**1.1 Background**

The rise velocity of Taylor bubbles is otherwise known as structure velocity. It can also be defined as the velocity of periodic structures in the slug [7, 8]. Some researchers have carried out studies on the rise velocity of Taylor bubbles through stagnant liquid. Mao and Dukler [9] from their experimental results explained that for a wide range of viscosity and surface tension, the rise velocity can be expressed in terms of a constant Froude number.

$$Fr = \frac{U\_N}{\sqrt{\mathbf{gD}}} = constant \tag{1}$$

Hence, the rise velocity of Taylor bubble is given as:

$$U\_N = \mathcal{F}r\sqrt{\mathbf{g}\mathbf{D}} \tag{2}$$

where *g* is the acceleration due to gravity and *D* is the diameter of the tube.

The rise velocity of Taylor bubbles in stagnant liquids was first studied by Dumitrescu [10] and Davies and Taylor [11] in which observed bubbles were of characteristics shape referred to as Dumitrescu or Taylor bubbles. Griffith and Wallis [12] eventually proposed the name as Taylor bubbles. Dumitrescu [10] carried out a study on the rise velocity of bubbles using water in a vertical tube and it was established both theoretically and experimentally that the bubble velocity was:

$$U\_N = \mathbf{0.35} \sqrt{\mathbf{gD}} \tag{3}$$

This is synonymous to the proposition of Mao and Dukler [9], where Froude's number is given as 0.35.

Dumitrescu [10] assumed that the bubble would have a spherical nose, solving simultaneously the flow around the bubble and the asymptotic film which eventually led to the bubble velocity [13] given as Eq. (3).

*The Effect of Liquid Viscosity on the Rise Velocity of Taylor Bubbles in Small Diameter Bubble… DOI: http://dx.doi.org/10.5772/intechopen.92754*

Davies and Taylor [11] gave the bubble velocity as:

$$U\_N = \mathbf{0.328} \sqrt{\mathbf{gD}} \tag{4}$$

after solving the problem using different assumptions.

Nicklin et al. [7] later postulated that the Davies and Taylor [11] solution was not unique but should tend to the limiting value given as:

$$U\_N = \mathbf{0.346} \sqrt{\mathbf{gD}} \tag{5}$$

Eqs. (3) and (4) proposed by Dumitrescu [10] and Davies and Taylor [11], respectively, assume that the Taylor bubble was obtained from a gas of zero density [13]. Neal [14] proposed that if the bubble density is significant, the bubble velocity is given as:

$$\mathbf{U}\_{N} = \mathbf{c}\sqrt{\mathbf{g}\mathbf{D}\left(\frac{\Delta\rho}{\rho\_{L}}\right)}\tag{6}$$

where *c* is approximately 0.35, *Δρ* ¼ *ρ<sup>L</sup>* � *ρG*, *ρ<sup>L</sup>* and *ρ<sup>G</sup>* are the liquid and gas densities respectively.

Brown [15] from his experimental studies found that the solutions of Dumitrescu [10] and Davies and Taylor [11] were not suitable for high viscosity liquids, that they only describe the behaviour of gas bubbles in low viscosity liquids [13]. So, Brown [15] gave the bubble velocity as:

$$\mathbf{U}\_N = \mathbf{0}.35\sqrt{\mathbf{g}(\mathbf{D} - \mathbf{2}\delta\_\bullet)}\tag{7}$$

$$\text{where } \delta\_{\bullet} = \frac{\mathbf{D}\sqrt{\mathbf{1} + \mathbf{N}\_{LB}} - \mathbf{D}}{\mathbf{N}\_{LB}} \tag{8}$$

and

parameters include density of liquid, surface tension of liquid, liquid viscosity, acceleration due to gravity, diameter of bubbles etc. [5]. Mao and Dukler [6] explained that in a situation whereby the liquid is flowing, the rise velocity of a Taylor bubble must depend on the velocity of the liquid flowing upstream as well as the rise due to buoyancy. A typical example of bubble rising through a stagnant liquid as taken from a high-speed video camera (from the current study) is shown

*A single Taylor bubble rising through a stagnant silicone oil liquid (viscosity, 1000 mPa s).*

