Segmented gas–liquid flow characterization in rectangular microchannels

Abstract

We used optical methods such as Laser Induced Fluorescence (LIF) and confocal Laser Scanning Microscopy (LSM) to characterize gas–liquid phase distribution in rectangular microchannels. Using a 2 m long microchannel with a hydraulic diameter of 200 μm enables the precise measurement of important parameters such as liquid slug length, bubble length, pressure drop and film thickness at the wall as well as in the corner of the microchannel for low Capillary numbers (Ca) ranging from 2 × 10⁻⁴ to 1 × 10⁻². This range of Ca was obtained by using different fluid pairs such as ethanol, water and different concentrated aqueous solutions of glycerol in combination with nitrogen.

The investigated segmented gas–liquid flow (Taylor flow) was very stable, meaning a standard deviation of the measured gas bubble lengths of below 5% and 10% for the liquid slug length, respectively. Using higher viscosities than 10 mPas resulted in an unstable flow – mainly due to the pressure drop. For viscosities in the range of 10 mPas the flow pattern changes: the slug lengths are much longer than the channel diameter.

We demonstrate that the film thickness in the corner slightly decreases with Ca. For low Ca the film thickness at the wall stayed nearly constant. We observe a contribution of the film in the corner to the total film area of about 70%. The obtained gas bubble length depends mainly on the viscosity and on the pressure at the gas inlet. As the measured liquid holdup is in all cases higher than the theoretical holdup defined by the flow rates, the bubbles move faster than the liquid phase. The measured values are compared with literature data.

Introduction

Microreaction technologies are of great interest for industry and research in chemical engineering. The excellent heat and mass transfer properties, continuous operation mode, advanced reaction control and enhanced process safety enable microreactors as an efficient tool for the fine chemical industry and provide new possibilities in the performance of hazardous reactions (Jensen, 2001). Depending on the microfluidic channel geometry and the flow rates, three main flow regimes for gas liquid co-current flow in microchannels can be differentiated: (1) The bubble flow regime, where sphere-like gas bubbles flow within the continuous liquid phase. (2) Taylor flow, which is discussed in this study, is characterized by gas bubbles (gas bubble length l_B < channel diameter d_h) alternating with short (liquid slug length l_S ∼ d_h) liquid slugs. (3) Annular flow is defined as a continuous gas core surrounded by a liquid film at the channel wall. The liquid film in a rectangular microchannel consists of a thin liquid layer at the channel wall and liquid filled channel corners.

Taylor flow in microreactors has attracted great interest for many chemical applications (e.g., Khan et al., 2004). By a recirculating motion in the liquid slugs mass transfer is enhanced between the gaseous and the liquid phase and between the bulk liquid and the liquid film (Waelchli and Rudolf von Rohr, 2006). Compared to single phase flow, Taylor flow reduces axial dispersion (Trachsel et al., 2005). In addition to recirculation, the bubble length, slug length, film thickness and their distributions are other important parameters for an optimized mass transfer. Knowledge about bubble length, slug length and film thickness is crucial for a quantitative analysis of the axial dispersion, gas–liquid mass transfer coefficient and the transport to a catalytic channel wall through the liquid film. Taylor flow in circular and rectangular capillaries was reviewed by Kreutzer et al. (2005a).

The total pressure drop in gas–liquid flow consists of the pressure drop caused by the friction, pressure drop due to acceleration, caused by gravity and by the shape of the bubbles.

$$(\mathrm{\Delta }p{)}_{\text{tot}}=(\mathrm{\Delta }p{)}_{\text{fric}}+(\mathrm{\Delta }p{)}_{\text{acc}}+(\mathrm{\Delta }p{)}_{\text{grav}}+(\mathrm{\Delta }p{)}_{\text{B}}$$

It can be assumed, that the pressure drop due to friction is the dominant part. The pressure drop caused by acceleration can be neglected for small pressure drop values. Friedel (1978) stated, that this is the case for $\frac{\mathrm{\Delta }p}{p}<0.2$. Otherwise the increase in the gas holdup and therefore in the volumetric flow rate due to the pressure drop will lead to an increase in the velocities. In this case the pressure drop due to acceleration has to be calculated by:

$$\mathrm{\Delta }{p}_{\text{acc}}={\dot{m}}^2\left({\left[\frac{{\dot{x}}_G^2}{{\rho }_G{ϵ}_G}+\frac{{\dot{x}}_{\text{L}}^2}{{\rho }_{\text{L}}{ϵ}_{\text{L}}}\right]}_{L=L_{\text{R}}}-{\left[\frac{{\dot{x}}_G^2}{{\rho }_G{ϵ}_G}+\frac{{\dot{x}}_{\text{L}}^2}{{\rho }_{\text{L}}{ϵ}_{\text{L}}}\right]}_{L=0}\right)$$

