Mixing (process engineering)

The type of operation and equipment used during mixing depends on the state of materials being mixed (liquid, semi-solid, or solid) and the miscibility of the materials being processed. In this context, the act of mixing may be synonymous with stirring-, or kneading-processes.[1]

Mixing of liquids occurs frequently in process engineering. The nature of liquids to blend determines the equipment used. Single-phase blending tends to involve low-shear, high-flow mixers to cause liquid engulfment, while multi-phase mixing generally requires the use of high-shear, low-flow mixers to create droplets of one liquid in laminar, turbulent or transitional flow regimes, depending on the Reynolds number of the flow. Turbulent or transitional mixing is frequently conducted with turbines or impellers; laminar mixing is conducted with helical ribbon or anchor mixers.[2]

Dry blenders are a type of industrial mixer which are typically used to blend multiple dry components until they are homogeneous. Often minor liquid additions are made to the dry blend to modify the product formulation. Blending times using dry ingredients are often short (15–30 minutes) but are somewhat dependent upon the varying percentages of each component, and the difference in the bulk densities of each. Ribbon, paddle, tumble and vertical blenders are available. Many products including pharmaceuticals, foods, chemicals, fertilizers, plastics, pigments, and cosmetics are manufactured in these designs. Dry blenders range in capacity from half-cubic-foot laboratory models to 500-cubic-foot production units. A wide variety of horsepower-and-speed combinations and optional features such as sanitary finishes, vacuum construction, special valves and cover openings are offered by most manufacturers.

Blending powders is one of the oldest unit-operations in the solids handling industries. For many decades powder blending has been used just to homogenize bulk materials. Many different machines have been designed to handle materials with various bulk solids properties. On the basis of the practical experience gained with these different machines, engineering knowledge has been developed to construct reliable equipment and to predict scale-up and mixing behavior. Nowadays the same mixing technologies are used for many more applications: to improve product quality, to coat particles, to fuse materials, to wet, to disperse in liquid, to agglomerate, to alter functional material properties, etc. This wide range of applications of mixing equipment requires a high level of knowledge, long time experience and extended test facilities to come to the optimal selection of equipment and processes.

Machine for incorporating liquids and finely ground solids

Solid-solid mixing can be performed either in batch mixers, which is the simpler form of mixing, or in certain cases in continuous dry-mix, more complex but which provide interesting advantages in terms of segregation, capacity and validation.[3] One example of a solid–solid mixing process is mulling foundry molding sand, where sand, bentonite clay, fine coal dust and water are mixed to a plastic, moldable and reusable mass, applied for molding and pouring molten metal to obtain sand castings that are metallic parts for automobile, machine building, construction or other industries.

Liquid–solid mixing is typically done to suspend coarse free-flowing solids, or to break up lumps of fine agglomerated solids. An example of the former is the mixing granulated sugar into water; an example of the latter is the mixing of flour or powdered milk into water. In the first case, the particles can be lifted into suspension (and separated from one another) by bulk motion of the fluid; in the second, the mixer itself (or the high shear field near it) must destabilize the lumps and cause them to disintegrate.

One example of a solid–liquid mixing process in industry is concrete mixing, where cement, sand, small stones or gravel and water are commingled to a homogeneous self-hardening mass, used in the construction industry.

Solid suspension

Suspension of solids into a liquid is done to improve the rate of mass transfer between the solid and the liquid. Examples include dissolving a solid reactant into a solvent, or suspending catalyst particles in liquid to improve the flow of reactants and products to and from the particles. The associated eddy diffusion increases the rate of mass transfer within the bulk of the fluid, and the convection of material away from the particles decreases the size of the boundary layer, where most of the resistance to mass transfer occurs. Axial-flow impellers are preferred for solid suspension because solid suspension needs momentum rather than shear, although radial-flow impellers can be used in a tank with baffles, which converts some of the rotational motion into vertical motion. When the solid is denser than the liquid (and therefore collects at the bottom of the tank), the impeller is rotated so that the fluid is pushed downwards; when the solid is less dense than the liquid (and therefore floats on top), the impeller is rotated so that the fluid is pushed upwards (though this is relatively rare). The equipment preferred for solid suspension produces large volumetric flows but not necessarily high shear; high flow-number turbine impellers, such as hydrofoils, are typically used. Multiple turbines mounted on the same shaft can reduce power draw.[5]

Solid volume fraction in a mixing tank [6]