The rise velocity of Taylor bubbles is otherwise known as structure velocity. It can also be defined as the velocity of periodic structures in the slug [7, 8]. Some researchers have carried out studies on the rise velocity of Taylor bubbles through stagnant liquid. Mao and Dukler [9] from their experimental results explained that for a wide range of viscosity and surface tension, the rise velocity can be expressed

*Fr* <sup>¼</sup> *UN*

Hence, the rise velocity of Taylor bubble is given as:

ally led to the bubble velocity [13] given as Eq. (3).

ffiffiffiffiffiffi

*UN* <sup>¼</sup> *Fr* ffiffiffiffiffiffi

where *g* is the acceleration due to gravity and *D* is the diameter of the tube. The rise velocity of Taylor bubbles in stagnant liquids was first studied by Dumitrescu [10] and Davies and Taylor [11] in which observed bubbles were of characteristics shape referred to as Dumitrescu or Taylor bubbles. Griffith and Wallis [12] eventually proposed the name as Taylor bubbles. Dumitrescu [10] carried out a study on the rise velocity of bubbles using water in a vertical tube and it was established both theoretically and experimentally that the bubble

*UN* <sup>¼</sup> **<sup>0</sup>***:***<sup>35</sup>** ffiffiffiffiffiffi

This is synonymous to the proposition of Mao and Dukler [9], where Froude's

Dumitrescu [10] assumed that the bubble would have a spherical nose, solving simultaneously the flow around the bubble and the asymptotic film which eventu-

*gD* <sup>p</sup> <sup>¼</sup> *constant* (1)

*gD* p (2)

*gD* p (3)

in **Figure 1**.

**Figure 1.**

**1.1 Background**

velocity was:

**200**

number is given as 0.35.

in terms of a constant Froude number.

*Vortex Dynamics Theories and Applications*

$$N\_{LB} = \left(\frac{14.5\rho\_L^2 D^3 \mathbf{g}}{\mu\_L^2}\right) \tag{9}$$

where *NLB* is the liquid viscosity number and *μ<sup>L</sup>* is the liquid viscosity.

Zukoski [1] proposed an expression for velocity of large bubbles in a closed horizontal pipe with large diameter (neglecting surface tension effects) given as:

$$U\_N = \mathbf{0.54} \sqrt{\mathbf{gD}} \tag{10}$$

where the Froude number is 0.54.

A correlation for the bubble rise velocity was proposed by Griffith and Wallis [12] based on the studies on vertical slug flow given as:

$$\mathbf{U}\_{N} = (\mathbf{U}\_{\mathbf{S}\mathbf{G}} + \mathbf{U}\_{\mathbf{S}\mathbf{L}}) + \mathbf{K}\_{\mathbf{1}} \mathbf{K}\_{\mathbf{2}} \sqrt{\mathbf{g}\mathbf{D}} \tag{11}$$

where *USG* and *USL* are the superficial gas and liquid velocities respectively, and *K***<sup>1</sup>** = 0.35.

They investigated the effect of different velocity profiles in the liquid slug by varying *K***<sup>2</sup>** [16].

Nicklin et al. [7] from their vertical slug experiments proposed the rise velocity of a Taylor bubble in the liquid in a vertical tube as:

$$\mathbf{U}\_N = \mathbf{C}\_\bullet (\mathbf{U}\_{SG} + \mathbf{U}\_{SL}) + \mathbf{U}\_\bullet \tag{12}$$

where *Uo* is the translational velocity in a stagnant liquid or velocity of bubble propagating into stagnant liquid, given as:

$$U\_{\mathfrak{o}} = \mathbf{0}.35\sqrt{\mathbf{g}\mathbf{D}}\tag{13}$$

number, inverse dimensionless viscosity and Froude number were used to analyse the experimental results to clearly explain the effect of liquid viscosity on structure

*Rising Taylor bubble from (a) high speed camera and (b) ECT instrument for 1000 mPa.s silicone oil at*

*The Effect of Liquid Viscosity on the Rise Velocity of Taylor Bubbles in Small Diameter Bubble…*

The Reynolds number gives a measure of the ratio of inertia forces to viscous forces. Hence, it can be used to depict the competitive interplay between the effect

*Reynolds number*, *Re* <sup>¼</sup> *Inertia forces*

Reynolds number can also be used to characterize flow regimes into laminar or turbulent flow. The occurrence of laminar flow is at low Reynolds number in which viscous forces dominate. This is characterized by smooth, constant fluid motion. Turbulent flow on the other hand is at high Reynolds numbers which is associated

The slug Reynolds number which is the Reynolds number of the rising slug in

*Re* <sup>¼</sup> *<sup>ρ</sup>UMD μ*

where *μ* = dynamic viscosity of the fluid, *ρ* = density of the fluid, *D* = diameter of

with chaotic eddies, vortices and other flow instabilities [25].

the gas–liquid mixture [26–28] is expressed as:

column and *UM* is the mixture velocity [26, 29].

