eqn ( 6) and (7).…”

Section: Interfacial Position and Pressure Drop In A Liquid-liquid Pa...mentioning

confidence: 77%

Gas–liquid–liquid three-phase flow pattern and pressure drop in a microfluidic chip: similarities with gas–liquid/liquid–liquid flows

2014

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We report a three-phase slug flow and a parallel-slug flow as two major flow patterns found under the nitrogen-decane-water flow through a glass microfluidic chip which features a long microchannel with a hydraulic diameter of 98 μm connected to a cross-flow mixer. The three-phase slug flow pattern is characterized by a flow of decane droplets containing single elongated nitrogen bubbles, which are separated by water slugs. This flow pattern was observed at a superficial velocity of decane (in the range of about 0.6 to 10 mm s(-1)) typically lower than that of water for a given superficial gas velocity in the range of 30 to 91 mm s(-1). The parallel-slug flow pattern is characterized by a continuous water flow in one part of the channel cross section and a parallel flow of decane with dispersed nitrogen bubbles in the adjacent part of the channel cross section, which was observed at a superficial velocity of decane (in the range of about 2.5 to 40 mm s(-1)) typically higher than that of water for each given superficial gas velocity. The three-phase slug flow can be seen as a superimposition of both decane-water and nitrogen-decane slug flows observed in the chip when the flow of the third phase (viz. nitrogen or water, respectively) was set at zero. The parallel-slug flow can be seen as a superimposition of the decane-water parallel flow and the nitrogen-decane slug flow observed in the chip under the corresponding two-phase flow conditions. In case of small capillary numbers (Ca ≪ 0.1) and Weber numbers (We ≪ 1), the developed two-phase pressure drop model under a slug flow has been extended to obtain a three-phase slug flow model in which the 'nitrogen-in-decane' droplet is assumed as a pseudo-homogeneous droplet with an effective viscosity. The parallel flow and slug flow pressure drop models have been combined to obtain a parallel-slug flow model. The obtained models describe the experimental pressure drop with standard deviations of 8% and 12% for the three-phase slug flow and parallel-slug flow, respectively. An example is given to illustrate the model uses in designing bifurcated microchannels that split the three-phase slug flow for high-throughput processing.

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Section: Interfacial Position and Pressure Drop In A Liquid-liquid Pa...mentioning

confidence: 77%

Gas–liquid–liquid three-phase flow pattern and pressure drop in a microfluidic chip: similarities with gas–liquid/liquid–liquid flows

2014

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“…For very large values of R 1 and R 2 , where the interfacial surface is almost flat (as is the case with parallel flow), Dp is approximately 0. The assumption of a planar fluid interface formed in steady, converging microchannel flows has already been made by Galambos and Forster (1998) and Hitt and Macken (2004). In this work, the assumption was also made through experimental observation and contact angle measurement.…”

Section: Methods Of Solutionmentioning

confidence: 92%

“…They also numerically calculated the steady-state developed velocity profiles for two-phase parallel flow and Galambos and Forster (1998) used an analytical solution of simplified Navier-Stokes equations to obtain the velocity profile at steady-state and to predict the position of the interface of developed flow. Similarly, Hitt and Macken (2004) predicted the fully developed interfacial location downstream of a convergence of identical microchannels.…”

Section: Introductionmentioning

confidence: 99%

Parallel flow of immiscible liquids in a microreactor: modeling and experimental study

Pohar

Lakner

Plazl

2011

Microfluid Nanofluid

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Two-phase parallel flow can be utilized in microreactor engineering for performing reactions and extractions, and also for achieving efficient phase separation at the exit of the microreactor. Typical laminar flow at the microscale allows two phases to flow in parallel without mixing, allowing highly controlled conditions for a specific chemical process. Since the liquid with the higher viscosity has a tendency to occupy a larger fraction of the microchannel, the position of the interface can be controlled through the adjustment of flow rates. The prediction of the position of the interface is important for microreactor design and operation and requires the solution of the governing equations of fluid mechanics. In this work, the theoretical description for two-phase parallel flow, based on the Navier-Stokes equations in three dimensions was expressed with a mathematical model and validated with experimental observations. The movement of the interface was achieved through the adjustment of fluid properties according to the position of the central streamlines. The predicted position of the interface was in good agreement with experimental data. A correlation for the flow rate ratio required for positioning the interface in the middle of the channel for various viscosity ratios was proposed, as well as a correlation for the prediction of the parallel to slug transition for a water/n-hexane system.

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“…It is known from the microfluidics literature that the spreading of parallel streams is related to the viscosity ratio between the streams. 26,27 In expansion flow, the recirculation length and width are set by the degree of spreading of the concentrated core region downstream of the expansion. The overlap of the three curves in Fig.…”

Section: ͑3͒mentioning

confidence: 99%

Pressure drop enhancement in a concentrated suspension flowing through an abrupt axisymmetric contraction-expansion

Moraczewski

Shapley

2007

Physics of Fluids

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In this work, we investigate the pressure drop of concentrated suspensions flowing through a 4:1:4 axisymmetric contraction-expansion at low Reynolds number. Pressure drop measurements across the narrow tube show an enhanced pressure drop relative to a Newtonian fluid at the same flow rate. A linear increase in pressure drop as a function of flow rate is observed for the suspensions, with a steeper slope at higher particle volume fraction. However, due to shear-induced particle migration, the pressure drop at each concentration is lower than would be expected for a uniform Newtonian fluid of the same viscosity as the bulk suspension viscosity. The Krieger ͓I. M. Krieger, Adv. Colloid Interface Sci. 3, 111 ͑1972͔͒ expression for the relative viscosity provides an accurate estimate of the dependence of the normalized suspension pressure drop on particle volume fraction, although the bulk suspension viscosity follows the more rapidly increasing curve of Zarraga ͓I. E. Zarraga, D. A. Hill, and D. T. Leighton, J. Rheol. 44, 185 ͑2000͔͒. As the particle volume fraction increases, the normalized pressure drop rises in a similar manner to the area of the recirculation regions in the corner of the expansion and also to the ratio of suspension viscosities in the tube center and recirculation regions. The pressure measurements, along with nuclear magnetic resonance imaging results, suggest that the viscosity ratio between the center and recirculation regions of the suspension, recirculation region size, and pressure drop are all related in contraction-expansion flows of suspensions.

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A Simplified Model for Determining Interfacial Position in Convergent Microchannel Flows

Cited by 10 publications

References 13 publications

Gas–liquid–liquid three-phase flow pattern and pressure drop in a microfluidic chip: similarities with gas–liquid/liquid–liquid flows

Gas–liquid–liquid three-phase flow pattern and pressure drop in a microfluidic chip: similarities with gas–liquid/liquid–liquid flows

Parallel flow of immiscible liquids in a microreactor: modeling and experimental study

Pressure drop enhancement in a concentrated suspension flowing through an abrupt axisymmetric contraction-expansion

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