The degree of homogeneity of a solid-liquid suspension can be described by the RSD (Relative Standard Deviation of the solid volume fraction field in the mixing tank). A perfect suspension would have a RSD of 0% but in practice, a RSD inferior or equal to 20% can be sufficient for the suspension to be considered homogeneous,[7] although this is case-dependent. The RSD can be obtained by experimental measurements or by calculations. Measurements can be performed at full scale but this is generally unpractical, so it is common to perform measurements at small scale and use a "scale-up" criterion to extrapolate the RSD from small to full scale. Calculations can be performed using a computational fluid dynamics software or by using correlations built on theoretical developments, experimental measurements and/or computational fluid dynamics data. Computational fluid dynamics calculations are quite accurate and can accommodate virtually any tank and agitator designs, but they require expertise and long computation time. Correlations are easy to use but are less accurate and don’t cover any possible designs. The most popular correlation is the ‘just suspended speed’ correlation published by Zwietering (1958).[8] It’s an easy to use correlation but it is not meant for homogeneous suspension. It only provides a crude estimate of the stirring speed for ‘bad’ quality suspensions (partial suspensions) where no particle remains at the bottom for more than 1 or 2 seconds. Another equivalent correlation is the correlation from Mersmann (1998).[9] For ‘good’ quality suspensions, some examples of useful correlations can be found in the publications of Barresi (1987),[10] Magelli (1991),[11] Cekinski (2010) [12] or Macqueron (2017).[6] Machine learning can also be used to build models way more accurate than "classical" correlations.[6][13]

Liquids and gases are typically mixed to allow mass transfer to occur. For instance, in the case of air stripping, gas is used to remove volatiles from a liquid. Typically, a packed column is used for this purpose, with the packing acting as a motionless mixer and the air pump providing the driving force. When a tank and impeller are used, the objective is typically to ensure that the gas bubbles remain in contact with the liquid for as long as possible. This is especially important if the gas is expensive, such as pure oxygen, or diffuses slowly into the liquid. Mixing in a tank is also useful when a (relatively) slow chemical reaction is occurring in the liquid phase, and so the concentration difference in the thin layer near the bubble is close to that of the bulk. This reduces the driving force for mass transfer. If there is a (relatively) fast chemical reaction in the liquid phase, it is sometimes advantageous to disperse but not recirculate the gas bubbles, ensuring that they are in plug flow and can transfer mass more efficiently.

Rushton turbines have been traditionally used to disperse gases into liquids, but newer options, such as the Smith turbine and Bakker turbine are becoming more prevalent.[14] One of the issues is that as the gas flow increases, more and more of the gas accumulates in the low pressure zones behind the impeller blades, which reduces the power drawn by the mixer (and therefore its effectiveness). Newer designs, such as the GDX impeller, have nearly eliminated this problem.

Gas–solid mixing may be conducted to transport powders or small particulate solids from one place to another, or to mix gaseous reactants with solid catalyst particles. In either case, the turbulent eddies of the gas must provide enough force to suspend the solid particles, which otherwise sink under the force of gravity. The size and shape of the particles is an important consideration, since different particles have different drag coefficients, and particles made of different materials have different densities. A common unit operation the process industry uses to separate gases and solids is the cyclone, which slows the gas and causes the particles to settle out.

Multiphase mixing occurs when solids, liquids and gases are combined in one step. This may occur as part of a catalytic chemical process, in which liquid and gaseous reagents must be combined with a solid catalyst (such as hydrogenation); or in fermentation, where solid microbes and the gases they require must be well-distributed in a liquid medium. The type of mixer used depends upon the properties of the phases. In some cases, the mixing power is provided by the gas itself as it moves up through the liquid, entraining liquid with the bubble plume. This draws liquid upwards inside the plume, and causes liquid to fall outside the plume. If the viscosity of the liquid is too high to allow for this (or if the solid particles are too heavy), an impeller may be needed to keep the solid particles suspended.

Schematic drawing of a fluidized bed reactor

For liquid mixing, the nomenclature is rather standardized:

• Impeller Diameter, "D" is measured for industrial mixers as the maximum diameter swept around the axis of rotation.
• Rotational Speed, "N" is usually measured in revolutions per minute (RPM) or revolutions per second (RPS). This variable refers to the rotational speed of the impeller as this number can differ along points of the drive train.
• Tank Diameter, "T" The inside diameter of a cylindrical vessel. Most mixing vessels receiving industrial mixers will be cylindrical.
• Power, "P" Is the energy input into a system usually by an electric motor or a pneumatic motor
• Impeller Pumping Capacity, "Q" The resulting fluid motion from impeller rotation.

Many of the equations used for determining the output of mixers are empirically derived, or contain empirically-derived constants. Since mixers operate in the turbulent regime, many of the equations are approximations that are considered acceptable for most engineering purposes.