*Viscous forces* (15)

(16)

velocity.

**203**

**Figure 2.**

*1.2.1 Reynolds number, Re*

*0.361 m/s gas superficial velocity.*

of inertia forces and viscous forces [24].

*DOI: http://dx.doi.org/10.5772/intechopen.92754*

where *Co* is the distribution coefficient which is close to 1.2 for fully developed turbulent flow (low viscous liquid e.g. water) and close to 2 for laminar flow (high viscous liquid e.g. 1000 mPa s silicone oil) [7, 17–19].

From the experimental work reported by Sylvester [20], the rise velocity of Taylor bubble was presented as:

$$\mathbf{U}\_{N} = \mathbf{C}\_{\sigma} (\mathbf{U}\_{\rm SG} + \mathbf{U}\_{\rm SL}) + \mathbf{C}\_{\mathbf{1}} \left[ \frac{\mathbf{g} \mathbf{D} (\rho\_L - \rho\_G)}{\rho\_L} \right]^{1/2} \tag{14}$$

where *D* is the pipe diameter. They proposed *Co* and *C***<sup>1</sup>** to be 1.2 and 0.35, respectively.

From the experiment carried out by Bendiksen [21] in a vertical tube with flowing liquid, the distribution coefficient, *Co* was obtained to be 1.2 for Reynold's number in the range 5000–110,000, i.e. low viscous liquid.

Nicklin et al. [7] interpreted their equation as:

Rise velocity of Taylor bubble (structure velocity) is equal to the velocity of the liquid at the tip of the bubble nose plus the rise velocity of bubble in a stagnant liquid (translational velocity).

Mao and Dukler [6] called this effective upstream velocity (rise velocity of Taylor bubble), the centreline velocity of the liquid.

White and Beadmore [22] carried out an experimental investigation on the rise velocity of Taylor bubbles through liquids in a vertical tube using three dimensionless parameters: Froude number, *Fr*, Eotvos number, *Eo* and Morton number, *Mo*. A recent review on vertical gas–liquid slug flow which highlights previous works on the rise velocity of Taylor bubbles is provided by Morgado et al. [23]. They discussed experimental, theoretical and numerical methods of investigating the rise velocity of Taylor bubbles, where the so-called numerical methods involve the use of empirical correlations. The limitations of these studies that have been addressed in the current study include (1) low range of liquid viscosities and more emphasis on low viscosities rather than high viscosities, (2) consideration of column or pipe diameter greater than 50 mm, (3) limited exploration of the effect of forces such as surface tension, inertia, gravitational and viscous forces acting on Taylor bubble, (4) limited exploration of the relationship between fluid dimensionless parameters and the Taylor bubble rise velocity, and (5) detailed comparison between different methods for obtaining the Taylor bubble rise velocity.

The rising Taylor bubble in a stagnant liquid as observed from the high-speed camera and ECT instrument 3D image (from current study) can be seen in **Figure 2**.

#### **1.2 Fluid flow studies using dimensionless numbers**

A significant number of dimensionless parameters have been identified to be of relevance in fluid flow studies. Examples of such include bond number, capillary number, drag coefficient, Froude number, inverse dimensionless viscosity, Reynolds number and Weber number to mention a few. In this study, the Reynolds

*The Effect of Liquid Viscosity on the Rise Velocity of Taylor Bubbles in Small Diameter Bubble… DOI: http://dx.doi.org/10.5772/intechopen.92754*

**Figure 2.**

*UN* ¼ *Co*ð Þþ *USG* þ *USL Uo* (12)

*gD*ð Þ *ρ<sup>L</sup>* � *ρ<sup>G</sup> ρL* � �**<sup>1</sup>***=***<sup>2</sup>**

*gD* p (13)