Δp_acc is the pressure drop due to acceleration, $\dot{m}$ is the mass flux, L_R is the reactor length, ϵ is the holdup, ρ the density and $\dot{x}$ stands for the mass transport fraction. The subscript G characterizes the gas phase, L denotes the liquid phase. The pressure drop due to gravity, $(\frac{\mathrm{\Delta }p}{\mathrm{\Delta }L}{)}_{\text{Grav}}$, defined by

$${\left(\frac{\mathrm{\Delta }p}{\mathrm{\Delta }L}\right)}_{\text{Grav}}=({ϵ}_G{\rho }_G+{ϵ}_{\text{L}}{\rho }_{\text{L}})g\sin \phi$$

can be neglected in horizontal pipes, as the inclination angle φ will be 0.

The pressure drop over a moving bubble due to the different shape of the bubble front and bubble tail, caused by surface tension effects, was found by Bretherton (1961) to be

$$\mathrm{\Delta }{p}_{\text{B}}=3.58\frac{\sigma }{r}\sqrt[3]{9{\mathit{Ca}}^2}$$

r is the bubble radius and Ca is the Capillary number defined as

$$\mathit{Ca}=\frac{\eta u_{\text{B}}}{\sigma }\text{.}$$

η is the fluids dynamic viscosity, u_B the bubble velocity and σ the surface tension. For Ca calculation, the total superficial velocity was used. The model was validated experimentally in a circular glass tube with a length of 1 m and an inner diameter of d_h = 1 mm.

The frictional pressure drop can be calculated by:

$${\left(\frac{\mathrm{\Delta }p}{L_{\text{R}}}\right)}_{\text{fric}}=f{\rho }_{\text{L}}{j}^2\frac{2}{d_{\text{h}}}{ϵ}_{\text{L}}$$

For one-phase flow, the holdup ϵ_L is equal to 1. In case of two-phase flow, the velocity j is the sum of the superficial velocity of both phases. For the friction factor f different correlations for Taylor flow can be found in literature. They are summarized in Table 1. In these correlations, l_S denotes the liquid slug length whereas the Reynolds number Re is defined as Re = ρ_L · (j_L + j_G) · d_h/η_L. Since the liquid phase is the continuous one, the liquid fluid properties as well as the velocity of the slug has to be used.

In all these experiments, the observed bubble velocity was slightly increased compared to the superficial velocity, indicating a liquid film surrounding the gas bubble.

Lockhart and Martinelli (1949) proposed, that the pressure drop of two phase flow will be correlated to the equivalent pressure drop in one phase flow by the two-phase multiplier Ψ²:

$${\left(\frac{\mathrm{\Delta }p}{L}\right)}_{2P\text{,fric}}={\Psi }_{\text{L}}^2{\left(\frac{\mathrm{\Delta }p}{L}\right)}_{\text{L,fric}}={\Psi }_G^2{\left(\frac{\mathrm{\Delta }p}{L}\right)}_{\text{G,fric}}\text{.}$$

Chisholm (1967) stated the dependence of Ψ² from the so called Lockhart–Martinelli parameter X and a factor C:

$$X=\sqrt{\frac{(\mathrm{\Delta }p/L{)}_{\text{L}}}{(\mathrm{\Delta }p/L{)}_G}}$$

$${\Psi }_{\text{L}}^2=1+\frac{C}{X}+\frac{1}{X^2}\text{,}{\Psi }_G^2=1+\mathit{CX}+X^2\text{.}$$

In the past, various correlations for the factor C were proposed. They are summarized in Table 2.

The phase distribution can be quantified in different ways: one is the liquid holdup, defined by

$${ϵ}_{\text{L}}=\frac{V_S}{V_S+V_{\text{B}}}\text{.}$$

V_S and V_B stand for the volume of the slug and the bubble, respectively, in a unit cell. Due to the fact that we analyze the length of the gas bubble and liquid slug in the channel center via LIF, the volume of the gas and the liquid phase has to be estimated by assuming the gas bubble front and tail to be a rotational ellipsoid. In contrast to the liquid holdup (Eq. (16)) a volumetric flow ratio can be defined by:

$${ϵ}_{\text{L}}^{\ast }=\frac{j_{\text{L}}}{j_{\text{L}}+j_{\text{G}}}$$

These values characterize the relative amount of liquid in the channel.