When a mixing impeller rotates in the fluid, it generates a combination of flow and shear. The impeller generated flow can be calculated with the following equation:

${\displaystyle Q=Fl*N*D^{3}}$

Flow numbers for impellers have been published in the North American Mixing Forum sponsored Handbook of Industrial Mixing.[15]

The power required to rotate an impeller can be calculated using the following equations:

${\displaystyle P=P_{o}\rho N^{3}D^{5}}$ (Turbulent regime)[16]

${\displaystyle P=K_{p}\mu N^{2}D^{3}}$ (Laminar regime)

${\displaystyle P_{o}}$ is the (dimensionless) power number, which is a function of impeller geometry; ${\displaystyle \rho }$ is the density of the fluid; ${\displaystyle N}$ is the rotational speed, typically rotations per second; ${\displaystyle D}$ is the diameter of the impeller; ${\displaystyle K_{p}}$ is the laminar power constant; and ${\displaystyle \mu }$ is the viscosity of the fluid. Note that the mixer power is strongly dependent upon the rotational speed and impeller diameter, and linearly dependent upon either the density or viscosity of the fluid, depending on which flow regime is present. In the transitional regime, flow near the impeller is turbulent and so the turbulent power equation is used.

The time required to blend a fluid to within 5% of the final concentration, ${\displaystyle {\theta _{95}}}$, can be calculated with the following correlations:

${\displaystyle {\theta _{95}}={\frac {5.40}{P_{o}^{1 \over 3}N}}({\frac {T}{D}})^{2}}$ (Turbulent regime)

${\displaystyle {\theta _{95}}={\frac {34596}{P_{o}{1 \over 3}N^{2}D^{2}}}({\frac {\mu }{\rho }})({\frac {T}{D}})^{2}}$ (Transitional region)

${\displaystyle {\theta _{95}}={\frac {896*10^{3}K_{p}^{-1.69}}{N}}}$ (Laminar regime)

The Transitional/Turbulent boundary occurs at ${\displaystyle P_{o}^{1 \over 3}Re=6404}$

The Laminar/Transitional boundary occurs at ${\displaystyle P_{o}^{1 \over 3}Re=186}$

A magnetic stirrer

At a laboratory scale, mixing is achieved by magnetic stirrers or by simple hand-shaking. Sometimes mixing in laboratory vessels is more thorough and occurs faster than is possible industrially. Magnetic stir bars are radial-flow mixers that induce solid body rotation in the fluid being mixed. This is acceptable on a small scale, since the vessels are small and mixing therefore occurs rapidly (short blend time). A variety of stir bar configurations exist, but because of the small size and (typically) low viscosity of the fluid, it is possible to use one configuration for nearly all mixing tasks. The cylindrical stir bar can be used for suspension of solids, as seen in iodometry, deagglomeration (useful for preparation of microbiology growth medium from powders), and liquid–liquid blending. Another peculiarity of laboratory mixing is that the mixer rests on the bottom of the vessel instead of being suspended near the center. Furthermore, the vessels used for laboratory mixing are typically more widely varied than those used for industrial mixing; for instance, Erlenmeyer flasks, or Florence flasks may be used in addition to the more cylindrical beaker.

When scaled down to the microscale, fluid mixing behaves radically different.[17][18] This is typically at sizes from a couple (2 or 3) millimeters down to the nanometer range. At this size range normal advection does not happen unless it is forced by a hydraulic pressure gradient. Diffusion is the dominant mechanism whereby two different fluids come together. Diffusion is a relatively slow process. Hence a number of researchers had to devise ways to get the two fluids to mix. This involved Y junctions, T junctions, three-way intersections and designs where the interfacial area between the two fluids is maximized. Beyond just interfacing the two liquids people also made twisting channels to force the two fluids to mix. These included multilayered devices where the fluids would corkscrew, looped devices where the fluids would flow around obstructions and wavy devices where the channel would constrict and flare out. Additionally channels with features on the walls like notches or groves were tried.

One way to know if mixing is happening due to advection or diffusion is by finding the Peclet number. It is the ratio of advection to diffusion. At high Peclet numbers (> 1), advection dominates. At low Peclet numbers (< 1), diffusion dominates.