(14)

where *Uo* is the translational velocity in a stagnant liquid or velocity of bubble

*Uo* <sup>¼</sup> **<sup>0</sup>***:***<sup>35</sup>** ffiffiffiffiffiffi

From the experimental work reported by Sylvester [20], the rise velocity of

where *D* is the pipe diameter. They proposed *Co* and *C***<sup>1</sup>** to be 1.2 and 0.35,

From the experiment carried out by Bendiksen [21] in a vertical tube with flowing liquid, the distribution coefficient, *Co* was obtained to be 1.2 for Reynold's

Rise velocity of Taylor bubble (structure velocity) is equal to the velocity of the liquid at the tip of the bubble nose plus the rise velocity of bubble in a stagnant

White and Beadmore [22] carried out an experimental investigation on the rise velocity of Taylor bubbles through liquids in a vertical tube using three dimensionless parameters: Froude number, *Fr*, Eotvos number, *Eo* and Morton number, *Mo*. A recent review on vertical gas–liquid slug flow which highlights previous works on the rise velocity of Taylor bubbles is provided by Morgado et al. [23]. They

discussed experimental, theoretical and numerical methods of investigating the rise velocity of Taylor bubbles, where the so-called numerical methods involve the use of empirical correlations. The limitations of these studies that have been addressed in the current study include (1) low range of liquid viscosities and more emphasis on low viscosities rather than high viscosities, (2) consideration of column or pipe diameter greater than 50 mm, (3) limited exploration of the effect of forces such as surface tension, inertia, gravitational and viscous forces acting on Taylor bubble, (4) limited exploration of the relationship between fluid dimensionless parameters and the Taylor bubble rise velocity, and (5) detailed comparison between different

The rising Taylor bubble in a stagnant liquid as observed from the high-speed camera and ECT instrument 3D image (from current study) can be seen in **Figure 2**.

A significant number of dimensionless parameters have been identified to be of relevance in fluid flow studies. Examples of such include bond number, capillary number, drag coefficient, Froude number, inverse dimensionless viscosity, Reynolds number and Weber number to mention a few. In this study, the Reynolds

Mao and Dukler [6] called this effective upstream velocity (rise velocity of

where *Co* is the distribution coefficient which is close to 1.2 for fully developed turbulent flow (low viscous liquid e.g. water) and close to 2 for laminar flow (high

propagating into stagnant liquid, given as:

*Vortex Dynamics Theories and Applications*

Taylor bubble was presented as:

liquid (translational velocity).

respectively.

**202**

viscous liquid e.g. 1000 mPa s silicone oil) [7, 17–19].

*UN* ¼ *Co*ð Þþ *USG* þ *USL C***<sup>1</sup>**

number in the range 5000–110,000, i.e. low viscous liquid. Nicklin et al. [7] interpreted their equation as:

Taylor bubble), the centreline velocity of the liquid.

methods for obtaining the Taylor bubble rise velocity.

**1.2 Fluid flow studies using dimensionless numbers**

*Rising Taylor bubble from (a) high speed camera and (b) ECT instrument for 1000 mPa.s silicone oil at 0.361 m/s gas superficial velocity.*

number, inverse dimensionless viscosity and Froude number were used to analyse the experimental results to clearly explain the effect of liquid viscosity on structure velocity.

#### *1.2.1 Reynolds number, Re*

The Reynolds number gives a measure of the ratio of inertia forces to viscous forces. Hence, it can be used to depict the competitive interplay between the effect of inertia forces and viscous forces [24].

$$\text{Reynolds number, } \text{Re} = \frac{\text{Inertia forces}}{\text{Viscous forces}} \tag{15}$$

Reynolds number can also be used to characterize flow regimes into laminar or turbulent flow. The occurrence of laminar flow is at low Reynolds number in which viscous forces dominate. This is characterized by smooth, constant fluid motion. Turbulent flow on the other hand is at high Reynolds numbers which is associated with chaotic eddies, vortices and other flow instabilities [25].

The slug Reynolds number which is the Reynolds number of the rising slug in the gas–liquid mixture [26–28] is expressed as:

$$\text{Re} = \frac{\rho \mathbf{U}\_M \mathbf{D}}{\mu} \tag{16}$$

where *μ* = dynamic viscosity of the fluid, *ρ* = density of the fluid, *D* = diameter of column and *UM* is the mixture velocity [26, 29].

