# Second Law Analysis of Adiabatic and Non-Adiabatic Pipeline Flows of Unstable and Surfactant-Stabilized Emulsions

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background

#### 2.1. Non-Adiabatic Flow

#### 2.2. Adiabatic Flow

#### Entropy Production in Adiabatic Pipeline Flow

## 3. Experimental Work: Adiabatic Pipeline Flow of Emulsions

^{3}) at room temperature (25 °C). The tank was equipped with baffles, high shear impeller-type mixers, heating/cooling coil, and a temperature controller. The emulsion prepared in the mixing tank was circulated to the pipeline test sections, one at a time, by a centrifugal pump. The pressure drops in the pipeline test sections were measured by means of the pressure transducers. The flow rate of the emulsion was measured by allowing it to pass through the metering section equipped with electro-magnetic and orifice flowmeters before returning to the mixing tank. For each pipeline test section, enough entry length (more than 100 pipe diameters) was provided for the flow to become hydrodynamically fully developed. The exit lengths after the test sections were in the range of 35 to 55 pipe diameters. The pressure transducers and the flow meters were all calibrated prior to any experimental work. The friction factor versus Reynolds number data obtained from the pipeline test sections using single-phase Newtonian fluids were found to be in good agreement with the standard friction factor relations valid for the laminar and turbulent flow of single-phase Newtonian fluids. Further details about the experimental set-up can be found in our earlier publications [13,14,15].

^{3}and its viscosity was 2.41 mPa·s at 25 °C. The experiments were started with continuous phase (oil, oil-surfactant mixture, water, water-surfactant mixture, depending on the type of emulsion) into which a required amount of the dispersed-phase was added to prepare an emulsion. The concentration of the dispersed-phase was increased by successive additions of the dispersed-phase. The temperature of the emulsion was maintained constant at 25 °C with the help of a temperature controller installed in the mixing tank.

#### Measurement Uncertainties

## 4. Results and Discussion: Adiabatic Pipeline Flow of Emulsions

#### 4.1. Entropy Generation in Adiabatic Pipeline Flow of Unstable Oil-in-Water (O/W) Emulsions

#### 4.2. Entropy Generation in Adiabatic Pipeline Flow of Surfactant-Stabilized Oil-in-Water (O/W) Emulsions

#### 4.3. Entropy Generation in Adiabatic Pipeline Flow of Unstable Water-in-Oil (W/O) Emulsions

#### 4.4. Entropy Generation in Adiabatic Pipeline Flow of Surfactant-Stabilized Water-in-Oil (W/O) Emulsions

#### 4.5. Discussion

## 5. Simulation Work: Non-Adiabatic Pipeline Flow of Emulsions

_{p}is the constant-pressure heat capacity of the fluid. From Equations (35) and (36), it follows that:

#### 5.1. Estimation of Friction Factor, Heat Transfer Coefficient, and Outlet Temperature

#### 5.2. Estimation of Thermophysical Properties of Emulsions

#### 5.3. Simulation Results and Discussion

_{in}) and the wall temperature (T

_{b}). The values of these variables used in the simulations are: L = 0.5 m, D = 1.0 cm, T

_{in}= 293 K, and T

_{b}= 310 K. The thermophysical properties of emulsions are assumed to be approximately constant within the temperature range considered in this work. This is a reasonable approximation as the oulet temperature of the emulsion was within a few degrees of the inlet temperature of 293 K.

## 6. Conclusions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Heat reservoirs are placed directly at the control volume boundary such that the temperature at the boundary is the same as that of the heat reservoir.

**Figure 4.**Dimensionless rate of entropy generation ${({\dot{S}}_{G}^{\prime})}^{\ast}$ versus $\mathrm{Re}$ data for differently concentrated unstable O/W emulsions, without the presence of any surfactant, obtained from a pipe of diameter 8.89 mm.

**Figure 5.**${({\dot{S}}_{G}^{\prime})}^{\ast}$ versus $\mathrm{Re}$ data for unstable O/W emulsions obtained from a pipe of diameter of 15.8 mm.

