Introduction

Through time people are progressively shifting their life towards industrialization and operating such industries entails a lot of energy. To attain a huge amount of energy the big resource is the combustion of fossil fuel (Mahmoudi Marjanian et al. 2021; Aghel et al. 2018). With instant advantages of these industries like refineries, coal fire-power plants, transportation, etc., are responsible for the present as well as the future condition of the environment (Aghel et al. 2018; Davison 2007; Guo et al. 2020) where acid gases (Kundu and Bandyopadhyay 2006) becoming the major origin of the numerous difficulties around the world. From prior literature data and the factual observations that give information about the recent state of the atmosphere such as a rapid change in climate (Tan et al. 2012; Buckingham et al. 2021), the rise of earth's temperature due to greenhouse gases (Wang et al. 2021), and solution to the control this problem is the major concern of the researchers (Ochedi et al. 2020; Ahmed et al. 2020). The composition of greenhouse gases is Carbon dioxide, Methane, Nitrous oxide (Extavour and Bunje 2016), Water vapor (Modak and Jana 2018), and Fluorinated gases (Yoro and Daramola 2020) which CO2 is highly responsible for the major environmental problem. According to Energy Agency (IEA 2022), the concentration of CO2 emission ranges to the average value of 412.5 ppm in 2020, and the climate service of India (IMD 2022) reported the effect of CO2 emission on the temperature rise and divergence in rainfall is represented in Fig. 1.

Fig. 1
figure 1

Anomaly time series of temperature (°C) and rainfall (%depth) reported by IMD Ministry of Earth Sciences

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Furthermore, researchers have suggested several techniques and methods that are represented in Fig. 2. For separation/capturing of CO2 like absorption (Lee et al. 2013), adsorption (Ahmed et al. 2020; Bhown and Freeman 2011), cryogenic (Göttlicher and Pruschek 1997), and membrane (Leung et al. 2014; Kenarsari et al. 2013), and calcium looping (Criado et al. 2017) use in conventional equipment (Rouzitalab et al. 2020; Zhang et al. 2016) that provide effective results (Mukherjee et al. 2019; Bonaventura et al. 2017).

Fig. 2
figure 2

CO2 separation processes are broadly categorized as adsorption, membrane-separations, cryogenics, calcium looping, and absorption

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For the different ranges of temperatures (Gul 2022), pressures (Khan et al. 2017), and gas absorption is the most utilized and promising method that can be used to capture or separate CO2 (Ye et al. 2013). Removal of CO2 can be enhanced by providing sufficient contact time and interface area by the use of different solvents like Water (Zunlong et al. 2021), NH3 (Liu et al. 2009), H2S (Huang et al. 2017), KOH (Rastegar and Ghaemi 2022), NaOH (Krauβ and Rzehak 2017), Na2CO3 (Rodríguez-Mosqueda et al. 2018) or Na2CO3 integrated with CaCO3 (Barzagli et al. 2017), Alcohols (Gui et al. 2011), Amines (Simons et al. 1975; Adak et al. 2020), Glycols (Hayduk and Malik 1971), Nanofluids (Zhang et al. 2018), Ionic fluids (Ramdin et al. 2012), equipment other than conventional channels e.g., mini/microfluidic-devices (Khatoon et al. 2022; Yao et al. 2014; Kuhn and Jensen 2012) using experimental (Ghadyanlou et al. 2022) and numerical method (Harkou et al. 2021; Li et al. 2022).

Microfluidics is the most advanced term in the field of research and technology. At the beginning of this field, its applications were limited to the heat transfer (Tuckerman and Pease 1981) purpose but in recent times it has had several applications [hydrodynamics (Khan et al. 2018; Chandra et al. 2016), high rate of heat (Chandra et al. 2015), and mass transfer (Pohar and Plazl 2009; Chen et al. 2008; Kenig et al. 2013), good reaction control (Renken and Kiwi-Minsker 2010)] in the different areas like process industries (Pua and Rumbold 2003; Palo et al. 2006), biomedical (King 2006), pharmaceuticals (Huang et al. 2019), emulsification (Ganguli and Pandit 2021), and electronics (Dix and Jokar 2018), etc.

