Hydrodynamic Cavitation in Food and Fermentation Processing

Nomenclature

Unless otherwise stated, quantities are expressed in SI units. Product specific analytical units are retained where they are conventional in the cited literature.

Symbol	Definition	SI unit or status
a	Specific interfacial area	m² m⁻³
C	Concentration or model constant, as defined locally	varies
C∞	Asymptotic extracted concentration	kg m⁻³ or equivalent
$c_p$	Specific heat capacity	J kg⁻¹ K⁻¹
d	Particle or droplet diameter	m
d32	Sauter mean diameter	m
D10, D50, D90	Particle or droplet diameters below which 10%, 50%, or 90% of volume lies	m
$D_h$	Hydraulic diameter	m
DP2, DP3, DP4+	Glucose oligomer fractions in HPLC analysis	concentration
$E_s$	Specific energy input, hydraulic or electrical as specified	J kg⁻¹
$E_a$	Apparent activation energy	J mol⁻¹
F	Equivalent process lethality at a reference temperature	time
$f_p$	Nominal pass or loop turnover frequency	s⁻¹
g	Gravitational acceleration	m s⁻²
G	Glucose concentration in the UFTG equation	mass concentration
$h_L$	Irreversible head loss	m of fluid
k	Apparent first order rate constant	s⁻¹
k0	Arrhenius pre exponential factor	s⁻¹
$k_{La}$	Volumetric mass transfer coefficient	s⁻¹
K	Consistency coefficient in a rheological model	Pa sⁿ
LR	Microbial log reduction	dimensionless
m	Mass	kg
$m_{s,max}$	Maximum theoretical soluble extract	kg
N, N0	Viable population after treatment and initially	CFU mL⁻¹ or CFU g⁻¹
n	Flow behavior index	dimensionless
$n_p$	Nominal cumulative number of passes	dimensionless
P	Product amount or power, as defined locally	varies
$P_{el}$	Electrical power	W
$P_h$	Hydraulic power	W
p	Pressure	Pa
$p_B$	Pressure inside a bubble	Pa
$p_h$	Perimeter of an orifice hole	m
$p_{mp}$	Internal perimeter of the downstream main pipe	m
$p_r$	Recovery or downstream pressure	Pa
$p_v$	Liquid vapor pressure	Pa
Q	Volumetric flow rate	m³ s⁻¹
R	Bubble radius or universal gas constant, as defined locally	m or J mol⁻¹ K⁻¹
R_E	Incremental ethanol energy return	dimensionless
Re	Reynolds number	dimensionless
$r_P$	Productivity	kg m⁻³ s⁻¹ or equivalent
S, O	Soy base and okara stream masses	kg
T	Absolute or Celsius temperature, as specified	K or °C
t	Time	s
u	Mean liquid velocity	m s⁻¹
$u_{rel}$	Relative velocity responsible for deformation or breakup	m s⁻¹
$u_t$	Throat or restriction velocity	m s⁻¹
UFTG	Unfermented total glucose equivalent	mass concentration
V	Process volume	m³
$V_L$	Total liquid holdup in a recirculating loop	m³
$v_s$	Settling or creaming velocity	m s⁻¹
We	Weber number	dimensionless
$x_p$	Protein mass fraction	kg kg⁻¹
Yp	Protein extraction yield	%
$Y_{P/S}$	Product yield on substrate	kg kg⁻¹
z	Temperature sensitivity parameter in thermal lethality modeling	K
$C_v$	Cavitation number defined from downstream pressure, vapor pressure, density, and restriction velocity	dimensionless
$V_a$	Active internal volume of the cavitation device	m³
τ̄	Mean nominal residence time in the active device	s
$\mathrm{\Delta }{T}_{ad}$	Ideal adiabatic temperature rise from the specified energy input	K

Abbreviations: AA, alpha amylase; CFU, colony forming units; CIP, cleaning in place; CO2, carbon dioxide; DDGS, distillers dried grains with solubles; DSD, droplet size distribution; HC, hydrodynamic cavitation; HPH, high pressure homogenization; HPLC, high performance liquid chromatography; HTD, hydrothermodynamic; MPC, milk protein concentrate; N2, nitrogen; O2, oxygen; PHE, plate heat exchanger; PME, pectin methylesterase; PPO, polyphenol oxidase; PSD, particle size distribution; SSF, simultaneous saccharification and fermentation; UFTG, unfermented total glucose; WPC, whey protein concentrate.

Greek Letters

Symbol	Letter name	Meaning
α	alpha	Orifice plate geometry parameter or alpha amylase designation, depending on context
β	beta	Orifice or area ratio parameter, where used in cited studies
γ	gamma	Surface or interfacial tension
Δ	delta	Difference between two states, such as pressure or temperature rise
ε	epsilon	Turbulent energy dissipation rate per unit mass
η	eta	Efficiency, extraction efficiency, or heating efficiency, as subscripted
μ	mu	Dynamic or apparent viscosity, also, the SI prefix micro when preceding a unit
ρ	rho	Density
σ	sigma	Cavitation number
${\sigma }_{mod}$	sigma modified	Geometry adjusted cavitation number for a multi hole plate
τ	tau	Shear stress
τ0	tau zero	Yield stress
τR	tau R	Mean residence time
γ̇	gamma dot	Shear rate