ABSTRACT
Valuable insights into the mixing operation can be gained from a consideration of system behavior as a function of the Reynolds number 7VRe [27]. This is shown schematically in Fig. 3, in which various dimensionless parameters (dimensionless velocity, v/ND; pumping number, Q/ND3; power number, NP = (Pgc)/(pN3D5); and dimensionless mixing time, tmN) are represented as a log-log function of AfRe. Although density, viscosity, mixing vessel diameter, and impeller rotational speed are often viewed by formulators as independent variables, their interdependency, when incorporated in
Fig. 3 Various dimensionless parameters (dimensionless velocity, v* = v/ND; pumping number, NQ = Q/ND3; power number, NP = (Pgc)/(pN3D5); and dimensionless mixing time, r* = tmN) as a function of the Reynolds number for the analysis of turbine-agitator systems. (Adapted from Ref. 27.)
the dimensionless Reynolds number, is quite evident. Thus, the schematic relationships embodied in Fig. 3 are not surprising.*
Mixing time is the time required to produce a mixture of predetermined quality; the rate of mixing is the rate at which mixing proceeds toward the final state. For a given formulation and equipment configuration, mixing time tm depends on material properties and operation variables. For geometrically similar systems, if the geometrical dimensions of the system are transformed to ratios, mixing time can be expressed in terms of a dimensionless number, i.e., the dimensionless mixing time 0m or tJSf
tmN = Qm = /(iVRe, NFr) =>/(iVRe) (5) The Froude number, NFr = v/^/Zg , is similar to AfRe; it is a measure of the inertial stress to the gravitational force per unit area acting on a fluid. Its inclusion in Eq. (5) is justified when density differences are encountered; in the absence of substantive differences in density, e.g. for emulsions more so than for suspensions, the Froude term can be neglected. Dimensionless mixing time is independent of the Reynolds number for both laminar and turbulent flow regimes, as indicated by the plateaus in Fig. 3. Nonetheless, as there are conflicting data in the literature regarding the sensitivity of 6m to the rheological properties of the formulation and to equipment geometry, Eq. (5) must be regarded as an oversimplification of the mixing operation. Considerable care must be exercised in applying the general relationship to specific situations.