## *1.2.2 Inverse dimensionless viscosity, N <sup>f</sup>*

According to Lu and Prosperetti [30], the inverse dimensionless viscosity is directly proportional to the fourth root of the Eotvos number raised to a power of three and inversely proportional to the fourth root of the Morton number. Morton number, *Mo* is used alongside with Eotvos number, *Eo* to characterize the shape of bubbles or drops moving in a surrounding fluid or continuous phase.

The inverse dimensionless viscosity is given as:

$$\mathbf{N}\_f = \left(\frac{E\_o^3}{\mathbf{M}\_o}\right)^{1/4} \tag{17}$$

where Morton number is given as:

$$M\_{\mathfrak{o}} = \frac{\mathbf{g}\mu\_L^4}{\rho\_{\mathfrak{g}}\sigma\_L^3} \tag{18}$$

bubble column through the single nozzle gas injector with an orifice diameter of 6.8 mm. A range of silicone oil with viscosities 5, 100, 1000 and 5000 mPa s was used. The liquid holdup obtained from the ECT was used to obtain the structure velocity (rise velocity of Taylor bubbles) via cross-correlation between two

*The Effect of Liquid Viscosity on the Rise Velocity of Taylor Bubbles in Small Diameter Bubble…*

planes, 30 mm. The ECT sensor used is shown in **Figure 3**.

periodic structures velocity at real-time measurements.

two variables (in this case, time series data sets) are correlated.

*Rxy*ð Þ¼ *τ* **lim**

The correlation coefficient function is expressed as:

*Cxy*ð Þ*<sup>τ</sup>* ffiffiffiffiffiffiffiffi

*T*!∞

**1** *T* ð *T*

**0**

*Cxx* <sup>p</sup> ð Þ **<sup>0</sup>** *Cyy*ð Þ **<sup>0</sup>** <sup>¼</sup> *Rxy*ð Þ� *<sup>τ</sup> <sup>μ</sup>xμ<sup>y</sup>* ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *Rxx*ð Þ� **0** *μ***<sup>2</sup>**

*x* � � *Ryy*ð Þ� **<sup>0</sup>** *<sup>μ</sup>***<sup>2</sup>**

r � �

*x t*ð Þ*y t*ð Þ þ *τ dτ* (20)

*y*

(21)

**3. Rise velocity of Taylor bubbles**

*DOI: http://dx.doi.org/10.5772/intechopen.92754*

**3.1 Cross-correlation**

**Figure 3.**

*The twin-plane ECT sensor used.*

between them is given as:

*ρxy*ð Þ¼ *τ*

**205**

planes—plane 1 and plane 2 putting into consideration the distance between the two

In this study, the rise velocity of Taylor bubbles was obtained from ECT (via cross-correlation between signals from planes 1 and 2 as shown in **Figure 3**), manual time series analysis and the high-speed camera. This rise velocity of Taylor bubbles is also referred to as structure velocity which is from the Taylor bubble

Correlation is the measure of the degree of linear relationship between two variables. Cross-correlation is a statistical method of estimating the degree to which

The structure velocity was computed from the cross-sectional time averaged void fraction data measured by the ECT for both planes 1 and 2. The cross-correlation between the signals obtained from the two planes gave the structure velocity. Given two functions *x t*ð Þ and *y t*ð Þ, the cross-correlation function, *Rxy*ð Þ*τ*

Further details of the experimental arrangements are given in Kajero et al. [32, 33].

Eotvos number is given as:

$$E\_o = \frac{\rho \mathbf{g} \mathbf{D}}{\sigma\_L} \tag{19}$$

#### *1.2.3 Froude number*

Apart from the effect of viscous force, gravitational force also affects the rise velocity of Taylor bubble through the liquid. Froude number is a dimensionless parameter which gives a relationship between inertia and gravitational forces. It describes different flow regimes of open channel flow as in the case of the bubble column in this study.

The slug Froude number [31] is given as Eq. (1). Llewellin et al. [5] called the Froude number a dimensionless velocity.

## **2. Experimental arrangements**

The bubble column experimental set-up consists of a 50 mm internal diameter and 1.6 m long perspex column in a vertical orientation. At the bottom of the column is a single nozzle gas distributor through which gas is introduced into the column. A phantom high-speed camera was used to obtain the video of the gas– liquid flow in the column. A frame rate of 1000 pictures per second (pps) and exposure time of 100 μs was used. The geometry specified from the high-speed camera setting gives the image width by image height as 512 by 512 pixel.