On the other hand, geometrical representation is also an important characteristic that plays a very vital role in the two-phase flow system. A vast study of literature (Ansari et al. 2010; Venkateshwarlu and Bharti 2023; Boruah et al. 2018; Liu et al. 2016) reported that 1–1 cross-T microfluidic junction (less costly and low maintenance required) gives a higher rate of mixing (Santos and Kawaji 2011; Qian and Lawal 2006) for two-phase flow system (Sarkar et al. 2014; Mastiani et al. 2017). Two-phase separation phenomena are affected by the different parameters i.e., diameter of the main arm, diameter ratio (side arm to the main arm), inclination of the main arm, inclination of sidearm, radius of curvature, outlet inclination, flow regime, pressure drops (during phase separation), densities of phases, mass split ratio, gas/liquid superficial velocities, and flow regime in the main pipe (Ejaz et al. 2021).

From the study of several kinds of literature (Ni et al. 2017; Dong and Hibiki 2018; Kreutzer et al. 2005; Lim et al. 2019), it is found that in microchannels different types of flow patterns like annular, bubbly, slug (Chaoqun et al. 2013), churn, wavy, etc. (Triplett et al. 1999; Bordbar et al. 2018), can be obtained with the variation in the fluid velocities. Fluctuations in flow rate create vibrations in the pipes with rising velocities of gas at a constant liquid flow rate flow pattern shifted from plug to slug flow. It was seen that slug flow appeared for a wide range of velocities/flow rates (Yin 2022) with the high-pressure fluctuation in the T-junction. To maintain the constant slug length in the channels it is necessary to choose the accurate inner diameter of the channels and fluid flow rates may also have a small effect on its stability (Kang et al. 2021).

In the present work to capture/separate the CO2, cross-T junction microfluidic equipment, slug flow, with the absorption method was used but the selection of the solvents was the main challenge for this study. The purpose of the recent work is the minimization of the processing cost and use of energy (energy consumed to recover or regenerate the costly solvents) by the utilization of physical solvents i.e., water, glycols, and alcohols. Physical solvents drop the chances of microchannels from getting blocked and their limit can be pulled beyond the limit of chemical solvents.

A numerical gas–liquid-based model was developed for the current work and compared with the experimental observations at two different temperatures in a cross-T-junction microchannel. Obtained results are related to the hydrodynamics and mass transfer study and are associated with the literature data for the conventional channel as well. An attempt is made the development of empirical co-relation for the measurement of bubble length. In conventional, mini, and microchannels it was found that microchannels offer high CO2 capturing rate with the physical absorption method at a particular combination of gas and liquid phase velocities.

Material and methods

Computational approach

In the present study, computational fluid dynamics (CFD) numerical simulation was performed using the finite volume method with the help of the ANSYS 2021 R2 platform. The volume of fluid (VOF) is an Eulerian method that is the most renowned, reliable, and numerically expensive technique to track the interphase for the study of multiphase flow system (Nekouei and Vanapalli 2017; Chiriac et al. 2022). Here, the VOF method was used for the analysis of a two-phase (gas–liquid) flow system, a cross-T-junction in which gas enters through the side arm, liquid enters from the main arm, and Taylor/slug flow is observed in the running arm.

Hydrodynamic model

Two-dimensional (2D) Laminar fluid flow for CO2-different solvents is considered for the present work with the following assumptions:

  1. 1.

    Newtonian and incompressible fluid

  2. 2.

    Gravity effect is not considered (due to the small horizontal channel with a small diameter i.e., mm)

  3. 3.

    Geometry is not responsible for the change in the physical properties of the fluid

  4. 4.

    No slip condition considered at the wall

  5. 5.

    Marangoni effect is neglected so the surface tension remains constant during fluid flow in the microchannel

Detail description of geometry

Here, the 2D cross-T junction geometry selected for the present study has two inlets (at 90°), with 1 mm hydraulic diameter, one outlet with 1 mm hydraulic diameter, length of the main arm, side arm, and running arms are 3 mm, 3 mm, and 47 mm respectively. This geometry (Fig. 3) was created using ANSYS 2021 R2 design modular (DM).

