# Influence of Droplet Size on Exergy Destruction in Flow of Concentrated Non-Newtonian Emulsions

## Abstract

**:**

## 1. Introduction

_{o}, v

_{o}, and s

_{o}are specific internal energy, specific volume, and specific entropy of the system in the dead state, respectively; P

_{o}and T

_{o}are the environment pressure and temperature, respectively; g is acceleration due to gravity; and z is the elevation of the system. In Equation (1), it is assumed that the kinetic energy of the system is zero, that is, the system is stationary. The thermo-mechanical exergy associated with a fluid stream per unit mass is given as follows:

_{o}is the specific enthalpy of the fluid in the dead state, and V is the velocity of the fluid.

## 2. Theoretical Background

_{o}be $\dot{Q}$ on a unit volume basis. The exergy balance on the fluid gives:

#### Exergy Destruction in a Cone-and-Plate Viscometer

_{r}and V

_{θ}) are zero. Since ${\mathsf{\theta}}_{1}\approx \frac{\mathsf{\pi}}{2}$ and $\mathsf{\theta}\approx \frac{\mathsf{\pi}}{2}$, this expression of velocity simplifies to${V}_{\phi}=\Omega r\mathrm{cos}\mathsf{\theta}/\mathrm{cos}{\mathsf{\theta}}_{1}$.

## 3. Experimental Section

## 4. Results and Discussion

#### 4.1. Droplet Size Distribution of Emulsions

#### 4.2. Rheology of Emulsions

#### 4.3. Reliability of Rheological Measurements

#### 4.4. Exergy Destruction in Emulsions

_{o}= 298.15 K. Figure 7 shows the plots of exergy destruction rate per unit volume of emulsion (${\dot{\mathsf{\psi}}}_{D}$) as functions of shear stress. For any given shear stress, the exergy destruction rate is the lowest in fine emulsion. The exergy destruction rate is much higher in the case of coarse emulsion. This appears to be counter-intuitive as fine emulsion is much more viscous and energy dissipative in comparison with the coarse emulsion. The main reason for this apparent contradiction is that the shear rate in coarse emulsion is much higher than that in the fine emulsion when comparison is made at the same shear stress. Therefore it is more appropriate to compare exergy destruction rates in different emulsions at the same shear rate (instead of the same shear stress). To that end, the data of Figure 7 are re-plotted in Figure 8 as ${\dot{\mathsf{\psi}}}_{D}$ versus shear rate. Now the exergy destruction rate in fine emulsion is the highest as expected.

## 5. Simulation of Exergy Destruction in Pipeline Flow of Emulsions

_{o}is the surroundings temperature. Equations (21) and (22) are used to simulate the influence of droplet size on ${{\dot{\mathsf{\psi}}}^{\prime}}_{D}$ in adiabatic pipeline flow of power-law O/W emulsions. The influence of droplet size on ${{\dot{\mathsf{\psi}}}^{\prime}}_{D}$ enters the analysis through the power-law parameters K and n, which are dependent on the droplet size distribution of emulsion (see Figure 5).

## 6. Conclusions

- The shear-stress τ versus shear rate $\dot{\mathsf{\gamma}}$ behavior of concentrated oil-in-water emulsions (fine, coarse, and their mixtures) investigated in this work can be described satisfactorily by a power-law model $\mathsf{\tau}=K{\dot{\mathsf{\gamma}}}^{n}$. The power-law parameters K and n vary with the droplet size and droplet size distribution of emulsions. When fine emulsion (small droplet size) is mixed with the coarse emulsion (large droplet size), keeping the dispersed-phase concentration fixed, the consistency index K goes through a minimum and the power-law index n goes through a maximum at a certain proportion of fine emulsion content of the mixed fine and coarse emulsion.
- The exergy destruction rate per unit volume of emulsion exhibits a minimum when fine emulsion is mixed with the coarse emulsion. The minimum in exergy destruction rate is observed at low shear rates around the fine emulsion proportion of 35%.
- The thermodynamic efficiency of pumping emulsion through a pipeline increases when fine emulsion is mixed with the coarse emulsion provided that the flow regime is laminar and that the Reynolds number is not high (less than about 100).
- At high Reynolds number in the turbulent regime, the exergy loss in pipeline flow of emulsion increases upon mixing fine emulsion with the coarse emulsion, keeping the dispersed-phase concentration fixed. The increase in exergy loss upon increasing the droplet size distribution is due an increase in the flow behavior index n (a decrease in pseudo-plasticity).