Additional, the ratio and the sum of the gas bubbles and the liquid slugs can be used to characterize the flow.

Knowledge about the liquid film thickness is essential, for axial and radial mass transfer analysis. Quantification of axial mass transfer behavior the liquid films in the corner of a rectangular microchannel is of great importance, since the communication of subsequent liquid slugs mainly occurs through the liquid filled corners. Fairbrother and Stubbs (1935) investigated the thickness of the remaining liquid film when a long gas bubble (l_B > 1.5d_h) passes a capillary. Using a 1 m long circular capillary with an inner diameter of d_h = 2.25 mm, they found out, that the bubble moves faster than the liquid. Both, the velocity of the bubble and the remaining film thickness were found to be dependent on $\sqrt{\mathit{Ca}}$. The film thickness δ was expressed by

$$\delta =\frac{d_{\text{h}}}{4}\sqrt{\mathit{Ca}}\text{.}$$

Marchessault and Mason (1960) corrected this correlation to

$$\delta =0.5d_{\text{h}}\sqrt{\frac{\eta }{\sigma }}(-0.05+0.89\sqrt{u_{\text{B}}})\text{.}$$

Taylor (1961) extended the range of experimental data up to Ca = 2, where a limiting value of 4δ/d_h = 0.56 was suggested. Numerical considerations done by Bretherton (1961), assuming negligible inertia and gravity effects in horizontal capillaries, refined the results done by Fairbrother and Stubbs (1935):

$$\delta =0.66d_{\text{h}}{\mathit{Ca}}^{2/3}\text{.}$$

Irandoust and Andersson (1989) did experimental research on upward and downward Taylor flow in vertical tubes of an inner diameter of d_h = 1–2 mm and a length of L = 0.4 m. They modified the correlation in Eq. (20) to

$$\delta =0.18d_{\text{h}}[1-\exp (-3.1{\mathit{Ca}}^{0.54})]\text{.}$$

Investigations with varying fluids and varying tube radii done by Aussillous and Quere (2000) gave the following inertia-dependent correlation:

$$\delta \sim d_{\text{h}}\frac{{\mathit{Ca}}^{2/3}}{1+{\mathit{Ca}}^{2/3}-\mathit{We}}$$

with We = ρ_Lu²/σ. All correlations presented above for liquid film thickness discuss semi-infinite bubbles in circular capillaries. In rectangular microchannel one observes the forming of two different film regions. Fig. 1(a) shows a schematic phase distribution in Taylor flow in capillaries. In contrast to circular capillaries, where a constant film thickness is created (Fig. 1(b)), square capillaries form a corner film region and a wall film region with dimensions of different magnitude (Fig. 1(c)). The gas bubble is non axisymmetric. For the wall film thickness in square capillaries often correlations for circular capillaries were used. The wall film is present only in the middle of the channel. A transition region between the corner and wall film is observed, where the liquid film reaches a minimum thickness. These contact lines of the gas bubble with the channel wall were also discussed by Wong et al. (1995). For higher Ca numbers an axisymmetric gas bubble is formed as the film increases in thickness (Fig. 1(d)). In our observed Taylor flow regime short gas bubbles in the order of several channel diameter occur. Measurements of the liquid film in square capillaries were conducted by Kolb and Cerro, 1991, Thulasidas et al., 1995. The numerical simulation by Hazel and Heil (2002) for the wall film thickness could not be validated by the results from (Kolb and Cerro, 1991). At the limit Ca → 0, (Wong et al., 1995) found the film in rectangular microchannels to be non uniform in thickness in lateral and axial direction.

In our study we characterize Taylor flow in rectangular microchannels with a hydraulic diameter of (d_h = 200 μm) made of Silicon and glass. Confocal Laser Scanning Microscopy (LSM) and Laser Induced Fluorescence (LIF) are used for the optical investigation of Taylor flow at different liquid and gas flow rates. Bubble and slug lengths as well as their distributions and film thicknesses at the wall and in the corners of the channel were measured. LSM enables a precise spatial measurement of time averaged liquid and gas distribution in a microfluidic channel. Liquid holdup was analyzed by LIF. Measurements were conducted at low Ca in the range of O(10⁻⁴)–O(10⁻²). At these low Ca surface tension dominates and little impurities may cause large deviation in film and bubble geometry in the microchannel due to Maragoni effects. Experimental determination of film thickness is crucial since numerical methods have difficulties to resolve the thin films which rearrange over a long axial length scale (Hazel and Heil, 2002, Taha and Cui, 2006).