Fig. 3
figure 3

Schematic representation of cross-T junction microchannel

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Volume of fluid (VOF) method

The volume of fluid is a numerical technique that is used in literature for the analysis of the interface between two or more phase flow simply and economically. This method helps to find out the continuity of the surface, the physical properties of the fluid at the chosen surface, and tangential velocities (Hirt and Nichols 1981). Basic equations that were used in this method is written in the form of volume fraction (α) which play an important role in tracking the interface between two/multiphase system.

Governing equations

The following equations are written for each phase of two flow systems according to the present work (Khan et al. 2018):

$$\alpha_L + \alpha_G = 1$$
(1)
$$\rho = \rho_G + (\rho_L - \rho_G )\alpha_L$$
(2)
$$\mu = \mu_G + (\mu_L - \mu_G )\alpha_L$$
(3)

where \(\rho_L\), \(\rho_G\), \(\mu_L\), and \(\mu_L\) are the density and viscosity of gas and liquid phase respectively, while \(\alpha_G\) is the volume fraction of gas. Based the local value of \(\alpha_G\) the appropriate properties and variables will be assigned to each control volume within the domain.

Continuity equation

$$\frac{\partial }{\partial t}\left( {\rho_i \alpha_i } \right) + \nabla \cdot \left( {\rho_i \alpha_i \vec{u}_i } \right) = 0$$
(4)

For incompressible fluid the above equations can be rewritten for a two-phase flow system as follows (Chandra et al. 2016):

$$\frac{\partial }{\partial t}\left( {\alpha_L } \right) + \nabla \cdot \left( {\vec{u}_L {\upalpha }_L } \right) = 0$$
(5)
$$\frac{\partial }{\partial t}\left( {\alpha_G } \right) + \nabla \cdot \left( {\vec{u}_G {\upalpha }_G } \right) = 0$$
(6)

Navier–Stokes equation

Navier Stokes equation was coupled with the continuity equation, VOF method, and with the body force, F is body force that shows the combined effect of surface tension as well as interfacial properties (Liu et al. 2016).

$$\frac{\partial }{\partial t}\left( {\rho \vec{u}} \right) + \nabla \cdot \left( {\rho \vec{u}\vec{u}} \right) = - \nabla P + \left( {\mu (\nabla^2 \vec{u}{ }} \right) + \vec{F}$$
(7)
$$\vec{F} = \frac{2\rho \sigma \kappa \nabla \alpha }{{\rho_L + \rho_G }}$$
(8)

where u is used for the velocity of the fluid, \(\sigma\) is surface tension, \(\kappa\) is surface curvature, and P represents the pressure (Pham et al. 2012).

Mass transfer equation:

In gas–liquid microchannels available interfacial surface area enhances the mass transfer rate several times (Khan et al. 2021) by utilizing the absorption concept in the slug flow pattern. A generalized transport equation used for the mass transfer of gas into liquid is mentioned below (Zunlong et al. 2021; Yao et al. 2014; Yang et al. 2014; Makarem et al. 2021):

$$\rho \frac{\partial C_i }{{\partial t}} + \vec{u} \cdot \nabla C_i = \rho D_i \nabla^2 C_i + R_i$$
(9)

Two film theory mass transfer models were used to track the movement of gas molecules into the liquid through the interface (Baten and Krishna 2004) (Fig. 4).

$$R_i = k_G \left( {P_i^{Bulk} - P_i^{Interface} } \right) = k_L \left( {C_i^{Interface} - C_i^{Bulk} } \right)$$
(10)

where C is concentration, D is diffusion coefficient, R is the rate of gas absorption, and k is the mass transfer coefficient at a given temperature.

Fig. 4
figure 4

Interfacial representation of Taylor bubble and liquid slug using two film theories

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Boundary conditions

All the information that was required for the recent model and the values were considered in ANSYS FLUENT 2021 R2 with the inlet, outlet, and surface boundary conditions listed in Tables 1 and 2 respectively.

