**1. Introduction**

Slug flow is characterized by Taylor bubbles, which has large pockets of bullet shaped bubbles occupying almost the entire cross-section of the column. The Taylor bubble is surrounded by a thin film of liquid, and below, it is the liquid slugs, which are agglomerate of small bubbles. Zukoski [1], Tomiyama et al. [2] and Mandal and Das [3] described the Taylor bubble length to exceed 1.5 times of the tube diameter or its diameter is greater than 60% of the tube diameter. The rise velocity of a single isolated Taylor bubble is dependent on inertia and drag forces [4]. A number of parameters affect the rise velocity of Taylor bubbles through a stagnant liquid; such

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

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

after solving the problem using different assumptions.

unique but should tend to the limiting value given as:

[13]. So, Brown [15] gave the bubble velocity as:

where the Froude number is 0.54.

[12] based on the studies on vertical slug flow given as:

of a Taylor bubble in the liquid in a vertical tube as:

is given as:

and

*K***<sup>1</sup>** = 0.35.

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varying *K***<sup>2</sup>** [16].

densities respectively.

*UN* <sup>¼</sup> **<sup>0</sup>***:***<sup>328</sup>** ffiffiffiffiffiffi

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

*UN* <sup>¼</sup> **<sup>0</sup>***:***<sup>346</sup>** ffiffiffiffiffiffi

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

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

q

where *<sup>δ</sup><sup>o</sup>* <sup>¼</sup> *<sup>D</sup>* ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

*NLB* <sup>¼</sup> **<sup>14</sup>***:***5***ρ***<sup>2</sup>**

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:

*UN* <sup>¼</sup> **<sup>0</sup>***:***<sup>54</sup>** ffiffiffiffiffiffi

A correlation for the bubble rise velocity was proposed by Griffith and Wallis

where *USG* and *USL* are the superficial gas and liquid velocities respectively, and

They investigated the effect of different velocity profiles in the liquid slug by

Nicklin et al. [7] from their vertical slug experiments proposed the rise velocity

*UN* ¼ ð Þþ *USG* þ *USL K***1***:K***<sup>2</sup>**

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *gD <sup>Δ</sup><sup>ρ</sup> ρL*

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *g D*ð Þ � **2***δ<sup>o</sup>*

**<sup>1</sup>** <sup>þ</sup> *NLB* <sup>p</sup> � *<sup>D</sup> NLB*

> *LD***<sup>3</sup>** *g*

*μ***2** *L*

*UN* ¼ *c*

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

*UN* ¼ **0***:***35**

Nicklin et al. [7] later postulated that the Davies and Taylor [11] solution was not

*gD* p (4)

*gD* p (5)

<sup>s</sup> � � (6)

� � (9)

*gD* p (10)

*gD* p (11)

ffiffiffiffiffiffi

(7)

(8)

**Figure 1.** *A single Taylor bubble rising through a stagnant silicone oil liquid (viscosity, 1000 mPa s).*

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 in **Figure 1**.
