Introduction & Context

Mixer type selection is a fundamental task in Process Engineering, ensuring that the mechanical energy provided by an impeller is effectively transferred to the fluid to achieve specific process objectives such as blending, solids suspension, or gas dispersion. Selecting the correct impeller geometry is critical to avoid inefficient power consumption, mechanical failure, or inadequate mixing performance.

This calculation is typically used during the design phase of stirred tank reactors or when scaling up processes from laboratory to industrial production. By characterizing the fluid regime through dimensionless numbers, engineers can match the impeller type to the fluid's physical properties and the required mixing intensity.

Methodology & Formulas

The selection process relies on calculating the Impeller Reynolds Number to determine the flow regime, followed by the application of Power Number correlations to estimate the energy requirements.

First, the rotational speed is converted from revolutions per minute to revolutions per second:

\[ n_rps = impeller_rpm / 60.0 \]

The fluid viscosity is converted from centipoise to Pascal-seconds:

\[ mu = mu_cp * 0.001 \]

The Impeller Reynolds Number (Re) is calculated to identify the flow regime:

\[ reynolds_number = (rho * n_rps * (impeller_diameter^2)) / mu \]

The Power Draw (P) is determined using the Power Number (Np), which varies based on the flow regime and impeller geometry:

\[ power_draw = np_val * rho * (n_rps^3) * (impeller_diameter^5) \]

Finally, the mixing intensity is evaluated by calculating the Power per Unit Volume:

\[ power_per_volume = power_draw / tank_volume \]

Flow Regime	Reynolds Number (Re) Range	Impeller Type	Power Number (Np) Logic
Laminar	Re < 10.0	Anchor	`np_val = 300.0 / reynolds_number` (Typical for anchor impellers)
Transitional	10.0 ≤ Re ≤ 10000.0	Pitched-Blade Turbine	`np_val = 1.5` (Approximate constant for 45° PBT; note: Np can vary with Re)
Turbulent	Re > 10000.0	Rushton Turbine	`np_val = 5.0` (Typical constant for standard Rushton turbines)

When selecting equipment for high-viscosity applications, process engineers must evaluate the following criteria:

The rheological profile of the fluid, specifically whether it is Newtonian or non-Newtonian.
The required shear rate to achieve the desired product homogeneity.
The torque capacity of the drive system to prevent motor stall during startup.
The geometric configuration of the impeller to ensure effective bulk turnover without dead zones.

The Reynolds number dictates the flow pattern and the necessary impeller design:

Low Reynolds numbers (laminar flow) require high-solidity impellers like anchors or helical ribbons to move the entire fluid mass.
High Reynolds numbers (turbulent flow) allow for the use of high-speed, low-solidity impellers like axial flow turbines to promote rapid blending.
Transition zones often require hybrid impeller designs to manage varying viscosity levels during the batch cycle.

Static mixers are preferred when the process meets these specific conditions:

The application involves continuous inline processing rather than batch production.
The fluid components have low to medium viscosity and are easily miscible.
There is a strict requirement to minimize maintenance costs and eliminate moving parts.
The pressure drop across the system is within the allowable limits of the pump capacity.

Worked Example: Impeller Selection for Blending

A process engineer needs to select an appropriate mixer for blending two low-viscosity aqueous solutions in a batch tank. The goal is to achieve homogeneity within a reasonable time.

Knowns:

Fluid density, \( \rho = 1000.0 \text{ kg/m}^3 \)
Fluid viscosity, \( \mu = 1.0 \text{ cP} \)
Tank working volume, \( V = 0.785 \text{ m}^3 \)
Proposed impeller diameter, \( D = 0.33 \text{ m} \)
Proposed impeller speed, \( N = 150.0 \text{ rpm} \)
Process objective: Blending

Step-by-Step Calculation:

Convert rotational speed to revolutions per second (rps):
\( N_{\text{rps}} = \frac{150.0}{60} = 2.5 \text{ rps} \).
Convert viscosity to SI units:
\( \mu = 1.0 \text{ cP} \times 0.001 = 0.001 \text{ Pa} \cdot \text{s} \).
Calculate the impeller Reynolds number to determine the flow regime:
\( Re = \frac{\rho \cdot N_{\text{rps}} \cdot D^{2}}{\mu} = \frac{1000.0 \cdot 2.5 \cdot (0.33)^{2}}{0.001} = 272250.0 \).
Since \( Re > 10000 \), the flow is fully turbulent.
Select impeller type and its Power Number (\(N_p\)). For turbulent flow, a Rushton turbine is appropriate with a constant \(N_p\).
\( N_p = 5.0 \).
Calculate the power draw from the impeller:
\( P = N_p \cdot \rho \cdot N_{\text{rps}}^{3} \cdot D^{5} = 5.0 \cdot 1000.0 \cdot (2.5)^{3} \cdot (0.33)^{5} = 305.745 \text{ W} \).
Calculate the power input per unit tank volume:
\( P/V = \frac{P}{V} = \frac{305.745}{0.785} = 389.484 \text{ W/m}^{3} \).

Final Answer:

The calculated Reynolds number of 272250.0 confirms turbulent flow, validating the initial choice of a Rushton turbine. The required power input is 305.745 W, resulting in a mixing intensity of 389.484 W/m³. This value falls within the typical range for vigorous blending or solids suspension, confirming the selection is suitable for the stated objective.

"Un projet n'est jamais trop grand s'il est bien conçu." — André Citroën

"La difficulté attire l'homme de caractère, car c'est en l'étreignant qu'il se réalise." — Charles de Gaulle