An integrated multiphase flow sensor for microchannels

The flow regimes of microscale multiphase flows affect the yield and selectivity of microchemical systems, and the heat transfer properties of micro heat exchangers. We describe an integrated optical sensor that uses total internal reflection to detect the structure of multiphase flows in microchannels. The non-intrusive sensor enables detection of individual slugs, bubbles, or drops, and can be used to continuously determine their number and velocity. The sensor performance is modeled using ray-tracing techniques, and tested for several channel geometries. Both gas-liquid and liquid-liquid flows are investigated in microchannels with rectangular and triangular cross-sections. Statistical properties of the flow, derived from the sensor signal, compare favorably to commonly-used dynamic pressure measurements. We demonstrate the integration of the sensor into a planar multichannel microreactor. An existing glass layer used as a waveguide allows us to monitor flows in optically inaccessible channels. This sensor configuration can be integrated into layers of vertically-stacked multichannel microreactors.

List of symbols

Roman symbols a Radius of largest sphere inscribed in channel m] - A_ch Channel cross-sectional area m²] - Ca Capillary number -] - Critical capillary number -] - d_h Hydraulic diameter m] - d_sensor Distance prism surface-sensor origin m] - E₀ Incident light energy J] - E_r Emerging light energy J] - f(t_pass) Probability density function (PDF) of slug dwell times 1/s] - f Focal length m] - f_slug Slug frequency Hz] - F(t_pass) Probability distribution of slug dwell times -] - g(t) Arbitrary function of time -] - h Liquid film thickness m] - j_G Superficial gas velocity m/s] - j_L Superficial liquid velocity m/s] - l Slug length m] - N Number of samples -] - n Refractive index -] - N_c Number of channel corners -] - n_i Refractive index of incident medium -] - n_r Number of reflections -] - n_t Refractive index of transmitting medium -] - n_slug Number of slugs -] - p Gas inlet pressure Pa] - r Reflectance -] - R_XX(x,) Autocorrelation function -] - R_Xp(x,) Cross correlation function -] - r Slug radius at infinite distance from leading slug tip m] - s Standard deviation of measured slug dwell times s] - t Time s] - t Measurement time interval s] - t_pass Slug dwell time s] - U_b Slug (bubble) velocity m/s] - W Bin size of slug dwell time histogram -] - x Streamwise coordinate m] - X(x,t) Phase density function -] - Y Surface tension of the gas-liquid interface N/m] - Volumetric gas flow rate m³/s] - Volumetric liquid flow rate m³/s] - Volumetric oil flow rate m³/s] - Volumetric water flow rate m³/s] - z Normal coordinate m]Greek symbols Void fraction -] - _c Critical angle for total internal reflection ^°] - _i Incident angle ^°] - Laser wavelength m] - µ Liquid viscosity Pa s] - Normalization factor -] - _h Dimensionless liquid film thickness -] - _r Dimensionless radius -] - _x Dimensionless streamwise position -] - _r Dimensionless slug radius at infinite distance from leading slug end -] - Standard deviation of the slug dwell time distribution s] - Time shift s] - Contact angle ^°]