Fitted midway to the column is the twin-planes electrical capacitance tomography (ECT) sensor with an interplanar spacing of 30 mm. The 8-electrode system consists of measurement and driven guard electrodes, which is connected to the electrical capacitance tomography processor box, TFLR 5000–20. This sensor electronics gives 28 measurements which are relayed to the computer where image reconstruction occurs, and the data are acquired and processed to obtain the liquid holdup (which is the fraction of liquid in the gas-liquid mixture). The void fraction otherwise known as gas holdup is hence obtained from this.

The ECT is located about 0.7 m above the nozzle, while the liquid level is located about 0.095 m above the ECT sensor. On injecting the gas, the gas flows into the

*The Effect of Liquid Viscosity on the Rise Velocity of Taylor Bubbles in Small Diameter Bubble… DOI: http://dx.doi.org/10.5772/intechopen.92754*

**Figure 3.** *The twin-plane ECT sensor used.*

*1.2.2 Inverse dimensionless viscosity, N <sup>f</sup>*

*Vortex Dynamics Theories and Applications*

where Morton number is given as:

Froude number a dimensionless velocity.

**2. Experimental arrangements**

Eotvos number is given as:

*1.2.3 Froude number*

column in this study.

**204**

According to Lu and Prosperetti [30], the inverse dimensionless viscosity is directly proportional to the fourth root of the Eotvos number raised to a power of three and inversely proportional to the fourth root of the Morton number. Morton number, *Mo* is used alongside with Eotvos number, *Eo* to characterize the shape of

*Nf* <sup>¼</sup> *<sup>E</sup>***<sup>3</sup>**

*Mo* <sup>¼</sup> *<sup>g</sup>μ***<sup>4</sup>** *L ρgσ***<sup>3</sup>** *L*

*Eo* <sup>¼</sup> *<sup>ρ</sup>gD σL*

Apart from the effect of viscous force, gravitational force also affects the rise velocity of Taylor bubble through the liquid. Froude number is a dimensionless parameter which gives a relationship between inertia and gravitational forces. It describes different flow regimes of open channel flow as in the case of the bubble

The slug Froude number [31] is given as Eq. (1). Llewellin et al. [5] called the

The bubble column experimental set-up consists of a 50 mm internal diameter

Fitted midway to the column is the twin-planes electrical capacitance tomography (ECT) sensor with an interplanar spacing of 30 mm. The 8-electrode system consists of measurement and driven guard electrodes, which is connected to the electrical capacitance tomography processor box, TFLR 5000–20. This sensor electronics gives 28 measurements which are relayed to the computer where image reconstruction occurs, and the data are acquired and processed to obtain the liquid holdup (which is the fraction of liquid in the gas-liquid mixture). The void fraction

The ECT is located about 0.7 m above the nozzle, while the liquid level is located about 0.095 m above the ECT sensor. On injecting the gas, the gas flows into the

and 1.6 m long perspex column in a vertical orientation. At the bottom of the column is a single nozzle gas distributor through which gas is introduced into the column. A phantom high-speed camera was used to obtain the video of the gas– liquid flow in the column. A frame rate of 1000 pictures per second (pps) and exposure time of 100 μs was used. The geometry specified from the high-speed camera setting gives the image width by image height as 512 by 512 pixel.

otherwise known as gas holdup is hence obtained from this.

*o Mo* **<sup>1</sup>***=***<sup>4</sup>**

(17)

(18)

(19)

bubbles or drops moving in a surrounding fluid or continuous phase.

The inverse dimensionless viscosity is given as:

bubble column through the single nozzle gas injector with an orifice diameter of 6.8 mm. A range of silicone oil with viscosities 5, 100, 1000 and 5000 mPa s was used.

The liquid holdup obtained from the ECT was used to obtain the structure velocity (rise velocity of Taylor bubbles) via cross-correlation between two planes—plane 1 and plane 2 putting into consideration the distance between the two planes, 30 mm. The ECT sensor used is shown in **Figure 3**.

Further details of the experimental arrangements are given in Kajero et al. [32, 33].
