Emulsification and Homogenization in Rotor-Stator Mixers

16 Measurement, sampling, and validation

Reliable experimental evidence depends on a defined relationship between the process, the collected sample, and the reported measurement. Droplet size, topology, power, and temperature should be measured on a consistent basis so that apparent processing effects can be distinguished from analytical artifacts. The procedures below specify the information needed for reproducible comparison and for validation of the illustrative calculation.

16.1 Droplet size measurement

A measurement strategy must distinguish the droplet population from aggregates, entrained bubbles, and sampling artifacts. Laser diffraction provides volume sensitive distributions over a broad range of droplet sizes. Dynamic light scattering is useful for sufficiently dilute submicron dispersions, but the scattering response can be strongly influenced by a small population of larger objects. Microscopy reveals topology, flocculation, shape, and coarse droplets, although its field of view and resolution limit representativeness. Validated image analysis can provide a number based distribution. Complementary methods are therefore preferable when the product contains several structural scales.

The refractive index, absorption assumptions, inversion or dispersion model, obscuration, dilution medium, sonication, and sample handling should be documented. Dilution can change ionic strength or emulsifier availability, disrupt flocs, and induce osmotic transport. A qualified protocol should distinguish intentionally coarse and fine samples without creating the change it is intended to measure.

16.2 Sampling location and time

Sampling defines which part of the process is actually represented by a reported distribution. A sample from the vessel surface may differ from the discharge of the active head. Batch samples should be collected from a reproducible location and after a specified circulation interval. Inline sample lines should have minimal stagnant volume and be flushed before collection. Prompt analysis followed by analysis after a defined rest interval helps separate the immediate breakup result from subsequent aggregation or coalescence.

For a specified diameter statistic, an empirical homogenization efficiency can be expressed as

where $d_0$ and df are the initial and final values of the same diameter statistic and $d_{\text{lim}}$ is its fitted limiting value.

This index provides convenient normalization within the fitted model, but it does not replace the coarse fraction or stability measurements. A high value can coexist with unacceptable large droplets. The value of the fitted limiting diameter and the conditions over which it was obtained should be reported.

16.3 Power, torque, flow, and pressure measurement

Hydrodynamic and energy comparisons require measurements of actual operating conditions. Shaft torque and rotational speed provide a direct estimate of shaft power; calibrated electrical measurements require corrections for drive and motor efficiency. The baseline must be evaluated at comparable speed and thermal conditions using a method compatible with the equipment. Inline trials should record flow, upstream and downstream pressures, and product temperature. Time resolved pressure measurements are particularly useful when periodic forcing or cavitation is part of the proposed mechanism.

16.4 Experimental acceptance criteria

Acceptance criteria should describe reproducible product and process performance. An illustrative qualification plan may require several consecutive batches, or an appropriate period of continuous operation, to meet limits for droplet distribution, temperature, power, and storage stability. The number of replicates and observation period should be chosen from the process variability and intended use. Process capability should be assessed only after the measurement procedure, and operating conditions have been demonstrated to be stable.

Table 16.1. Recommended reporting set for rotor stator emulsification studies.

Category	Minimum reported information
Formulation	Identity and mass or volume fraction of all phases and emulsifiers
Fluid properties	Density, viscosity, interfacial tension, temperature, and measurement methods
Mixer geometry	Rotor diameter, stator type, gap, open area, slot or hole size, number of stages
Operation	Speed, tip speed, flow, processing time, passes, feed order, temperature, backpressure
Energy	Net power, torque method, specific energy, pressure loss, cooling duty
Product	$d_{10}$, $d_{32}$, $d_{43}$ or $d_{90}$, span, rheology, topology, stability
Sampling	Location, time, dilution, storage before measurement
Statistics	Replicates, uncertainty, fitting range, and excluded data
Mechanical	Wear state, generator condition, seal arrangement, cleaning state