Mixing (process engineering)

The mixing is a basic operation in mechanical process engineering .

In process engineering, machines are generally referred to as mixers in which mixed components that are present as a solid phase dominate.

In process engineering, machines are generally referred to as stirrers in which the main mixture components are in the form of a liquid phase.

In contrast to processes that can be described with stirring, the goal of a mixing process is usually clearly defined statistically via the mixing quality.

Definition

In the case of mixing processes, the constituents of at least two separately present mixture components are repositioned by relative movement so that a new arrangement is created. This produces a mixture (mixture) and under certain conditions a new substance. The so-called main phase is present as a continuous phase while the so-called additional phase is initially discontinuous.

Special terms for mixing processes

		discontinuous phase
		gaseous	liquid	firmly
continuous phase	gaseous	Homogenize	Atomize	Atomizing, swirling
	liquid	Gas	(soluble components) homogenizing, (insoluble) dispersing, emulsifying	Suspend, stir up
	firmly	Fluidizing	Moisturizing, coating	Mixing of solids, powdering

driver

The following three drivers for mixing processes are subclasses of convective mixing : In distributive mixing , two substances that are soluble in one another are mixed with low shear forces. Since microorganisms can only withstand low shear forces, distributive mixing in bioreactors is of great importance.
When associations of the substances to be mixed are crushed, mutually wet and finally kept in suspension, one speaks of dispersive mixing . This requires higher shear forces than distributive mixing. Examples are suspension (main phase liquid / additional phase solid), emulsification (liquid / liquid) and gassing (liquid / gaseous).
In turbulent mixing , a stream of material flowing in with high Reynolds numbers creates strong longitudinal mixing in the direction of the flow. At right angles to this, turbulence ensures cross-mixing.
The final classification of mixing drivers is diffusive mixing , in which no external force is driving the mixing. Diffusive mixing is therefore the slowest of all the drivers mentioned.

Mixing quality

The primary goal is to achieve an even distribution of the components to be mixed. This can be quantified via the mixing quality. It considers the distribution of the observed parameter: If the variance over a control volume is KV and the highest locally encountered variance, then the following applies: ${\displaystyle \sigma }$ ${\displaystyle \sigma _{\mathrm {max} }}$

${\displaystyle \sigma ^{2}={\frac {1}{\left|V\right|}}\int \limits _{V_{KV}}\left(c-{\bar {c}}\right)^{2}{\text{d}}V}$

and

${\displaystyle \sigma _{\mathrm {max} }^{2}={\bar {c}}\left(c-{\bar {c}}\right){\text{ ,}}}$

where stands for a control volume, for the mean concentration and for the highest concentration to be found locally. ${\displaystyle V_{KV}}$ ${\displaystyle {\bar {c}}}$ ${\displaystyle c_{\mathrm {max} }}$

According to Danckwert, the segregation intensity is now defined as ${\displaystyle I}$

${\displaystyle I={\frac {\sigma ^{2}}{\sigma _{\mathrm {max} }^{2}}}{\text{.}}}$

Bothe transforms this into a mixture of intensity ${\displaystyle M}$

${\displaystyle M=1-{\sqrt {I}}=1-{\frac {\sigma }{\sigma _{\mathrm {max} }}}}$

${\displaystyle M=0}$or describes a completely inhomogeneous mixture. or describes a completely homogeneous mixture. ${\displaystyle I=1}$ ${\displaystyle M=1}$ ${\displaystyle I=0}$

The objective of the mixing task has been reached empirically when a statistically secured number of samples reflects a composition that corresponds to a required mixing quality with reference to the population .

The mixing quality is a quality characteristic, ie it makes a statement about the distribution of a size, not about the size itself.

Whether a desired mixing quality can be achieved is fundamentally dependent on the selected mixing method or the selected mixing technology and the parameters with which this method (e.g. speeds, number, shape, arrangement of mixing tools, etc.) is operated.

Calculation of mixing processes

The mathematical modeling of mixing processes is sufficient. Simulations are still very computationally intensive, but can be validated with experimental results in the context of numerical simulation .