**Figure 6.**All the experimental data for differently concentrated unstable O/W emulsions obtained from two different diameter pipes.

**Figure 7.**Dimensionless rate of entropy generation ${({\dot{S}}_{G}^{\prime})}^{\ast}$ versus $\mathrm{Re}$ data for differently concentrated surfactant-stabilized O/W emulsions obtained from a pipe of diameter 8.89 mm.

**Figure 8.**${({\dot{S}}_{G}^{\prime})}^{\ast}$ versus $\mathrm{Re}$ data for surfactant-stabilized O/W emulsions obtained from a pipe of diameter of 15.8 mm.

**Figure 9.**All the experimental data for differently concentrated surfactant-stablized O/W emulsions obtained from two different diameter pipes.

**Figure 10.**Dimensionless rate of entropy generation ${({\dot{S}}_{G}^{\prime})}^{\ast}$ versus $\mathrm{Re}$ data for differently concentrated unstable W/O emulsions, without the presence of any surfactant, obtained from a pipe of diameter 8.89 mm.

**Figure 11.**${({\dot{S}}_{G}^{\prime})}^{\ast}$ versus $\mathrm{Re}$ data for unstable W/O emulsions obtained from a pipe of diameter of 15.8 mm.

**Figure 12.**All the experimental data for differently concentrated unstable W/O emulsions obtained from two different diameter pipes.

**Figure 13.**Dimensionless rate of entropy generation ${({\dot{S}}_{G}^{\prime})}^{\ast}$ versus $\mathrm{Re}$ data for differently concentrated surfactant-stabilized W/O emulsions obtained from a pipe of diameter 8.89 mm.

**Figure 14.**${({\dot{S}}_{G}^{\prime})}^{\ast}$ versus $\mathrm{Re}$ data for surfactant-stabilized W/O emulsions obtained from a pipe of diameter of 15.8 mm.

**Figure 15.**All the experimental data for differently concentrated surfactant-stabilized W/O emulsions obtained from two different diameter pipes.

**Figure 16.**Variation of entropy generation rates (${\dot{S}}_{G,f}$ and ${\dot{S}}_{G,t}$ in units of J/(K·s)) and Bejan number ($Be$) with Reynolds number in laminar flow of emulsion ($\mathsf{\phi}=$ 0.20).

**Figure 17.**Variation of entropy generation rates (${\dot{S}}_{G,f}$ and ${\dot{S}}_{G,t}$ in units of J/(K·s)) and Bejan number ($Be$) with Reynolds number in laminar flow of emulsion ($\mathsf{\phi}=$ 0.50).

**Figure 18.**Variation of entropy generation rates (${\dot{S}}_{G,f}$ and ${\dot{S}}_{G,t}$ in units of J/(K·s)) and Bejan number ($Be$) with Reynolds number in laminar flow of emulsion ($\mathsf{\phi}=$ 0.60).

**Figure 19.**Variation of entropy generation rates (${\dot{S}}_{G,f}$ and ${\dot{S}}_{G,t}$ in units of J/(K·s)), viscosity ($\mathsf{\mu}$ in units of Pa·s) and Bejan number ($Be$) with $\mathsf{\phi}$ in laminar flow of emulsions at a fixed $\mathrm{Re}$ of 1500.

**Figure 20.**Variation of entropy generation rates (${\dot{S}}_{G,f}$ and ${\dot{S}}_{G,t}$ in units of J/(K·s)) and Bejan number ($Be$) with Reynolds number in turbulent flow of emulsion ($\mathsf{\phi}=$ 0.20).

**Figure 21.**Variation of entropy generation rates (${\dot{S}}_{G,f}$ and ${\dot{S}}_{G,t}$ in units of J/(K·s)) and Bejan number ($Be$) with Reynolds number in turbulent flow of emulsion ($\mathsf{\phi}=$ 0.50).

**Figure 22.**Variation of entropy generation rates (${\dot{S}}_{G,f}$ and ${\dot{S}}_{G,t}$ in units of J/(K·s)) and Bejan number ($Be$) with Reynolds number in turbulent flow of emulsion ($\mathsf{\phi}=$ 0.60).