Table 1 Model, methods, and initialization conditions for the present work (Fluent Thoery Guide 2013)
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Table 2 Initial boundary condition for each system in the cross-T junction microchannel
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Selection of mesh size and grid independency test

Selection of an exactly suitable grid was quite challenging and it took a lot of time to choose the optimum result for a recent study. It's really necessary to predict the degree of accuracy to justify the consequential decision. After several trials with the size of elements, it was gained around 0.6 million nodes, fluctuation in the pressure and slug length became constant at the precise position of the microchannel, Fig. 5.

Fig. 5
figure 5

Diagram shows the effect of the number of nodes on the slug length and pressure drop (GIT)

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Quadrilateral, uniform, and structured mesh type was used to study hydrodynamics in cross-T junction microchannel, Fig. 6. For the mass transfer observation, unstructured (useful for complex geometry for arbitrary position) and the quadrilateral mesh were employed for the reason of the bubble shape, Fig. 7.

Fig. 6
figure 6

Representation of meshed geometry i.e., cross-T junction

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Fig. 7
figure 7

Representation of unstructured meshed Taylor bubble inside the microchannel (running arm)

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Experimental approach

The gas–liquid operation was executed for the study of hydrodynamics and mass transfer in the laboratory in the cross-T junction (Fig. 8), with the similar geometry that was explained (used for numerical approach) in section of computational approach. To perform the experiments, a microreactor setup was purchased from Amar Equipment Pvt. Ltd. Kurla Mumbai, India. This set up consists two peristaltic pumps, microchannel or microreactor, camera, sensors, MFC’s to control the fluid flow, control panel, beakers, and data acquisition system.

Fig. 8
figure 8

Schematic image of experimental set up and cross-T junction (hydraulic dia = 1 mm) used in the laboratory

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In this experiment, fluid flow data is inserted with the help of computer programme. As per given instructions to the computer, gas introduced in to one inlet and the solvent from the other inlet with the help of peristaltic pump. First step was related to the hydrodynamics of the CO2–water system to check out the range where Taylor/slug flow can be obtained. Once slug flow pattern was attained at a particular combination of velocity for a diffusing system (CO2–water), this velocity data was utilized for the study of hydrodynamics and mass transfer study of the other diffusing system i.e., CO2–ethyl alcohol and CO2-glycols. Mixture of gas–liquid system was collected in a beaker from the outlet of cross T-junction. For the present work, solvents were chosen with physical absorption criteria, no reactions were considered for both (numerical and experimental) approaches.

An online method (Yao et al. 2014) was used to calculate the mass transfer coefficient values from the experimental data for each diffusive system and validated with numerical results. As the CO2 started to absorb in the liquid, the size of the bubble ongoing to shrink. The mass transfer rate from a gaseous phase to the liquid phase for the unit slug length (Fig. 9) can be calculated from the following equation:

$$\frac{dV_G }{{dx}}U_G = - k_L a\left( {C_G - C^0 } \right)\frac{V_L RT}{P}$$
(11)
Fig. 9
figure 9

Schematic representation of unit slug length

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The volumetric mass transfer coefficient (\(k_L a\)) was obtained from the equation that is mentioned below (Yue et al. 2007):

$$k_L a = \frac{u_s }{x}\ln \left( {\frac{{C_{G, 0} - C^0 }}{C_G - C^0 }} \right)$$
(12)

By solving Eqs. 11 and 12, the length of the bubble (gaseous phase) can be expressed in terms of bubble position i.e., x (Eq. 13):

$$L_G = a + b \cdot exp( - c \cdot x)$$
(13)

where expansion of a, b, and c are listed below:

$$a = L_{G0} - \frac{{\left( {C_{G,0} - C^0 } \right)}}{U_G \cdot A_G } \cdot \frac{V_L RTu_s }{P},$$
(14)
$$b = \frac{{\left( {C_{G,0} - C^0 } \right)}}{u_G \cdot A_G } \cdot \frac{V_L RTu_s }{P}$$
(15)
$$c = \frac{k_L a}{{u_s }}$$
(16)

