Cavitation-Assisted Particle Dispersion

10 Scale-up, equipment selection, and troubleshooting

10.1 Parameters to preserve

No single similarity parameter guarantees scale up. A robust strategy preserves the variables that control the specific formulation:

• Cavitation number or a validated geometry specific inception margin.

• Local pressure drop profile and pressure recovery rate.

• Critical passage dimension relative to the incoming coarse tail.

• Local dissipation rate and collapse exposure.

• Nominal passes and residence time distribution.

• Solids loading, viscosity, surface tension, vapor pressure, and gas content.

• Inlet and outlet temperature.

• Stabilizer amount relative to newly created surface area.

• Wear material and collapse location.

Figure 10.1. Representative operating domains for selected cavitation dispersion devices. Boundaries are conceptual, not universal design limits [58].

10.2 Throughput scaling by numbering up

For parallel geometrically identical passages, throughput can be increased by adding passages while preserving the pressure history in each element. This numbering up approach is often more reliable than enlarging one micro orifice because enlargement changes velocity gradients, cavity structure, and nuclei behavior. The manifold must distribute flow uniformly and avoid dead legs.

Figure 10.2. Numbering up of identical critical passages in a recirculating production loop [58].

For larger static reactors, scale up can increase the number of holes or stages while preserving hole diameter and pressure drop. For dynamic processors, tip speed, gap, stage count, and power per unit throughput are relevant, but equal tip speed does not guarantee equal cavity cloud structure. Pilot testing remains necessary.

10.3 Heat removal

Even when particle breakup is highly localized, most supplied power ultimately becomes heat. At steady state, the required heat exchanger duty is approximately:

where $P_{motor}$ is motor power transferred to the process and the second term represents any allowable sensible temperature rise. The exchanger should be sized from measured power and temperature, not an assumed cavitation efficiency.

10.4 Stagewise development procedure

Figure 10.3. Recommended development workflow for cavitation-assisted particle dispersing.

A practical scale-up sequence is:

• Establish a reproducible feed preparation and analytical method.

• Define the primary particle, aggregate, agglomerate, and floc structure.

• Determine the minimum pressure and pass count that meet immediate size targets.

• Optimize stabilizer level and verify aged size and rheology.

• Confirm morphology, crystal structure, and purity.

• Measure temperature rise, pressure pulsation, flow, and wear.

• Increase batch volume while preserving the same critical reactor.

• Add parallel passages or stages before changing critical geometry.

• Verify manifold balance and actual pass distribution.

• Repeat aging, functional, cleaning, and contamination tests at production scale.

Table 10.1. Scale-up verification checks.

Check	Laboratory evidence	Production verification
Cavitation inception	Pressure, flow, acoustic or visual response	Same operating margin at every parallel element
Exposure	Pass count and loop residence time	Tracer test or validated recirculation model
Product size	PSD and microscopy	At line PSD using retained reference method
Stabilization	Aged PSD, zeta potential, rheology	Storage, thermal cycling, and shipping simulation
Heat	Reactor inlet and outlet temperature	Heat exchanger duty and steady state balance
Wear	Short duration inspection and blanks	Campaign length elemental and dimensional checks
Cleanability	Bench cleaning test	Full skid drainability and validated cleaning cycle

10.5 Troubleshooting

Table 10.2. Troubleshooting guide.

Observation	Probable cause	Corrective action
Little size reduction	Cavitation not established, recovery too slow, agglomerates too strong, viscosity too high	Verify pressure and flow, modify geometry, increase passes, predilute, use staged processing
$D_{50}$ decreases but $D_{90}$ remains high	Bypass, poor tank mixing, plugging, small resistant population	Improve recirculation, inspect passages, add a coarse first stage, extend exposure cautiously
Size improves immediately but rebounds	Inadequate stabilizer, unfavorable pH or ionic strength, high collision rate	Add stabilizer before processing, adjust chemistry, reduce handling intensity after processing
Viscosity rises sharply	Increased surface area, network formation, excessive dispersion, temperature change	Optimize dispersant, reduce exposure, control temperature, verify solids concentration
Viscosity decreases but conductivity or strength worsens	Flake or fiber aspect ratio damage	Reduce pressure or passes, use larger passages, verify morphology
Metal concentration increases	Cavitation erosion or pump wear	Relocate collapse zone, change materials, install replaceable inserts, reduce severity
Coarse particles increase	Cavitation induced agglomeration or contamination	Review chemistry, gas content, pump suction, and stabilization; reduce cavitation
Poor repeatability	Variable nuclei, gas entrainment, temperature, sampling, or analytical dilution	Standardize degassing, tank level, temperature, sampling, and measurement protocol
Passage plugs	Incoming tail too large, sedimentation, poor premixing	Add screening or a coarse stage, increase passage size, improve tank suspension
Excessive foaming	Gas entrainment, surfactant, return line above liquid level	Submerge return, improve degassing, adjust formulation, reduce suction leakage