**9. References**


Coleman, G. N. & Mansour, N. N. (1991). Modeling the rapid spherical compression of isotropic turbulence, *Physics of Fluids*, vol. A 3, pp. 2255-2259.

412 Numerical Simulation – From Theory to Industry

RDT Rapid Distortion Theory DNS Direct Numerical Simulation

*u<sup>i</sup>* velocity fluctuation *p* pressure fluctuation

*ij λ* mean velocity gradient

*/q* turbulent kinetic energy

energy

*r* initial rapidity of the shear

*γ* ratio of specific heats

vol. 256, pp. 443-485.

8, pp. 2692-2705.

*et* <sup>0</sup> *R* initial turbulent Reynolds number

*a* mean sound speed *Δt* time-step size

*uu <sup>b</sup>* anisotropy tensor

*ρ* mean density *ν* kinematic viscosity

*Mg*, *Mg*0 gradient Mach number, initial gradient Mach number *Mt*, *Mt*<sup>0</sup> turbulent Mach number, initial turbulent Mach number

<sup>0</sup> *<sup>ε</sup>* initial total (solenoidal and dilatational) dissipation rate of turbulent kinetic

Blaisdell, G.A.; Mansour, N.N. & Reynolds, W.C. (1993). Compressibility effects on the growth and structure of homogeneous turbulent shear flow. *Journal of Fluid Mechanics*,

Blaisdell, G. A.; Coleman, G. N. & Mansour, N. N. (1996). Rapid distortion theory for compressible homogenous turbulence under isotropic mean strain. *Physics of Fluids*, vol.

*S* magnitude of the mean velocity gradient

**Abbreviations** 

**Nomenclature** 

2 <sup>2</sup>

*ij*

0

3 <sup>2</sup> *ijji*

*q*

**9. References** 

*δ*


Tavoularis, S. & Corrsin, S. (1981). Experiments in nearly homogeneous turbulent shear flow with a uniform mean gradient temperature. *Part I. Journal of Fluid Mechanics*, vol. 104, pp. 311-347.

**Chapter 19** 

© 2012 Pathak, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

distribution, and reproduction in any medium, provided the original work is properly cited.

In membrane emulsification process, micro or macro porous membranes are used to generate droplets by pressing the dispersed phase through the porous matrix of the

and reproduction in any medium, provided the original work is properly cited.

maintaining the combination of continuous and dispersed phase flow rate.

**Numerical Simulation of Droplet Dynamics** 

An emulsion is a two-phase liquid system of two immiscible liquids, where the liquid with lower mass fraction is dispersed in form of small droplets in other surrounding liquid of higher mass fraction. Emulsions are widely used to produce sol–gel, drugs, synthetic materials, and food products. Based on the size of droplet, emulsions can be classified as micro and macro emulsion. Karbstein and Schubert, (1995) have made a limiting droplet size of 0.1 µm, below which the emulsion is termed as micro emulsion and above that size the emulsion is termed as macro emulsion. Size and size distribution of droplets play important roles in the stability of emulsion. There are also other factors such as sedimentation, skimming, droplet aggregation and coalescence, which may affect the stability of the droplets. Thus for making a stable emulsion it is necessary to convert the dispersed phase into tiny droplets and stabilize them against coalescence. Some amount of energy is required in the process to break the dispersed phase into droplets. The amount of energy put in the dispersing phase also controls the resulting droplet size. The stability of newly formed droplets depends on how fast the used emulsifiers are able to occupy the newly created interfaces and how well they stabilize them. The common devices used to produce emulsions are rotor-stator-systems, stirrers and high-pressure homogenizers. During last two decades, new technologies of making emulsion have been developed. Compared to conventional method of emulsification such as rotor-stator method, these new techniques of emulsification have several advantages such as low energy consumption, controllable droplet size with proper distribution and easy scalability. These new methods are based on the microdroplet formation in micrometer sized channels. Three such new methods are T-junction emulsification, flow focusing emulsification, and membrane emulsification. In all these methods, controllable droplet formations are achieved by properly

**in Membrane Emulsification Systems** 

Additional information is available at the end of the chapter

Manabendra Pathak

http://dx.doi.org/10.5772/50180

**1. Introduction** 

Zeman, O. (1990). Dilatation dissipation: The concept and application in modeling compressible mixing layers. *Physics of Fluids*, vol. 2, pp. 178-188, ISSN 0899-8213.