It was considered overall volumetric mass transfer coefficient (\(k_L a\)) is a combination of the film bubble length side (\(k_L a_{FilmBubbleLengthSide}\)) and film bubble cap side volumetric mass transfer coefficient (\(k_L a_{FilmBubbleCapSide}\)), Eqs. 17, and 18 (Zunlong et al. 2021).

$$k_L a = k_L a_{FilmBubbleLengthSide} + k_L a_{FilmBubbleCapSide}$$
(17)
$$k_L a_{Film} = \frac{{D_{GL} }}{\delta }$$
(18)

Study of solvent performance

In the literature, several solvents give good solubility of CO2 without chemical reactions. The selection of solvent in the physical absorption process is an important criterion that highly depends on the functional group (OH, COO, C=O, –O–), temperature, and pressure (Gui et al. 2011; Simons et al. 1975). For the present study water, ethyl alcohol, and ethyl glycol were chosen solvents to capture the CO2 in the cross-T junction microchannel, listed in Table 3. The physical properties of all fluid are in mentioned Tables 4 and 5.

Table 3 A selected gas–liquid system for the recent study
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Table 4 Physical properties of the fluid at different temperature (Gui et al. 2011; Hayduk and Malik 1971; Yao et al. 2014; Snijder et al. 1996)
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Table 5 Physical properties of the fluid at temperature 298.15 K (Zunlong et al. 2021; Gui et al. 2011; Snijder et al. 1996; Souvignet and Olesik 1998)
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Results and discussion

To understand the performance of any equipment and transport phenomena characteristics it is always necessary to went through a detailed study of the hydrodynamics (change in velocities, pressure fluctuation) in that equipment. So, one can enhance the optimization condition of the system. In the present work, a hydrodynamic model was developed for case 1 with the help of continuity and Navier Stokes equation using the VOF method and obtained slug/Taylor flow for a wide range of velocities in the microchannels. After that developed model was used for the numerical simulation of case 1, 2, and case 3, obtained results were compared with experimental data. A mass transfer study is also performed to obtain the volumetric mass transfer coefficient value and also checked the effect of gas velocities, and bubble length on this parameter.

Hydrodynamics study for CO2–water system

Effect of velocity

On the several variations in the velocity range (0.2–0.5) of the two-phase flow system i.e., gas (CO2) and water (H2O), we have obtained a Taylor bubble flow pattern in the microchannel at uG = 0.2 m/s and uL = 0.4 m/s, Fig. 10. It was observed that the length of the bubble and slug have higher dimensions than the diameter of the microchannel and the interfacial area in the slug flow pattern (Fig. 10c) is much higher than the other two fluid flow patterns (Fig. 10a, b).

Fig. 10
figure 10

CO2–water phase contour at different combinations of velocities

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Mixing velocity enhances approx. 6 folds at the cross-T-junction and each slug have high average velocity and circulation rate than the Taylor bubble (Fig. 11).

Fig. 11
figure 11

Velocity fluctuation versus position plot in side T-junction microchannel

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Study of two-phase pressure drop in a microchannel

Because of the complicated behaviour of the two-phase flow system in microchannels, it is quite difficult to observe the pressure fluctuations. ANSYS FLUENT provides the platform for the study of pressure drop fluctuation at each point inside the microchannel. It was observed high-pressure fluctuation at the cross-T junction due to high mixing velocity (Fig. 12). The value of pressure was high inside the bubble than the slug, and bubble cap due to Laplace pressure which is also mentioned by different scholars (Yao et al. 2014; Abadie et al. 2012).

Fig. 12
figure 12

Representation of pressure fluctuation in the direction of flow

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Change in volume fraction in the direction of flow

In the volume of fluid (VOF) method, the volume fraction (\(\alpha\)) term is used to define the fluid phase and interface study. Figure 13 is a volume fraction plot that shows the variation for each phase at an interface in slug fluid flow with a repeated pattern between 0 and 1 values. In the plot, solid line was used for single phases and dotted lines represent interphase between the CO2–water system.

