Cavitation Driven Exfoliation of Graphene and Two Dimensional Materials

Nomenclature

Symbols are listed in the order used in this article. Unless otherwise stated, quantities are expressed in SI units.

Symbol	Meaning	Unit
A	Projected flake area, newly created surface area, or optical absorbance when written as Aλ; context is stated.	m² or dimensionless
$A_{\lambda }$	Absorbance at wavelength λ.	dimensionless
$A_R$	Equivalent flake aspect ratio.	dimensionless
Atr	Active transducer area.	m²
C	Dispersed nanosheet concentration.	kg m⁻³ or g L⁻¹
$C_0$	Initial dispersed concentration.	kg m⁻³ or g L⁻¹
cp	Specific heat capacity.	J kg⁻¹ K⁻¹
deq	Equivalent particle diameter used in a sedimentation approximation.	m
d95	Particle size below which 95 percent of the feed distribution falls.	m
Dh	Hydraulic diameter.	m
$e_m$	Specific process energy per mass of recovered product.	J kg⁻¹
ER	Erosion rate is based on mass loss.	kg m⁻² s⁻¹
Esys	Total energy within the selected process boundary.	J
Eu	Euler type pressure coefficient.	dimensionless
Ev	Cumulative hydraulic energy density.	J m⁻³
g	Gravitational acceleration, or effective gap when identified in a shear rate relation.	m s⁻² or m
Gc	Effective cleavage energy per unit area.	J m⁻²
h	Nanosheet thickness.	m or nm
$h_0$	Calibrated apparent AFM thickness per layer.	m or nm
$h_L$	Irreversible head loss.	m
Iac	Nominal acoustic intensity.	W m⁻²
ID, IG, I2D	Raman intensities of D, G, and 2D bands.	arbitrary units
La	Empirical in plane crystallite or defect spacing estimate.	nm
l	Optical path length.	m
m	Liquid mass in calorimetry.	kg
$m_0$	Dry starting mass of layered solid.	kg
$m_c$	Coarse reject or recycle mass.	kg
$m_f$	Fine fraction mass.	kg
$m_{\mathrm{loss}}$	Unaccounted mass loss.	kg
$m_p$	Recovered product mass.	kg
$m_{p,\mathrm{spec}}$	Recovered mass meeting the complete product specification.	kg
N	Approximate number of layers.	dimensionless
Np	Number of process passes or cycles.	dimensionless
n	Centrifuge rotational speed.	min⁻¹
p	Static pressure.	Pa
$p_B$	Pressure inside a bubble.	Pa
$p_{\infty }$	Far field liquid pressure.	Pa
$p_u$	Reference upstream pressure.	Pa
$p_v$	Liquid vapor pressure.	Pa
Pac	Acoustic power delivered to the liquid.	W
Pcal	Calorimetrically measured acoustic power.	W
Ph	Hydraulic pump power is associated with the useful pressure drop.	W
Q	Volumetric flow rate.	m³ s⁻¹
R	Bubble radius.	m
RCF	Relative centrifugal force.	multiples of g
Re	Reynolds number.	dimensionless
Rp	Usable production rate.	kg s⁻¹ or kg h⁻¹
S(t)	Normalized dispersion stability index.	dimensionless
t	Time.	s
tc	Idealized bubble collapse time.	s
texp	Cumulative nominal exposure time.	s
u	Characteristic liquid velocity.	m s⁻¹
$v_t$	Terminal settling velocity in a Stokes approximation.	m s⁻¹
Vactive	Active reactor volume.	m³
Wmin	Ideal minimum work to create new surfaces.	J
Yusable	Usable product yield.	%
z	Elevation head coordinate.	m

Greek Letters

Symbol	Meaning	Unit
αλ	Optical extinction coefficient at wavelength λ.	m² kg⁻¹ or L g⁻¹ m⁻¹
γ	Liquid surface tension.	N m⁻¹
γ̇	Shear rate.	s⁻¹
δD	Dispersive Hansen solubility parameter component.	MPa¹ᐟ²
δP	Polar Hansen solubility parameter component.	MPa¹ᐟ²
δH	Hydrogen bonding Hansen solubility parameter component.	MPa¹ᐟ²
Δp	Pressure difference across the active element.	Pa
Δρ	Density difference between particle and liquid.	kg m⁻³
Δu	Velocity difference across a gap or boundary layer.	m s⁻¹
ηE	Mass based energy efficiency.	kg J⁻¹
ηp	Overall pump efficiency.	dimensionless
κ	Selected conservative blockage ratio.	dimensionless
λ	Optical wavelength.	m or nm
λL	Raman laser wavelength.	nm
μ	Dynamic viscosity.	Pa s
ρ	Liquid density.	kg m⁻³
σ	Cavitation number.	dimensionless
τ	Viscous shear stress.	Pa
τpass	Nominal residence time in the active region per pass.	s