Nomenclature



Jy

dimensionless mass flux in Y direction

)

/s)

)

Particle Deposition in Microfluidic Devices at Elevated Temperatures

http://dx.doi.org/10.5772/intechopen.78240

131

/N m2 )

kB Boltzmann's constant (1.38064852 <sup>10</sup><sup>23</sup> J/K)

n dimensionless particle number concentration

Pe Peclet number based on average flow velocity

n∞,p particle number concentration in bulk liquid (/m3

Re Reynolds number based on average flow velocity

Uavg average flow velocity in microchannels (m/s)

Vvdw dimensionless van der Waals interaction potential

<sup>e</sup> elementary electric charge (1.602176620898 <sup>10</sup><sup>19</sup> C)

<sup>ε</sup><sup>0</sup> absolute dielectric constant of vacuum (8.845 <sup>10</sup><sup>12</sup> <sup>C</sup><sup>2</sup>

)

V dimensionless total interaction potential

Vedl dimensionless EDL interaction potential

VT dimensionless thermophoretic potential

λ London retardation wavelength (100 nm)

κ Debye-Hückel parameter (m)

μ dynamic viscosity of liquid (N s/m<sup>2</sup>

L length of the microchannel (m)

Q volume flow rate of liquid (m<sup>3</sup>

Sh Sherwood number

T absolute temperature (K)

T<sup>0</sup> reference temperature (293.15 K)

VG dimensionless gravity potential

VL dimensionless lift potential

z ionic valence

ε dielectric constant

ξ zeta potential (V)

Greek symbols

t time (s)

n particle number concentration (/m<sup>3</sup>


μ dynamic viscosity of liquid (N s/m<sup>2</sup> )

a<sup>2</sup> radius of interacting particle 2 (m)

B width of the microchannel (m)

Dx diffusivity in X direction (m2

Dy diffusivity in Y direction (m2

DT thermal diffusion coefficient (m<sup>2</sup>

D<sup>∞</sup> Stokes-Einstein diffusivity (m<sup>2</sup>

Fedl dimensionless EDL interaction force

FL dimensionless hydrodynamic lift force

H dimensionless particle-wall separation

jx particle flux in X direction (m<sup>2</sup> s

jy particle flux in Y direction (m<sup>2</sup> s

Jx dimensionless mass flux in X direction

FT dimensionless thermophoretic force

FG dimensionless gravity force

Fvdw dimensionless van der Waals interaction force

tion

3 (J)

130 Microfluidics and Nanofluidics

w half channel height (m)

A<sup>132</sup> Hamaker constant for the interaction between substances 1 and 2 in medium

/s)

/s)

/s)

/s)

Da double layer asymmetry number in the HHF expression for the EDL interac-

f1(H) UHCC correction function for diffusivity perpendicular to the solid surface

Dl double layer number in the HHF expression for the EDL interaction

f3(H) UHCC correction function for diffusivity parallel to the solid surface

f4(H) UHCC correction function for diffusivity along the flow direction (X)

Fx X component of the total force exerted on the particle (N)

Fy Y component of the total force exerted on the particle (N)

h minimum separation distance between particle and wall (m)

1 )

1 )

H<sup>0</sup> dimensionless primary energy minimum separation

H∞ dimensionless particle-wall separation in bulk fluid