**Figure 23.**Variation of entropy generation rates (${\dot{S}}_{G,f}$ and ${\dot{S}}_{G,t}$ in units of J/(K·s)), viscosity ($\mathsf{\mu}$ in units of Pa·s) and Bejan number ($Be$) with $\mathsf{\phi}$ in turbulent flow of emulsions at a fixed $\mathrm{Re}$ of 50,000.

Pipe Inside Diameter (mm) | Entrance Length (m) | Length of Test Section (m) | Exit Length (m) |
---|---|---|---|

8.89 | 0.89 | 3.35 | 0.48 |

15.8 | 1.65 | 2.59 | 0.56 |

Emulsion-Type | Oil-Phase | Aqueous-Phase | Dispersed-Phase Concentrations (% Vol.) |
---|---|---|---|

Unstable O/W (Set 1) | Refined mineral oil (Bayol-35) | Tap water | 28.76; 44.98; 55.07 |

Surfactant-stabilized O/W (Set 2) | Refined mineral oil (Bayol-35) | 1% by wt. surfactant solution in tap water; the surfactant used was Triton X-100 (isooctylphenoxypolyethoxy ethanol) | 16.53; 30.4; 44.41; 49.65; 55.14 |

Unstable W/O (Set 3) | Refined mineral oil (Bayol-35) | Tap water | 0; 10.51; 17.49; 26.72; 32.47; 38.14; 41.05 |

Surfactant-stabilized W/O (Set 4) | 1.5% by wt. surfactant solution in mineral oil (Bayol-35); the surfactant used was SPAN-80 (sorbitan monooleate) | Tap water | 0; 10.61; 18.25; 25.85 |

Property | Matrix (Water) | Dispersed-Phase (Oil) | Emulsion $\mathsf{\phi}\mathbf{=}\mathbf{0.20}$ | Emulsion $\mathsf{\phi}\mathbf{=}\mathbf{0.30}$ | Emulsion $\mathsf{\phi}\mathbf{=}\mathbf{0.40}$ | Emulsion $\mathsf{\phi}\mathbf{=}\mathbf{0.50}$ | Emulsion $\mathsf{\phi}\mathbf{=}\mathbf{0.60}$ |
---|---|---|---|---|---|---|---|

$\mathsf{\rho}(\mathrm{k}\mathrm{g}/{\mathrm{m}}^{3})$ | 1000 | 780 | 956 | 934 | 912 | 890 | 868 |

C_{p}(J/(kg·K)) | 4180 | 1470 | 3738 | 3501 | 3253 | 2992 | 2719 |

$\mathrm{k}(\mathrm{W}/(\mathrm{m}\xb7\mathrm{K}))$ | 0.60 | 0.15 | 0.488 | 0.436 | 0.388 | 0.343 | 0.30 |

$\mathsf{\mu}(\mathrm{m}\mathrm{P}\mathrm{a}\xb7\mathrm{s})$ | 1 | 2.5 | 1.79 | 2.61 | 4.13 | 7.44 | 16.57 |

Pr | 7 | 25 | 14 | 21 | 35 | 65 | 150 |

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**MDPI and ACS Style**

Pal, R.
Second Law Analysis of Adiabatic and Non-Adiabatic Pipeline Flows of Unstable and Surfactant-Stabilized Emulsions. *Entropy* **2016**, *18*, 113.
https://doi.org/10.3390/e18040113

**AMA Style**

Pal R.
Second Law Analysis of Adiabatic and Non-Adiabatic Pipeline Flows of Unstable and Surfactant-Stabilized Emulsions. *Entropy*. 2016; 18(4):113.
https://doi.org/10.3390/e18040113

**Chicago/Turabian Style**

Pal, Rajinder.
2016. "Second Law Analysis of Adiabatic and Non-Adiabatic Pipeline Flows of Unstable and Surfactant-Stabilized Emulsions" *Entropy* 18, no. 4: 113.
https://doi.org/10.3390/e18040113