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Effect of wall contact angle and carrier phase velocity on the flow physics of gas–liquid Taylor flows inside microchannels

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Abstract

This paper investigates numerically the characteristics of gas–liquid sliding Taylor flow in a two-dimensional (2D) T-junction rectangular microchannel having both inlets perpendicular to the horizontal mixing chamber. The governing equations describing the flow are discretized and solved by employing finite volume method based computational tool ANSYS Fluent 15.0. The volume of fluid (VOF) multiphase method is used for capturing the gas–liquid interface. A dynamic mesh, based on the adaption of gradients of volume fraction, is used for grid refinement to tackle sharp gradients during the two-phase flow. A focus is laid on exploring the influence of wall contact angle on the flow physics of sliding Taylor flows inside the microchannel in which the inlet liquid velocity is varied in the range 0.05 < uL < 0.25 m/s) (or inlet Reynolds number, 4.97 < Re < 248.75), and the wall contact angle is varied in the range 0° < Θo < 170°. The effect of contact angle hysteresis on the overall pressure drop, bubble and liquid slug lengths, and the dispersed phase volume fraction is reported. The bubble length and the overall pressure drop obtained from the simulations are compared with the benchmark correlations available in the literature. It is found that the trends of the variation of bubble length with liquid velocity are in reasonable match with the correlations. In addition, the pressure drop and slug length decrease in hydrophilic channels unlike in hydrophobic channels, which signifies the importance of contact angle in two-phase sliding Taylor flows.

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Abbreviations

a :

Constant (−)

b :

Constant (−)

C :

Courant number (−)

Ca:

Capillary number (−)

D :

Hydraulic diameter (m)

f :

Apparent friction factor (−)

h :

Channel width (m)

k :

Interface curvature (m−1)

L :

Length (m)

Nu:

Nusselt number (−)

Pe:

Peclet number (−)

N UC :

No. of unit cells (−)

R :

Microchannel radius (m)

Re :

Reynolds number (−)

S α :

Mass source term (kg/m3 s)

t :

Time (s)

U S :

Slug velocity (m/s)

U b :

Bubble velocity (m/s)

U TP :

Mixture velocity (m/s)

w :

Relative velocity of bubble w.r.t slug (m/s)

u cell :

Unit cell velocity (m/s)

We:

Weber number

ΔP :

Pressure drop (Pa)

α :

Dispersed phase volume fraction

β :

Homogeneous void fraction

δ :

Film thickness (m)

Δx cell :

Unit cell length (m)

λ m :

Roots of second-order Bessel function

ρ :

Density (kg/m3)

µ :

Dynamic viscosity (Pas)

σ :

Surface tension coefficient (N/m)

Θ :

Contact angle (°)

a :

Advancing

b :

Bubble

c :

Continuous/carrier phase

C :

Capillary

CA:

Contact angle effect

d :

Dispersed phase

G :

Gas phase

H :

Horizontal direction

i :

ith phase

L :

Liquid phase

MF:

MOVING film

r :

Receding

SF:

Stagnant film

S :

Liquid slug

TP:

Two-phase

UC:

Unit cell

V :

Vertical direction

w :

Wall

o :

Static

References

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Acknowledgements

The authors are grateful to the Ministry of Human Resource Development (MHRD), India, and National Institute of Technology, Warangal (India) for providing the necessary funds and computational facilities, respectively, to carry out the research work discussed in the present paper.

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Correspondence to V. R. K. Raju.

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On behalf of all authors, the corresponding author states that there is no conflict of interest.

Appendix

Appendix

In the present study, the fluids are assumed to be Newtonian fluids. The governing equations of continuity, momentum, and volume fraction, which were solved by ANSYS Fluent, are given by Eqs. (13), (14). and (15), respectively.

Continuity equation:

$$\frac{\partial \rho }{\partial t} + \nabla \cdot \left( {\rho V} \right) = 0,$$
(13)

where t is the time (s), ρ is the mixture density (kg m−3), and V is the velocity vector (m/s).

$$\rho = \rho_{\text{L}} \alpha_{\text{L}} + \rho_{\text{G}} \alpha_{\text{G}} ,$$

where αL and αG are the volume fractions of the liquid and gas phase, respectively.

Momentum equation:

$$\frac{\partial (\rho V)}{\partial t} + \nabla \cdot \left( {\rho VV} \right) = - \nabla P + \nabla \cdot \left[ {\mu \left( {\nabla V + \nabla V^{'} } \right)} \right] + F,$$
(14)

where µ is the dynamic viscosity of the mixture (Pas).

$$\mu = \mu_{\text{L}} \alpha_{\text{L}} + \mu_{\text{G}} \alpha_{\text{G}} .$$

.

The last term in Eq. (14) gives the body force term which includes surface tension (σ) at the gas–liquid interface, as given in the following equation:

$$F = \sigma k\frac{{\rho \nabla \alpha_{\text{G}} }}{{0.5\left( {\rho_{\text{L}} + \rho_{\text{G}} } \right)}},$$
(15)

where k is the interface curvature (m−1).

ANSYS Fluent is used as the computational package to carry out the present simulations. VOF method is employed to model the two-phase flow (Hirt and Nichols 1981). Continuum surface force (CSF) model is employed to model the surface tension (Brackbill et al. 1992). Surface tension arises from the difference in the molecular attractions between the two contacting phases which impose a pressure jump across the interface when the interface is curved. The volume fraction of phase i in each cell is represented by αi. In a gas–liquid two-phase flow, when a cell is filled with gas, the gas volume fraction, αG is 1 and the corresponding liquid volume fraction, αL is 0. When a cell is filled with liquid then αG is 0 and αL is 1. If the cell is partially filled with liquid and the rest with gas, αL and αG lies between 0 and 1, indicating that the interface passes through the cell. The volume of fluids model which solves an equation for volume fraction, α, is given by:

$$\frac{{\partial (\rho_{i} \alpha_{i} )}}{\partial t} + \nabla \cdot \left( {\rho_{i} \alpha_{i} V_{i} } \right) = S_{{\alpha_{i} }} ,$$
(16)

with the sum of the volume fractions for all phases adding up to 1, as given by Eq. (18):

$$\mathop \sum \limits_{i} \alpha_{i} = 1.$$
(17)

The interface curvature k was obtained using the method of Brackbill et al. (1992).

$$k = \nabla \cdot \tilde{n},$$
(18)

where the vector perpendicular to the interface is given by the following equation:

$$n = \nabla \alpha_{l} ,$$
(19)

and its corresponding unit normal vector is given by the following equation:

$$\tilde{n} = \frac{n}{|n|},$$
(20)

when the wall contact angle (\(\varTheta_{w}\)) is introduced, then the unit normal vector adjacent to the walls becomes

$$\tilde{n} = \tilde{n}_{w} \cos \varTheta_{w} + \hat{t}_{w} \sin \varTheta_{w} ,$$
(21)

where \(\tilde{n}_{w}\), \(\hat{t}_{w}\), and \(\varTheta_{w}\) are the corresponding unit normal vector to the wall, unit tangential vector to the wall, and given wall contact angle, respectively.

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Vivekanand, S.V.B., Raju, V.R.K. Effect of wall contact angle and carrier phase velocity on the flow physics of gas–liquid Taylor flows inside microchannels. Chem. Pap. 73, 1173–1188 (2019). https://doi.org/10.1007/s11696-018-0668-3

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  • DOI: https://doi.org/10.1007/s11696-018-0668-3

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