Peclet number = (flow velocity × mixing path) / diffusion coefficient

At an industrial scale, efficient mixing can be difficult to achieve. A great deal of engineering effort goes into designing and improving mixing processes. Mixing at industrial scale is done in batches (dynamic mixing), inline or with help of static mixers. Moving mixers are powered with electric motors that operate at standard speeds of 1800 or 1500 RPM, which is typically much faster than necessary. Gearboxes are used to reduce speed and increase torque. Some applications require the use of multi-shaft mixers, in which a combination of mixer types are used to completely blend the product.[19]

In addition to performing typical batch mixing operations, some mixing can be done continuously. Using a machine like the Continuous Processor, one or more dry ingredients and one or more liquid ingredients can be accurately and consistently metered into the machine and see a continuous, homogeneous mixture come out the discharge of the machine.[20] Many industries have converted to continuous mixing for many reasons. Some of those are ease of cleaning, lower energy consumption, smaller footprint, versatility, control, and many others. Continuous mixers, such as the twin-screw Continuous Processor, also have the ability to handle very high viscosities.

Turbines

A selection of turbine geometries and power numbers are shown below.

Selected Turbine Geometries and Power Numbers

Name	Power number	Flow direction	Blade angle (degrees)	Number of blades	Blade geometry
Rushton turbine	4.6	Radial	0	6	Flat
Pitched blade turbine	1.3	Axial	45–60	3–6	Flat
Hydrofoil	0.3	Axial	45–60	3–6	Curved
Marine Propeller	0.2	Axial	N/A	3	Curved

Axial flow impeller (left) and radial flow impeller (right).

Different types of impellers are used for different tasks; for instance, Rushton turbines are useful for dispersing gases into liquids, but are not very helpful for dispersing settled solids into liquid. Newer turbines have largely supplanted the Rushton turbine for gas–liquid mixing, such as the Smith turbine and Bakker turbine.[21] The power number is an empirical measure of the amount of torque needed to drive different impellers in the same fluid at constant power per unit volume; impellers with higher power numbers require more torque but operate at lower speed than impellers with lower power numbers, which operate at lower torque but higher speeds.

Other

Industrial Paddle Mixer

Industrial Paddle Mixer.

Industrial V Blender.

Industrial Ribbon Blender.

Industrial Double Cone Blender.

Industrial High shear Mixer/Granulator.

Drum-Blender

Double shaft mixer for high-viscosity materials

• Ribbon Blender

  Ribbon blenders are very common in process industries for performing dry-mixing operations. The mixing is performed thanks to 2 helix (ribbon) welded on the shafts. Both helix move the product in opposite directions thus achieving the mixing[27] (see picture of ribbon blender).

• V Blender
• Twin-Screw Continuous Blender[28]
• Continuous Processor
• Cone Screw Blender
• Screw Blender
• Double Cone Blender
• Double Planetary
• High Viscosity Mixer
• Counter-rotating
• Double & Triple Shaft
• Vacuum Mixer
• High Shear Rotor Stator
• Impinging mixer
• Dispersion Mixers
• Paddle
• Jet Mixer
• Mobile Mixers
• Drum Blenders
• Intermix mixer
• Horizontal Mixer
• Hot/Cold mixing combination
• Vertical mixer
• Turbomixer
• Planetary mixer

  A planetary mixer is a device used to mix round products including adhesives, pharmaceuticals, foods (including dough), chemicals, electronics, plastics and pigments.

  This mixer is ideal for mixing and kneading viscous pastes (up to 6 million centipoise) under atmospheric or vacuum conditions. Capacities range from 0.5 US pints (0.24 L; 0.42 imp pt) through 750 US gallons (2,800 L; 620 imp gal). Many options including jacketing for heating or cooling, vacuum or pressure, vari speed drives, etc. are available.

  The blades each rotate on their own axes, and at the same time on a common axis, thereby providing complete mixing in a very short timeframe.

• Banbury mixer

  The Banbury mixer is a brand of internal batch mixer, named for inventor Fernley H. Banbury. The "Banbury" trademark is owned by Farrel Corporation. Internal batch mixers such as the Banbury mixer are used for mixing or compounding rubber and plastics. The original design dates back to 1916.[29] The mixer consists of two rotating spiral-shaped blades encased in segments of cylindrical housings. These intersect so as to leave a ridge between the blades. The blades may be cored for circulation of heating or cooling. Its invention resulted in major labor and capital savings in the tire industry, doing away with the initial step of roller-milling rubber.[30] It is also used for reinforcing fillers in a resin system.

• Mixing paddle
• Dry blending

• Dry Blender Selection Criteria Technical Paper

• Wiki on equipment for mixing bulk solids and powders
• Visualizations of fluid dynamics in mixing processes
• A textbook chapter on mixing in the food industry Archived 3 February 2019 at the Wayback Machine
• Information on Solids mixing - powderprocess.net
• Mixing tank - ace-chn.com
• Mixing tank - MiXING-TANK.COM