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

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Abstract

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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Abbreviations

Bo :

Bond number (–)

Ca :

Capillary number (–)

D h :

Hydraulic diameter (m)

g :

Standard gravity (m/s2)

H :

Microchannel height (m)

Kn :

Knudsen number (–)

L :

Microchannel length (m)

p :

Pressure (Pa)

R 1 :

Radius of curvature (m)

R 2 :

Radius of curvature (m)

Re :

Reynolds number (–)

Re c :

Critical Reynolds number (–)

t :

Time (s)

u :

Velocity in the x direction (m/s)

uvw :

Overall flow field (m/s)

v :

Velocity in the y direction (m/s)

w :

Velocity in the z direction (m/s)

\( \bar{w}_{\text{h}} \) :

Average velocity of n-hexane at the inlet to the central channel (m/s)

\( \bar{w}_{\text{w}} \) :

Average velocity of water at the inlet to the central channel (m/s)

W :

Microchannel width (m)

We :

Weber number (–)

γ:

Interfacial tension (N/m)

μ :

Viscosity (Pa s)

ρ :

Density (kg/m3)

τ :

Artificial compressibility (s m/kg)

Φ 1 :

Flow rate of one phase (m3/s)

Φ 2 :

Flow rate of the other phase (m3/s)

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Authors and Affiliations

  1. Faculty of Chemistry and Chemical Technology, University of Ljubljana, Aškerčeva 5, 1000, Ljubljana, Slovenia

    Andrej Pohar & Igor Plazl

  2. Civil and Geodetic Faculty, University of Ljubljana, Jamova 2, 1000, Ljubljana, Slovenia

    Mitja Lakner

Authors
  1. Andrej Pohar
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  2. Mitja Lakner
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  3. Igor Plazl
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Correspondence to Igor Plazl.

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Pohar, A., Lakner, M. & Plazl, I. Parallel flow of immiscible liquids in a microreactor: modeling and experimental study. Microfluid Nanofluid 12, 307–316 (2012). https://doi.org/10.1007/s10404-011-0873-7

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  • DOI: https://doi.org/10.1007/s10404-011-0873-7

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