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**Shear stress versus shear rate plots for mixtures of fine and coarse O/W emulsions. In the figure “f” refers to proportion of fine emulsion and “c” refers to proportion of coarse emulsion.

**Figure 5.**Power law parameters (K and n) with error bars for mixtures of fine and coarse O/W emulsions.

**Figure 6.**Comparison of viscosity data of fine and coarse emulsions obtained from different instruments.

**Figure 7.**Exergy destruction rate versus shear stress for mixtures of fine and coarse O/W emulsions.

**Figure 9.**Shear rate and exergy destruction rate for mixtures of fine and coarse O/W emulsions at a fixed shear stress of 0.5 Pa.

**Figure 10.**Exergy destruction rate per unit volume for mixtures of fine and coarse O/W emulsions at a fixed shear rate of 5 s

^{−1}.

**Figure 11.**Exergy destruction rate per unit pipe length in adiabatic laminar flow of mixtures of fine and coarse O/W emulsions.

**Figure 12.**The effect of Re_n on exergy loss in adiabatic pipeline flow of mixtures of fine and coarse O/W emulsions.

**Figure 13.**Exergy destruction rate per unit pipe length in adiabatic turbulent flow of mixtures of fine and coarse O/W emulsions.

**Figure 14.**Exergy destruction rate in adiabatic turbulent flow of mixtures of fine and coarse O/W emulsions at a fixed Re_n of 85,223.

Emulsion Composition | Regression Correlation Coefficient, R^{2} | Flow Behavior Index, n | Consistency Index, K (Units of Pa·s^{n}) | 95% Confidence Interval of n | 95% Confidence Interval of K |
---|---|---|---|---|---|

Coarse (0f/100c) | 0.9956 | 0.442 | 1.12 | [0.427, 0.456] | [1.044, 1.199] |

10f/90c | 0.9999 | 0.622 | 0.425 | [0.619, 0.625] | [0.420, 0.430] |

20f/80c | 0.9975 | 0.753 | 0.208 | [0.734, 0.771] | [0.191, 0.227] |

35f/65c | 0.9976 | 0.822 | 0.152 | [0.802, 0.841] | [0.138, 0.167] |

50f/50c | 0.9989 | 0.733 | 0.323 | [0.722, 0.744] | [0.307, 0.340] |

65f/35c | 0.9996 | 0.585 | 0.937 | [0.580, 0.591] | [0.916, 0.959] |

80f/20c | 0.9966 | 0.466 | 2.418 | [0.454, 0.478] | [2.303, 2.539] |

90f/10c | 0.9973 | 0.431 | 3.522 | [0.422, 0.441] | [3.383, 3.667] |

Fine (100f/0c) | 0.9745 | 0.364 | 6.777 | [0.336, 0.392] | [5.927, 7.749] |

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Pal, R.
Influence of Droplet Size on Exergy Destruction in Flow of Concentrated Non-Newtonian Emulsions. *Energies* **2016**, *9*, 293.
https://doi.org/10.3390/en9040293

**AMA Style**

Pal R.
Influence of Droplet Size on Exergy Destruction in Flow of Concentrated Non-Newtonian Emulsions. *Energies*. 2016; 9(4):293.
https://doi.org/10.3390/en9040293

**Chicago/Turabian Style**

Pal, Rajinder.
2016. "Influence of Droplet Size on Exergy Destruction in Flow of Concentrated Non-Newtonian Emulsions" *Energies* 9, no. 4: 293.
https://doi.org/10.3390/en9040293