Fig. 13
figure 13

Variation in the volume fraction plot with the position in the direction of flow

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For detailed tracking of volume fraction, x = 19 mm position was selected and endeavored to observe the movement of the bubble through this position with the time that is mentioned in Fig. 14.

Fig. 14
figure 14

Movement of the bubble with time when the bubble passes over x = 19 mm

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In Fig. 14, it can be clearly seen that the vertical dotted line (probe) inside the running arm of microchannel, at time (t) = 0 s the only water was present there and as time passes this liquid was pushed by a bubble in the direction of flow. With the movement of fluid, in the first step water moves along the channel length with a defined position (x = 19 mm), after that interface comes in contact with the probe (dotted line), and then bubble crosses over there.

Figure 15 gives data about the change of the volume fraction in a unit cell and it can be seen the \(\alpha\) value is 1 for water, which started to decrease with time and this value tends to decrease towards 0 that means only bubble is present in time span t = 0.05–0.1 s. After that \(\alpha\) value started to increase reaches to 1 which means again water is present again at that position. Fluctuation (decreasing and increasing data between 0 and 1) in \(\alpha\) value reflects the interface between the CO2–water system.

Fig. 15
figure 15

Change in the value of volume fraction when a bubble passes from x = 19 mm

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Hydrodynamics and mass transfer study of CO2-different solvent system

Study of hydrodynamics for the diffusive system

Three sets of the simulation were performed for the CO2-different solvent with the velocities (uG = 0.2, and uL = 0.4 m/s) that were obtained in Sect. 3.1 with slug flow pattern. To simulate the present problem ANSYS FLUENT 2021 R2 was used with the solvents water, ethyl alcohol, and ethyl glycol and found that inlet velocities i.e., uG = 0.2, and uL = 0.4 m/s are suitable condition to gained the slug flow pattern in each case (Table 6).

Table 6 Flow pattern contour in the physical absorption process
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Extensive experiments were also performed in the laboratory to validate the above results and see the same slug flow pattern in cross-T junction microchannel with almost similar velocities (Table 7). For every case, the formation of each bubble per unit of time is represented in Table 7. In both the approaches (numerical and experimental) one thing is noticeable on the priority that is bubble length decreases.

Table 7 Slug flow pattern obtained for different CO-system experimentally in microreactor
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Calculation of volumetric mass transfer coefficient for the diffusive system

When CO2 started to pass over the solvents in the microchannel with slug flow pattern it was observed three different results for each diffusive system which can be seen in Figs. 16, 17 and Tables 6, 7. As CO2 began to diffuse in to the liquid, length of the bubble is almost the same for water, ethyl glycol, and has little difference with ethyl-alcohol due to different diffusion rate. It happens because of the presence of hydroxy group and hydrogen bond which inhibit the CO2 absorption in the solvents. Ethyl Glycol has two hydroxyl groups, while ethyl alcohol and water has just one. Water also having hydrogen bond which acts as a shield during absorption process. In Figs. 16 and 17, it can be seen clearly that the size of the bubble and the slug reduces with position and in the direction of flow as well and it absorbs in these three solvents in the given order i.e., ethyl alcohol > water > ethyl glycol at temperature (T) = 298.15 K. Basically, solubility of CO2 into liquid directly affects the bubble size. If the bubble size reduction is faster that represents higher value of volumetric mass transfer coefficient of CO2 in the solvent. It was also observed that CO2–Ethyl Alcohol system having more bubble formation than the other two systems (CO2–water and CO2–ethyl glycol) in the same cross T-junction microchannel. Presence of a greater number of bubbles in CO2–Ethyl Alcohol system reduces the size of slug lengths.

Fig. 16
figure 16

Effect of the solvents on the length of the bubble

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Fig. 17
figure 17

Effect of the solvents on the slug length

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With the help of an experimental data (Figs. 16, 17), it was tried to develop a co-relation between bubble length and its position by finding the unknown terms of Eq. 13 i.e., a, b, and c. The graph was plotted between the measured length of a bubble (during the experiment) and its position by performing non-linear analysis regression curve fitting in MATLAB tool and the obtained values of a, b, and c are listed in Table 8.

