Low shear mixer principles

Fluid mixing

 

Mixing is a manipulation of a heterogeneous physical system with the intent to make it more homogeneous. This is a very general definition. There are many other terms used to describe specific effects of mixing. Examples of such are homogenization, deagglomeration, emulsification, dispersion etc. Important aspects are the type of materials to be mixed (liquids, gases, solids) as well as miscibility of the materials, which is more characteristic for liquids and gases.

 

In a physical sense, mixing can undergo process of distribution or process of dispersion or both. The goal of distribution is to create a mixture of different components with uniform distribution throughout the system. The goal of the dispersion process is to increase the homogeneity of the system by reducing the particle size of the “dispersed” phase. In many cases, reduced particle sizes lead to altering the nature of the system due to increased contact surface area between the components.

 

Miscibility is the property of the substances to dissolve in each other, forming a homogenous solution. Miscibility of the substances determines the approach for mixing of these substances. If components are miscible, then the mixing efforts should be concentrated on the distribution process. For immiscible systems, dispersion is the preferred mixing mechanism.

 

The process of mixing can also be separated into batch mixing and continuous mixing processes. In a batch mixing, discrete amount of substances is mixed in a vessel. In continuous mixing, the substances are fed through the piping into an inline mixing device with predetermined input and output.

 

Efficient mixing depends on many factors. There are many different types of mixers, which excel in specific applications. In industrial processes, parameters such as power consumption, automation, degree of homogeneity etc. are important input variables for the choice of optimal solution.

 

 

Low shear mixer design principles

 

Low shear mixing is characterized by blending the substances without reducing the particle sizes during the process. Low shear mixing is highly relevant for blending delicate or shear sensitive materials such as polymers, adhesives and structured food products. These types of materials tend to have a threshold of shear rate above which materials start to alter their properties. This behavior is usually referred to as shear degradation.

 

Shear forces present in the flow are proportional to the intensity of turbulence. As the kinetic energy in the turbulent flow cascades from large scale eddies down to smaller ones, energy dissipates into heat due to viscous forces. The energy dissipation rate, \varepsilon, is the parameter used to determine the amount of energy lost by the viscous forces in the turbulent flow (Turbulence and multiphase flow). In order to reduce shear forces, the mean energy dissipation rate must be reduced.

 

It is not straightforward to determine \varepsilon  in mixers, mainly because it varies spatially, being higher near the mixing head than in the rest of the fluid volume. Padron (2005) in his study of rotor-stator mixers proposed following approach for estimation of energy dissipation rate.  The average dissipation rate,  \varepsilon, can be approximated as power draw per unit mass:

 

\varepsilon=C_{{1}}\frac{P}{\rho_{{c}}\cdot V}                (1)

 

Where

 

\varepsilon average energy dissipation rate per unit mass, m2/s3.

C1 constant of proportionality.

P power draw, W or kg·m2/s3.

\rho_{{c}} density of continuous phase, kg/m3.

V volume involved in the mixing process, m3.

The power draw is equal to:

 

P=P_{{0}}\rho_{{c}}N ^{3}L ^{5}           (2)

 

Where

 

P_{{0}} power number, -.

N impeller rotational speed, s-1.

L characteristic length scale of the system, m (impeller diameter in rotor-stator mixers).

 

Since the volume involved in the mixing process is proportional to  L^{3}, the following expression is obtained:

 

\varepsilon=C_{{1}}\frac{\rho_{{c}}N ^{3}L ^{5}}{\rho_{{c}}L ^{3}}P_{{0}}=C_{{2}}N ^{3}L ^{2}                  (3)

 

Where

 

C_{{2}}  constant of proportionality, -.

 

The pressure variations have to be minimized as they induce high dissipation rates, and, hence, high shear forces. Pressure variations can occur in the zone of small rotor-stator gap in the mixer.

 

The effective distributive mixing can be achieved by maintaining low speed with preferably laminar flow. Cavity transfer mixing is the preferable method to ensure low shear operation. As fluids are pumped into the mixer, they meet the cavities in the rotor and stator. The fluids are transferred between the rotor and stator components as they move along the tortuous flow path, as they at the same time being cut and folded by the movement of the rotor. The large gaps and low speed cutting and folding promotes efficient blending with low levels of energy dissipation rates.

 

 

Additional reading

 

Padron, G., 2005. Effect of Surfactants on Drop Size Distributions in a Batch, Rotor-Stator Mixer. PhD Dissertation, University of Maryland, College Park, Maryland. (2005)

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