Hydrodynamic Cavitation in Emulsification and Homogenization

2 Emulsion Fundamentals and Product Metrics

2.1 Emulsion classes and terminology

Oil in water (O/W) emulsions contain oil droplets in an aqueous continuous phase. Water in oil (W/O) emulsions contain water droplets in an oil phase. Multiple emulsions, such as W/O/W and O/W/O, contain droplets within droplets. Pickering emulsions are stabilized predominantly by solid particles adsorbed at the interface. The terms macroemulsion, miniemulsions, nanoemulsion, and microemulsion are used inconsistently across disciplines, so every technical specification should state the actual measurement method and size statistics rather than rely on a category name alone [1,2,10,11].

Table 1. Practical classification of liquid dispersion systems. Size boundaries are approximate and overlap among fields.

System	Typical droplet scale	Thermodynamic status	Common preparation route	Design implication
Coarse or macroemulsion	1 to 100 µm, sometimes larger	Unstable at equilibrium; kinetically stabilized	Agitated tank, static mixer, rotor stator	Separation may be rapid unless viscosity or interfacial stabilization is sufficient
Miniemulsion or submicron emulsion	0.1 to 1 µm	Kinetically stabilized	High shear, high pressure homogenization, cavitation	Requires rapid surface coverage and control of the coarse tail
Nanoemulsion	Roughly 20 to 500 nm	Kinetically stabilized	High pressure homogenization, microfluidization, ultrasonication, cavitation, phase inversion	Optical appearance, ripening, and surfactant demand become dominant
Microemulsion	Commonly 10 to 100 nm	Thermodynamically stable over a composition region	Spontaneous self-assembly with high surfactant and often cosurfactant loading	Formulation, not mechanical energy, is the controlling variable
Multiple emulsion	Internal and external droplets may span submicron to tens of micrometres	Kinetically stabilized and structurally complex	Sequential emulsification	Excessive second stage stress can destroy internal droplets
Pickering emulsion	Broad range	Kinetically stabilized by particles	High shear plus particle wetting control	Particle wettability and adsorption energy govern stability

2.2 Droplet size distribution and interfacial area

A single mean diameter cannot fully describe an emulsion. Number weighted measurements emphasize small droplets, while volume weighted and scattering based methods emphasize large droplets. The generalized moment mean diameter for discrete size classes is:

where $n_i$ is the number of droplets in class $i$ and $d_i$ is the representative diameter. The Sauter mean diameter, which preserves the volume to area ratio, is:

The volume weighted mean diameter is:

For spherical droplets, the interfacial area per unit emulsion volume is related directly to $d_{32}$:

where ${\varphi }_d$ is the dispersed phase volume fraction. This equation explains why a modest reduction in diameter creates a large increase in surface area and surfactant demand. The breadth of a distribution is often summarized by the span:

where $d_{10}$, $d_{50}$, and $d_{90}$ are cumulative percentile diameters. A process may reduce $d_{32}$ while leaving an undesirable coarse tail. For quality control, the minimum reporting set should therefore include the measurement method, dilution protocol, basis of weighting, $d_{32}$ or Z average, $d_{90}$, span or polydispersity index, temperature, and the time between processing and analysis.

Table 2. Droplet size and distribution metrics used in emulsification studies.

Metric	Physical meaning	Strength	Main limitation
$d_{32}$	Diameter with the same volume to area ratio as the distribution	Directly related to interfacial area and many breakup models	Can conceal a coarse tail
$d_{43}$	Volume weighted mean	Sensitive to large droplets and useful for process failure detection	Strongly affected by a small number of coarse droplets
$d_{10}$, $d_{50}$, $d_{90}$	Cumulative distribution percentiles	Describe distribution location and coarse fraction	Depend on weighting basis and instrument model
Span	Relative width from $d_{10}$, $d_{50}$, $d_{90}$	Simple comparison of breadth	Does not show multimodality
PDI	Polydispersity index from dynamic light scattering	Useful for submicron systems	Not interchangeable with laser diffraction span
Z average	Cumulants mean from dynamic light scattering	Standard for many nanoemulsions	Sensitive to dilution and scattering assumptions
Specific interfacial area	Area per unit mass or volume	Connects droplet size to mass transfer and surfactant demand	Requires spherical droplet and composition assumptions

The reversible work required to create interface is the increase in interfacial free energy:

where γ is the interfacial tension. Mechanical equipment supplies far more energy than the thermodynamic minimum because most input is dissipated as bulk turbulence, heat, vibration, sound, viscous loss, and pump inefficiency. Interfacial area generated per unit energy is therefore a more revealing comparison metric than nominal power alone [2,12,13].

2.3 Stability mechanisms

Small droplets reduce gravitational separation, but they do not make an emulsion thermodynamically stable. In the dilute Stokes regime, the creaming or sedimentation velocity is approximated by

where ${\rho }_c$ and ${\rho }_d$ are continuous and dispersed phase densities, $g$ is gravitational acceleration, and ${\mu }_c$ is continuous phase viscosity. The quadratic diameter dependence is a major reason that homogenization slows creaming. The equation becomes inaccurate in concentrated, non Newtonian, flocculated, or hindered settling systems.

Ostwald ripening can be summarized by a cubic radius growth law:

where $K_{\text{OR}}$ depends on interfacial tension, solubility of the dispersed phase in the continuous phase, diffusivity, molar volume, temperature, and formulation. Hydrodynamic cavitation does not remove the need to control ripening, coalescence, or flocculation. It can even increase the driving force for instability by creating more interface. The resulting emulsion remains useful only when interfacial coverage, electrostatic or steric repulsion, continuous phase rheology, and storage conditions provide an adequate kinetic barrier [1,2,14].

Figure 3. Predictive hierarchy for cavitation assisted emulsification. Formulation and operating inputs determine the cavitation field and local stress distribution; breakup and stabilization models then predict the droplet size distribution and product properties [9].