Table 8 Regression coefficient and developed co-relation of bubble length
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Effect of the velocities

To determine the mass transfer coefficient, Eq. 16 (term ‘c’, including velocity itself) was utilized for each CO2-solvent system, experimentally. CO2 captures in these solvents (water, ethyl alcohol, and ethyl glycol) by physical absorption concept and found that the total volumetric mass transfer coefficient (kLa) value increases with the bubble velocity and it decreases with the rise of temperature for each case 1, 2, and 3 which is the proper justification of Eq. 16 and diffusion coefficient mention in Table 5. Predicted kLa values can be arranged for each solvent in decreasing order e.g., ethyl alcohol > water > ethyl glycol (Figs. 18, 19) which follows a similar pattern that from the numerical method in ANSYS FLUENT platform but these values are quite high and listed in Table 9.

Fig. 18
figure 18

Effect of the velocities on the bubble length at T = 298.15 K

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Fig. 19
figure 19

Effect of the velocities on the bubble length at T = 303.15 K

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Table 9 kLa values data obtained from experiments and simulation at different temperatures and velocities
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Effect of the film thickness

In Eq. 17 it has seen that the volumetric mass transfer coefficient is a combination of film bubble length side and film bubble cap side coefficients. Here it was tried to observe the dominating factor, either the film length side or cap side in the total volumetric mass transfer coefficient. We developed a model for a single bubble using two film theory concepts in ANSYS Workbench and checked the effect of film thickness on the mass transfer coefficient. Figures 20 and 21 show that the length side coefficient has a much higher value than the cap side mass transfer coefficient (almost negligible) because the interfacial area provided by the length side is much higher for case 1, 2, and 3. It was also found, as the film thickness (δ) increases from 0.01 to 0.05 mm the volumetric mass transfer coefficient started to decrease which is the justification of Eq. 18 at T = 298.15 K.

Fig. 20
figure 20

Effect of the film thickness on the length side volumetric mass transfer coefficient

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Fig. 21
figure 21

Effect of the film thickness on the cap side volumetric mass transfer coefficient

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Effect of the solvents

It can be seen form the Figs. 22 and 23 that the volumetric mass transfer coefficient for CO2 capturing was highest for ethyl alcohol and lowest for ethyl glycol. Further at a fixed temperature, the reduction in the size of the bubble (bubble length) is much higher for ethyl alcohol solvent than the other two solvents that happened because of the different solubilities of CO2 in these solvents, as discussed above. The reduction in bubble length indicates that some amount of the gas is transferred to the solvent and the corresponding total volumetric mass transfer coefficient values is comparatively high from those solvents that having relatively large bubble size.

Fig. 22
figure 22

Effect of the bubble length on the cap side volumetric mass transfer coefficient (T = 298.15 K)

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Fig. 23
figure 23

Effect of the bubble length on the cap side volumetric mass transfer coefficient (T = 303.15 K)

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Effect of the temperature

As the temperature increases the solubility of CO2 in the solvent is decreasing that can be seen in Fig. 24. Table 9 gives sufficient information about the values of total volumetric mass transfer coefficient which was obtained numerically as well as experimentally at T = 298.15 K and 303.15 K. Experimental and numerical results were also compared and deviation in the results are represented with the help of Figs. 26 and 27. After successful validation of both the methods it was tried to numerically check the effect of temperature for the large span. From Fig. 25, it can be clearly state that the total gas–liquid volumetric mass transfer coefficient decreases in CO2–ethyl alcohol, CO2–water, and CO2–ethyl glycol systems with the increase in temperature from 298.15 to 318.15 K. It can be explained as the temperature increases kinetic energy rises. The molecular motion of the gas increases as a result of the greater kinetic energy that breaking intermolecular bonds and molecules started to escape from the solvent and volumetric mass transfer coefficient decreases.

