**Abstract**

This work presents a short review of the theoretical developments in the application of vortex dynamics to the processing of environmental and biological systems. The mechanisms of complex fluid-particle interaction in vortex dominated and non-vortex dominated flows are briefly discussed from theoretical and practical perspectives. Micro vortex propagation, characteristics and their various applications in environmental process engineering are briefly discussed. Several existing and potential applications of vortex dynamics in turbulent flows are highlighted and as well as the knowledge gaps in the current understanding of turbulence phenomenon with respect to its applications in the processing of solid-liquid suspension and biological systems.

**Keywords:** hydrodynamics, turbulence, eddies, vortex, aggregation

## **1. Introduction**

Hydrodynamic-mediated interactions often occur in many technical and natural environmental processes. In the case of turbulent flows, this leads to the formation of turbulent eddies of various scales and sizes [1, 2]. These energy-carrying eddies often interact with particles and biological materials on various temporal and spatial scales. Eddy-particle interactions often play a crucial role in these processes and it is largely the dominant driver of mass and momentum transfer. In studying the dynamics of such complex interplay of forces, a good knowledge of the vortex dynamics and its influence on the fluid and particle dynamics is highly indispensable [3, 4].

Turbulent mixing, particle dispersion, and bioreactions have been topics of intense and sustained interest in many scientific inquiries [5, 6]. The role of mixing and turbulence-driven particle dispersion in many fluid-particle processes is wellunderstood owing an abundant body of knowledge from many scientific interrogations. However, turbulence as a phenomenon is still poorly understood due to its complex nature. Since mixing and chemical reactions are impacted by the presence of turbulence, it is therefore extremely important to understand the different scales of turbulence in mixing applications.

As mentioned earlier, turbulence has been shown to lead to the formation of eddies on different scales [7, 8]. The spatial degree of mixing such as the macro, meso and micro mixing are governed by the different scales of turbulence [5]. Mixing especially at high Reynolds number is often characterized by irregular,

rotational, and dissipative motion containing vorticities of different energy spectra or eddy sizes [3]. It is therefore imperative to carry out qualitative and quantitative assessment of mixing efficiency in many of the practical applications involving mixing and dispersion. A number of techniques are available for quantifying mixing performance in a wide range of applications. One widely used parameter for quantifying the mixing performance is the coefficient of variation proposed by Alloca and Streiff [6]. This approach relies on the statistical analysis of the spatiotemporal homogeneity of the particle dispersion in mixing applications [9]. Several other techniques are also available for quantifying the degree of mixing in bioreactor systems. In terms of the different phenomena responsible for fluid-particle mixing, advective, turbulent, and diffusive transport depicted in **Figure 1** are the dominant ones.

In turbulent mixing, energy transfer occurs on different eddy scales or energy spectrum. These turbulent eddies consist of the large energy carrying eddies at the inertia sub-range to the smallest ones at the dissipation sub-range as shown in **Figure 2**. The important scales of energy spectrums with respect to the different mixing regimes (i.e. micro, meso, and macro mixing) are the Kolmogorov, Batchelor, and Taylor length scales (Eqs. (1)–(3)). The Kolmogorov length scale of turbulence is used as a convenient reference point for comparison of different scales of mixing. A detailed description of the different time and length scales in turbulent flows is beyond the scope of this work. Further discussion on the subject matter can be found in the following reference texts [11, 12]. Therefore, getting the desired mixing regime is highly imperative for enhanced mass and momentum transfer.

In fluid-particle mixing there exist three distinct mixing regimes in most practical mixing applications namely: micro, meso, and macro mixing. In typical mixing conditions, the dividing line between micro and macro scale is between 100 and 1000 μm, respectively [13]. Consequently, it is often necessary to tailor the mixing performance to the physical, chemical, and biological processes in the target reactor systems.

Macromixing is largely driven by the largest scale of motion in the fluid or the integral length scale. Meso mixing on the other hand involves mixing on a smaller scale than the bulk circulation, but larger than the micro mixing, while micro mixing refers to the mixing on the smallest scale of fluid motion or molecular level. The largest eddies in turbulent dispersion which represents the macro scale of turbulence, are produced by the stirrer or the agitator head and contains most of the fluid energy [11, 14]. Turbulent flow can be viewed as an eddy continuum, with their sizes ranging from the dimension of the turbulence generating device to the Kolmogorov length scale. In between the energy-containing and energy-dissipating

#### **Figure 1.**

*Schematic representation of different mixing and transport mechanisms (a) advection (b) turbulence (c) diffusion (reproduced from [10] with permissions © 2011 Taylor & Francis).*

**5**

*The Role of Micro Vortex in the Environmental and Biological Processes*

eddies, there exists many eddies of other scales smaller than the integral scale that continually transfer the kinetic energy of the fluid through the other length scales. The Batchelor and Taylor scales given in Eqs. (2) and (3) are the examples of other

*Schematic view of energy spectrum in turbulent mixing (reproduced from [15] with permissions © 2007 IWA* 

The Taylor scale is an intermediate length scale in the viscous subrange that is representative of the energy transfer from large to small scales, but not a dissipation scale and does not represent any distinct group of eddies. Batchelor scale on the other hand is a limiting length scale where the rate of molecular diffusion is equal to

> 1 <sup>2</sup> v <sup>4</sup>

> > 1 2 4

> > > v

Colloidal materials in environmental and biological systems consist of small particles with very large surface area. Their typical sizes are in the range of 0.001– 10 μm as shown in **Table 1**. The stability of these colloidal materials when dispersed in fluid can be explained by their tendency to acquire electrostatic charges by adsorbing ions from their surroundings. Forces mediating particle-particle interactions can broadly be classified into the following categories depending

D v (2)

(1)

(3)

0 λ = <sup>ε</sup>

B

λ = <sup>ε</sup>

λ = ε <sup>T</sup> u 15

the rate of dissipation of turbulent kinetic energy of the fluid.