When describing mixing processes by means of dimensionless indicators, hydrodynamic indicators such as B. the Reynolds number is the Fourier number

${\displaystyle {\mathit {Fo}}={\frac {M\cdot t}{L^{2}}}}$

where stands for the mixing or dissipation coefficient and for the mixer length, and the Bodenstein number ${\displaystyle M}$ ${\displaystyle L}$

${\displaystyle {\mathit {Bo}}={\frac {u\cdot L}{M}}}$

of importance for the dynamics of mass transport.

Procedures and devices

Continuous or discontinuous operation
In continuous operation, the mixer is in a stationary state. The starting materials are continuously fed in and the mixture is continuously removed. One example is mixing in a conveyor pipe. In discontinuous operation, the cycle of filling in the starting materials; Mix; Repeatedly discharging the mixture . One example is a batch boiler.

Active or passive mixer
In active mixers, the energy required for the relative displacement of particles in the starting materials is not drawn from the starting materials themselves. Examples are ultrasonic waves, vibrations from rising bubbles and pulsating influx. In passive mixers, the required energy is extracted from the incoming raw materials. One example is the super focus mixer . Mixers that contain no moving parts are also known as static mixers. Examples are pipe mixers with steering internals or mixing silos.

Design

• Geometry of the mixing chamber (drum, cylinder, cube, cone, tetrahedron)
• Capacity (test scale (e.g. 2 l), pilot plant scale (20 l), mass production (200 l) or mixer in microreaction technology )

In the case of mixers whose containers and / or mixing tools are mounted on shafts, the number of shafts (single-shaft mixer, multi-shaft mixer) can also be classified.

Means of force input

• Mixer with movable mixing tools (slow-running: screw mixer, high-speed: paddle mixer), cascade vs. cataract
• Mixer with moving container ( drum mixer , conical mixer)
• pneumatic mixer ( fluidized bed mixer , gas jet mixer )

In the case of mixers whose containers and / or mixing tools are mounted on shafts, the following can also be classified according to the relative acceleration of the mixture:

• Free-fall and push mixer ( Froude number , subcritical cascade) ${\displaystyle {\mathit {Fr}}<1}$
• Litter mixer ( , supercritical cataract) ${\displaystyle {\mathit {Fr}}>1}$
• Centrifugal mixer ( ) ${\displaystyle {\mathit {Fr}}\gg 1}$

Substances to be mixed

• one or two phase

see definition of terms

• multi-phase
  • Chemical reaction engineering: catalyst with gas in liquid
  • Biological reaction technology: microorganism with gas in liquid

literature

• Heinrich Schubert: Manual of mechanical process engineering . Weinheim 2003.
• M. Stieß: Mechanical Process Engineering 1 . Springer, Berlin 1995/2008, ISBN 978-3-540-32551-2 .

Individual evidence

1. ↑ ^{a b} Matthias Kraume: Transport processes in process engineering. Springer-Verlag, Berlin / Heidelberg 2012, ISBN 978-3-642-25148-1 , pp. 592-598.
2. ^ PV Danckwerts: The definition and measurement of some characteristics of mixtures. In: Applied Scientific Research, Section A. Vol. 3, No. 4. Springer Netherlands, 1952, pp. 279-296.
3. ↑ Dieter Bothe: Evaluating the Quality of a Mixture: Degree of Homogeneity and Scale of Segregation. In: Micro and Macro Mixing. Springer, Berlin / Heidelberg 2010, ISBN 978-3-642-04548-6 , pp. 17-35.
4. ↑ Matthias Bohnet (Ed.): Mechanical process engineering. Wiley-VCH, Weinheim 2004, ISBN 3-527-31099-1 , pp. 213-229.
5. ↑ Matthias Bohnet (Ed.): Mechanical process engineering. Wiley-VCH, Weinheim 2004, ISBN 3-527-31099-1 , pp. 213-229.
6. ^ V. Hessel et al.: Chemical Micro Process Engineering, processing and plants. Wiley-VCH, Weinheim 2006, ISBN 3-527-30998-5 , p. 4.