Fig. 24
figure 24

Effect of the temperature on the volumetric mass transfer coefficient

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Fig. 25
figure 25

Numerical results to check effect of the temperature on the volumetric mass transfer coefficient for the values 298.15 K, 303.15 K, 308.15 K, 313.15 K and 318.15 K

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Fig. 26
figure 26

Comparison of the total volumetric mass transfer coefficient of the present study by both approaches at temperature (T) = 298.15 K

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Fig. 27
figure 27

Comparison of the total volumetric mass transfer coefficient of the present study by both approaches at temperature (T) = 303.15 K

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Validation of the results

Total volumetric mass transfer coefficient values obtained numerically are validated with the experimental data at temperature T = 298.15 K and 303.15 K and found relative error is approximately 12% and 15% respectively. The data that was obtained from numerical simulation is always higher than the experimental values (Figs. 26, 27). During numerical predictions the value of mass transfer coefficient is always higher than the experimental data as mentioned in Table 9 of the manuscript. The reason behind these predictions is:

  1. 1.

    All the momentum and mass transfer equations were solved at ideal conditions.

  2. 2.

    In real system, ideal assumptions that were considered during simulations are not applicable and real system always deviate with the ideal conditions.

  3. 3.

    During experimental approach some human error (during capturing the bubble image, measuring the length of bubble, fluctuations in the flow rate, and etc.) always be there.

The present work was compared with the literature data for the microchannel as well as the conventional channel. Operating conditions for each system (conventional/microchannels) are listed in Table 10.

Table 10 Experimental conditions used for the conventional and microchannels in present study and literature data
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In this work, it was found that the current study gives better observations by the use of cross T-junction microchannel than the conventional channel (packed tower) and other types of T-junction orientation with the slug flow pattern (Table 11).

Table 11 Comparison of total volumetric mass transfer coefficient (s−1) values with present and literature data
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Conclusion

In this article, gas–liquid hydrodynamics (velocity contour, pressure variation, and change in volume fraction) study was performed for CO2–Water, CO2–ethyl alcohol, and CO2–ethyl glycol and total volumetric mass transfer coefficient calculated for a diffusive system by physical absorption in a microchannel. Initially, the velocity range is decided for slug flow pattern in a microchannel with the help of an CO2–water system using volume of fluid method (VOF) in numerical simulation and this velocity range was imposed on the diffusive system for the calculation of total mass transfer coefficient. Obtained velocities from the simulation fit for experimental with quite low-velocity data that create the approximately 15% error in the coefficient values. Numerically, two film theory was the base to calculate the film bubble length side and cap side of the bubble volumetric mass transfer coefficient and found that kLaFilmBubbleLengthSide value is the major part of the total volumetric mass transfer coefficient. From the experimental data, an empirical co-relation was developed for the calculation of bubble size with its position in microchannel and cases 1, 2, and 3 that also helped to calculate the mass transfer coefficient in slug flow. Numerical and experimental results were compared and found 15% error with uncontrollable human and equipment errors.

It was observed with the increase of bubble velocities total mass transfer coefficient also increases, and with the film thickness it shows the opposite effect due to dominating parameters in the microchannel i.e., surface tension. With an increase in temperature, the diffusion coefficient started to decrease which slowed down the mass transfer rate. Therefore, mass transfer coefficient values decrease with the slug flow pattern in a cross-T-junction microchannel. For the temperature experimentally (298.15 K and 303.15 K) and numerically (298.15 K and 318.15 K) mass transfer coefficient increases in the given order CO2–ethyl Glycol, CO2–water, and CO2–ethyl alcohol system respectively.

It was also noticed that solvent in the physical absorption process is an important criterion that highly depends on the different functional groups (OH, COO, C=O, –O–, hydrogen bond) and for this work, it was estimated that alcohols have a greater ability to absorb the CO2 than the hydroxyl group, glycol group, and hydrogen bond.

In conventional, mini, and microchannel, it is found that cross-T junction microchannel provides the higher value of volumetric mass transfer coefficient in the physical absorption process with the slug flow.