**2. Colloidal stability and interaction forces**

*DOI: http://dx.doi.org/10.5772/intechopen.93531*

important length scales of fluid motion.

**Figure 2.**

*publishing).*

*The Role of Micro Vortex in the Environmental and Biological Processes DOI: http://dx.doi.org/10.5772/intechopen.93531*

#### **Figure 2.**

*Vortex Dynamics Theories and Applications*

dominant ones.

reactor systems.

rotational, and dissipative motion containing vorticities of different energy spectra or eddy sizes [3]. It is therefore imperative to carry out qualitative and quantitative assessment of mixing efficiency in many of the practical applications involving mixing and dispersion. A number of techniques are available for quantifying mixing performance in a wide range of applications. One widely used parameter for quantifying the mixing performance is the coefficient of variation proposed by Alloca and Streiff [6]. This approach relies on the statistical analysis of the spatiotemporal homogeneity of the particle dispersion in mixing applications [9]. Several other techniques are also available for quantifying the degree of mixing in bioreactor systems. In terms of the different phenomena responsible for fluid-particle mixing, advective, turbulent, and diffusive transport depicted in **Figure 1** are the

In turbulent mixing, energy transfer occurs on different eddy scales or energy spectrum. These turbulent eddies consist of the large energy carrying eddies at the inertia sub-range to the smallest ones at the dissipation sub-range as shown in **Figure 2**. The important scales of energy spectrums with respect to the different mixing regimes (i.e. micro, meso, and macro mixing) are the Kolmogorov, Batchelor, and Taylor length scales (Eqs. (1)–(3)). The Kolmogorov length scale of turbulence is used as a convenient reference point for comparison of different scales of mixing. A detailed description of the different time and length scales in turbulent flows is beyond the scope of this work. Further discussion on the subject matter can be found in the following reference texts [11, 12]. Therefore, getting the desired mixing regime is highly imperative for enhanced mass and momentum transfer.

In fluid-particle mixing there exist three distinct mixing regimes in most practical mixing applications namely: micro, meso, and macro mixing. In typical mixing conditions, the dividing line between micro and macro scale is between 100 and 1000 μm, respectively [13]. Consequently, it is often necessary to tailor the mixing performance to the physical, chemical, and biological processes in the target

Macromixing is largely driven by the largest scale of motion in the fluid or the integral length scale. Meso mixing on the other hand involves mixing on a smaller scale than the bulk circulation, but larger than the micro mixing, while micro mixing refers to the mixing on the smallest scale of fluid motion or molecular level. The largest eddies in turbulent dispersion which represents the macro scale of turbulence, are produced by the stirrer or the agitator head and contains most of the fluid energy [11, 14]. Turbulent flow can be viewed as an eddy continuum, with their sizes ranging from the dimension of the turbulence generating device to the Kolmogorov length scale. In between the energy-containing and energy-dissipating

*Schematic representation of different mixing and transport mechanisms (a) advection (b) turbulence (c)* 

*diffusion (reproduced from [10] with permissions © 2011 Taylor & Francis).*

**4**

**Figure 1.**

*Schematic view of energy spectrum in turbulent mixing (reproduced from [15] with permissions © 2007 IWA publishing).*

eddies, there exists many eddies of other scales smaller than the integral scale that continually transfer the kinetic energy of the fluid through the other length scales. The Batchelor and Taylor scales given in Eqs. (2) and (3) are the examples of other important length scales of fluid motion.

The Taylor scale is an intermediate length scale in the viscous subrange that is representative of the energy transfer from large to small scales, but not a dissipation scale and does not represent any distinct group of eddies. Batchelor scale on the other hand is a limiting length scale where the rate of molecular diffusion is equal to the rate of dissipation of turbulent kinetic energy of the fluid.

$$
\lambda\_{\boldsymbol{\alpha}} = \left[\frac{\mathbf{v}^{\boldsymbol{\alpha}}}{\boldsymbol{\alpha}}\right]^{\frac{1}{4}} \tag{1}
$$

$$
\lambda\_{\mathsf{B}} = \left[\frac{\mathsf{D}^2 \mathsf{v}}{\mathsf{c}}\right]^{\frac{1}{4}} \tag{2}
$$

$$
\lambda\_{\mathbf{r}} = \frac{\mathbf{u}\sqrt{\mathbf{u}\mathbf{\bar{s}}}}{\sqrt{\frac{\mathbf{c}}{\mathbf{v}}}} \tag{3}
$$
