Table 2 Nomenclature and typical values of DLD parameters
Notation | Description | Typical value | Units |
|---|---|---|---|
\(A\) | Area of the channel cross-section |  ~ 32 × 103 | µm2 |
\(a\) | Half-width of the rectangular channel | Â | Â |
\(A_1 ,\;A_n ,\;B_1 ,\;B_n\) | Arbitrary constants defined by boundary conditions | Â | Â |
\(B\) | Half-height of the rectangular channel | Â | Â |
\(C,\;D,\;E\) | Arbitrary constants defined by boundary conditions | Â | Â |
\(C_S\) | Lift coefficient for the shear gradient lift force | 0.5 | Â |
\(C_W\) | Lift coefficient for the wall interaction force | 0.5 | Â |
\(c\) | Radius of unit cell for the Happel’s model |  |  |
\(D_C\) | Critical particle diameter | Â | Â |
\(D_C^{Davis}\) s | Critical diameter introduced by Davis et. al |  ~ 9.97 | µm |
\(D_C^{Inglis}\) | Critical diameter introduced by Inglis et. al |  ~ 8.12 | µm |
\(D_C^{Zhang}\) | Critical diameter introduced by Zhang et. al | Â | Â |
\(D_H\) | Hydraulic diameter of the channel |  ~ 24 | µm |
\(D_P\) | Particle diameter | 10 | µm |
\(De\) | Dean number |  ~ 3.43 |  |
\(F_C\) | Centrifugal force |  ~ 0.0885 | nN |
\(F_D\) | Stokes drag force |  ~ 12.3 | nN |
\(F_S\) | Shear gradient lift force |  ~ 0.352 | nN |
\(F_W\) | Wall interaction force |  ~ 0.0255 | nN |
\(g\) | Gap between the two posts | 30 | µm |
\(h\) | Height of the channel | 20 | µm |
\({\text{j}}\) | Imaginary unit | Â | Â |
\(M\) | Whole number, period of the post array | 20 | Â |
\(N\) | Number of terms in the series | Â | Â |
\(n\) | Summation index | Â | Â |
\(P\) | Perimeter of the channel cross-section | Â | Â |
\(p\) | Pressure | Â | Â |
\(Q\) | Volume flow rate in the microfluidic channel | 6000 | μL h−1 |
\(r\) | Radial coordinate in cylindrical coordinates | Â | Â |
\(R\) | Radius of the cylindrical post | 10 | µm |
\(R_C\) | Radius of the channel curvature | Â | Â |
\(Re_C\) | Channel Reynolds number |  ~ 3.13 |  |
\(Re_P\) | Particle Reynolds number |  ~ 0.542 |  |
\(U_{Ave}\) | Average fluid velocity in the channel |  ~ 0.0521 | m s−1 |
\(U_{Max}\) | Maximum fluid velocity in the channel |  ~ 0.130 | m s−1 |
\(u\) | x-velocity component | Â | Â |
\(u(x),\;u(x,\;y)\) | Fluid velocity in the microchannel | Â | Â |
\(u_r\) | Radial velocity component | Â | Â |
\(v\) | y-velocity component | Â | Â |
\(v_\theta\) | Angular velocity component | Â | Â |
\(W\) | Total width of the microfluidic channel | 1600 | µm |
\(w\) | Auxiliary parameter for the Inglis diameter | Â | Â |
\(x,\;y,\;z\) | Cartesian coordinates | Â | Â |
\(\alpha\) | Volume fraction occupied by cylindrical posts | Â | Â |
\(\beta\) | Width of the first streamline | Â | Â |
\(\varepsilon\) | Row shift fraction | 0.05 | Â |
\(\varepsilon *\) | Column shift fraction | Â | Â |
\(\lambda\) | Transverse period of the post array | 50 | µm |
\(\lambda *\) | Longitudinal period of the post array | Â | Â |
\(\mu_f\) | Fluid viscosity | 1.0 | mPa s |
\(\theta\) | Angular coordinate in cylindrical coordinates | Â | Â |
\(\rho_f\) | Fluid density | 1000 | kg m−3 |
\(\rho_P\) | Particle density | 1100 | kg m−3 |
\(\omega\) | Vorticity | Â | Â |
\(\xi ,\;\zeta\) | Dimensionless geometric coefficients | Â | Â |
\(\Psi\) | Stream function | Â | Â |