Stirred tanks are common throughout the chemical process industries (CPI), used as batch reactors and continuous-flow reactors, as well as for physical processing of product formulations in which no chemical reaction is occurring. In all cases, fluid mixing — in which a rotating impeller in a cylindrical tank causes fluid motion and liquid blending to achieve desired process results — is a critical parameter. This one-page reference provides information on stirred tanks in industrial processes and the mixing mechanisms at play within them. The degree of mixing that occurs as a result of the stirring is influenced by various factors, including the internal configuration of the tank, the impeller geometry and the fluid properties.
Tank characteristics
For a stirred tank, equipment dimensions that are important for mixing include the impeller diameter (D), the tank diameter (T) and liquid level (H) (Figure 1). Lengths are often represented as ratios, such as D/T and H/T, to generalize the tank characteristics. The rotational speed of an impeller (N) is also important, and is typically expressed in revolutions per minute (rpm).
FIGURE 1. A basic stirred tank with its important parameters is shown here
An H/T ratio of 1:1 is often cost-effective for general blending. Taller tanks may require multiple impellers. For effective vertical mixing, a D/T ratio of 1:3 is common in a stirred tank with baffles. Baffles are narrow, flat panels attached to the interior of the tank walls to disrupt solid-body rotation of the fluid and create turbulence. Baffles help convert the rotational (tangential) flow created by the rotating impeller into the more effective axial or radial flow [1]. Baffle width, B, is typically about 1/10 to 1/12 of the tank diameter.
Mixing equipment manufacturers offer a wide range of impeller variations, including those with different blade shapes, blade widths, cambers (curvature) and angles relative to the horizontal. Many stirred tanks are mixed using a three- or four-blade turbine mounted at a 45-deg angle to the horizontal (pitched-blade impeller) with the actual blade width one-fifth of the impeller diameter [1]. Others (straight-blade impellers) have blades mounted vertically (90 deg relative to the horizontal plane).
Mixing regimes
Fluid mixing can be categorized into several types, including bulk transport, turbulence and molecular diffusion. In most industrial mixing applications, more than one mixing mechanism is at play simultaneously. For liquid mixing, fluid viscosity, interfacial tension and other factors determine the difficulty of creating and sustaining motion in the fluid.
Bulk transport refers to the large-scale movement of a relatively large portion of material (fluid elements, see section on fluid elements below) from one location in a vessel to another. Bulk transport effects the rearrangement of various portions of the fluid in the reactor. Adjacent volumes of fluid are shuffled in three dimensions.
The rotating impeller gives rise to large-scale flow patterns within the stirred tank that distribute bulk fluid within the tank and overcome segregation of different fluids (different reactants or different components of a formulation, for example). The bulk fluid transport also reduces or eliminates concentration and temperature gradients.
The action of the impeller and baffles also creates fluid turbulence, which generates eddies (fluid vortices) of various sizes and rotational velocities. These eddies physically stretch, fold and fragment large unmixed regions of fluid into smaller regions. This action greatly increases the contact surface between the components being mixed. In turbulent fluids, particles are chaotically moving in all directions and undergoing random velocity changes. Size scales for the eddies are limited by the size of the vessel on the large end, and viscosity of the fluid at the small end.
While turbulence is the most important factor in fluid mixing, random thermal motion of fluid molecules at small scales (molecular diffusion by Brownian motion) also plays a role in mixing at the molecular level. As turbulence reduces the scale of segregation to the smallest possible length scale (the Kolmogorov scale, which sets a limit for how small eddies get before viscosity dominates), molecular diffusion achieves true homogeneity within these smallest eddies.
Fluid elements
A fluid element can be defined as a group of molecules small enough to occupy no more than a microscopic volume (a “point”) in the reactor, but at the same time, large enough for the concept of reactant concentration to be meaningful. As a rough estimate, a clump may be considered to contain 1010 molecules, plus or minus a few orders of magnitude [2].
In a macrofluid, molecules move together in clumps; the clumps are distributed among different residence times within a vessel, but all molecules within a clump have the same age. In a microfluid, the clumps are dispersed, and all molecules move independently of one another, regardless of age. A real process fluid is generally neither a pure macrofluid, nor a pure microfluid, but may approach one or the other of these extremes [2].
References
1. Dickey, D., Liquid Mixing in Stirred Tanks, Chem. Eng., August 2019, pp. 24–35.
2. Dudukovic, M.P. and Felder, R.M., Mixing Effects in Chemical Reactors-Vol. 5 — Micromixing and the Segregated Flow Model, AIChE, Modular Instruction Series, 1984.