Hydrodynamic Cavitation in Food and Fermentation Processing

2 Food Specific Process Metrics and Kinetics

The hydraulic descriptors, bubble dynamics relations, equipment families, and energy definitions used in this article are summarized in this section. The relations retained below are those required to interpret microbial, enzymatic, extraction, texture, and quality responses in food and fermentation systems.

2.1 Microbial, enzymatic, extraction, and quality kinetics

Microbial and enzyme responses are generally nonlinear because cavitation simultaneously modifies temperature, aggregation state, membrane permeability, and mass transfer. A reported log reduction must therefore be associated with the complete time, temperature, and pressure history and with the initial population. Mild cavitation can disaggregate cell clusters and increase microbial exposure to heat or dissolved carbon dioxide, whereas higher severity can directly damage cell walls and membranes. Conversely, entrained gas can cushion bubble collapse and reduce mechanical lethality [19,20,25-27].

Extraction benefits arise from reduced particle size, broken cell walls, renewed liquid films, and rapid removal of solubilized material from the surface. The same mechanisms can release oxidative enzymes, cause excess fines, or increase downstream separation difficulty. Optimal treatment is therefore commonly observed before the maximum energy input. Orange juice, ice cream, dairy proteins, soy slurry, and corn mash all show evidence that additional passes or treatment time can eventually reduce quality or separation efficiency [21,28-31,35,40]. To quantify antimicrobial efficacy, microbial reduction is conventionally evaluated via log reduction ($L_R$):

where LR is microbial log reduction, N0 is the initial viable population, and N is the population after treatment. The analytical detection limit must be stated. For preliminary screening and evaluation of antimicrobial efficacy, a simple first order inactivation model is frequently employed:

where k is an apparent first order inactivation constant. This model is convenient for screening, but shoulders, tails, subpopulation differences, and time varying temperature may require more advanced models. The influence of temperature on the reaction or inactivation rate constant is commonly described by the Arrhenius relationship:

where k0 is the pre exponential factor, Ea is apparent activation energy, R is the universal gas constant, and T is absolute temperature. A cavitation assisted treatment may change both the apparent kinetic constant and the effective thermal history. The rate of solute extraction or dissolution in liquid solid or liquid liquid systems can be modeled via first order mass transfer kinetics:

where C(t) is the extracted or dissolved concentration, $C_{\infty }$ is the asymptotic concentration, and $k_{L}a$ is an overall mass transfer coefficient times specific interfacial area. Hydrodynamic cavitation significantly enhances extraction performance by increasing $k_{L}a$ through intensified microturbulence, shock waves, and accelerated surface renewal.

2.2 Hydraulic, thermal, and residence time descriptors

Pressure alone is not a transferable measure of cavitation severity. Food applications should report the pressure reference locations, local velocity, vapor pressure, flow rate, active volume, treatment time, number of passes, temperature history, and the energy boundary used for calculation. These descriptors support comparison among Venturi, orifice, vortex, and rotor devices while recognizing that equal dimensionless numbers do not guarantee equal product response [6-8,63]. The severity and inception of cavitation are commonly characterized by the dimensionless cavitation number ($C_v$):

where Cᵥ is cavitation number, P₂ is the fully recovered downstream pressure, Pᵥ is liquid vapor pressure at the measured temperature, ρ is density, and Vₜ is mean velocity at the active restriction. The exact pressure locations must be stated.

To evaluate the mechanical energy input delivered to the fluid system:

where Pₕ is hydraulic power delivered across the active pressure drop, Q is volumetric flow rate, and ΔP is the measured pressure difference. Pump input power is larger than Pₕ because pump and drive efficiencies are below unity.

The specific hydraulic energy ($E_s$) imparted to the product is defined as:

where Eₛ is specific hydraulic energy, t is treatment time, and m is treated product mass. For a continuous single pass process, m is the mass that crosses the device during the selected accounting interval.

For closed loop recirculation systems, the nominal pass count ($n_p$) is calculated as:

where nₚ is nominal pass count and Vₗ is the liquid inventory in the recirculation loop. This relation does not replace residence time distribution measurement when short circuiting, dead zones, or broad mixing times are possible.

The mean nominal residence time ($\overline{\tau }$) within the active restriction zone of the device is defined as:

where τ̄ is mean nominal residence time in the active device and Vₐ is active internal volume. The local bubble lifetime and high stress exposure are normally much shorter than the bulk residence time. The theoretical temperature increase resulting from viscous and hydraulic energy dissipation, assuming an adiabatic process, is expressed as:

where ΔTₐd is the ideal adiabatic temperature rise and cₚ is product specific heat capacity. The measured temperature rise will differ because of vessel heat loss, cooling, phase change, and energy dissipated outside the product.

The mechanical stability and breakup of droplets, bubbles, or suspended particles under hydrodynamic stress are evaluated using the dimensionless Weber number ($\text{We}$):

where We is Weber number, uᵣₑₗ is a representative relative velocity, d is a droplet, bubble, or particle length scale, and γ is interfacial tension. Values above the applicable breakup threshold favor deformation and fragmentation, but concentrated food systems require formulation specific validation.

For microbial or enzyme claims, hydraulic descriptors must be paired with the complete temperature and holding history. For emulsification and particle processing, they must be paired with the complete distribution, not only a mean size. For fermentation, they must be paired with viable cell response, substrate conversion, gas transfer, and product formation.

Figure 2.1. Relative importance of cavitation functions across the applications

Application	Extraction	Homogenization	Pasteurization aid	Heating	Emulsification	Gas dispersion	Fermentation aid
Beer / wort	primary	important	important	primary	supporting	primary	important
Juice / puree	important	primary	important	important	supporting	supporting	—
Milk / dairy	supporting	primary	important	important	important	important	—
Liquid egg	—	primary	primary	primary	supporting	—	—
Ice cream	—	primary	important	important	primary	important	—
Mayonnaise / dressing	—	important	supporting	supporting	primary	important	—
Corn ethanol	primary	important	supporting	important	—	—	primary

Figure 2.1. Relative importance of cavitation functions across the applications [66].