| Symbol | Meaning | Symbol | Meaning |
|---|---|---|---|
| $A,B,C$ | Coefficients of the Carreau Law | $S$ | Specific energy input |
| $A$ | Overall cross section of the screw channel | $S_{Ma}$ | Overall specific energy input of the entire machine |
| $A$ | Parameter for the temperature calculation in the melt film | $S_{Ve}$ | Specific energy input in the processing unit |
| $A_{1-4}$ | Area | $T$ | Temperature |
| $A_{1-4}$ | Variables for the calculation of the starting temperature profile | $T_{A,E}$ | Temperature at the beginning, end |
| $A_{\Delta}$ | Area of the triangular gap between kneading discs | $T_B,T_0$ | Reference temperature |
| $A_f$ | Filled cross section within a screw channel | $T_i$ | Mass temperature at the location i |
| $A_{fr}$ | Free cross section | $T_F$ | Solids temperature |
| $A_{Pr}$ | Cross section of the screw profile | $T_1$ | Reference temperature |
| $\overline{A_{zw}}$ | Average free surface in the intermeshing region | $T_{Fl}$ | Flow temperature |
| $A_{Zyl}$ | Cross sectional area of the barrel | $T_G$ | Glass transition temperature |
| $B$ | Variables for the calculation of the starting temperature profile | $T_K$ | Crystalline melt temperature |
| $C$ | Machine constant | $T_M, \overline{T}, T$ | Mass temperature |
| $C_{x,z},C_{1,2,3}$ | Parameter for the calculation of the wall shear rate | $T_{M,0-5}$ | Mass temperature at the location 0–5 |
| $D$ | Inner barrel diameter | $T_S$ | Melt temperature |
| $D_F$ | Pressure screen value | $\overline{T_{Start}}$ | Average start temperature |
| $D_N$ | Nominal screw diameter | $T_Z$ | Barrel temperature |
| $D_S$ | Outer screw diameter | $T_{Z,1-5}$ | Barrel temperature at the location 1–5 |
| $E$ | Extensive material data | $U_{max}$ | Maximum wetted circumference ($s_R = 0$) |
| $F$ | Distribution function | $U_{min}$ | Minimum wetted circumference ($s_R = 0$) |
| $F$ | Factor | $\overline{U}$ | Average wetted circumference ($s_R = 0$) |
| $F$ | Screen area | $U(\Theta^*)$ | Wetted circumference dependent on $\Theta^*$ |
| $\Delta H$ | Difference of enthalpies | $\dot{V}$ | Volumetric flow rate |
| $K$ | Coefficient of the power law | $\dot{V}_{ei}$ | Volumetric flow rate in the intermeshing region |
| $K_{Spalt}$ | Coefficient of the power law in the clearance | $\dot{V}_{fr1,2}$ | Free volume |
| $K_{Kanal}$ | Coefficient of the power law in the channel | $\dot{V}_{Leck}$ | Volumetric leakage flow rate |
| $K_{0T}$ | Consistency | $\dot{V}_{Kanal}$ | Volumetric flow rate in the screw channel |
| $L$ | Axial length, screw length | $\dot{V}_p$ | Pressure flow |
| $L_{Ele}$ | Axial length of the pair of screw elements | $V_{real}$ | Realistic free volume |
| $L_{ei}$ | Axial length of the intermeshing region | $V_{theor}$ | Theoretical free volume |
| $L_{fr}$ | Axial length of the free channel section | $\dot{V}_S$ | Drag flow rate |
| $L_{Kn}$ | Overall axial length of the kneading blocks | $\dot{V}_{Steg}$ | Leakage flow rate |
| $L_R$ | Axial backpressure length | $\dot{V}_x$ | Volumetric flow rate in x-direction |
| $L_{Zw}$ | Axial length of the intermeshing area | $\dot{V}_z$ | Volumetric flow rate in z-direction |
| $M_{1,2}$ | Centerpoints | $V_{Zw}$ | Average volume of the intermeshing region |
| $M_D$ | Torque | $X$ | Concentration of the additive |
| $M_{D\%}$ | Proportional torque | $X$ | Width of the solid bed |
| $P$ | Power | $X$ | Ratio of element length and lead |
| $P_{1-3}$ | Power in the functional sections | $X_{1,2}$ | Width of the solid bed |
| $P_{1-4}, P_{M1-M4}$ | Points | $Y_1$ | Parameter of the pressure-throughput equation |
| $P_{Ma.,exp.}$ | Experimentally determined machine power | $Y_2$ | Parameter of the pressure-throughput equation |
| $P_{Ve.,ber.}$ | Calculated power of the processing unit | $Z$ | Degree of dispersion |
| $Z_{ei}$ | Unwound length of the intermeshing region | ||
| $Z_{fr}$ | Unwound length of the channel region | ||
| $Z,z$ | Cartesian coordinate (channel direction), length |
| Symbol | Meaning | Symbol | Meaning |
|---|---|---|---|
| $\alpha$ | Staggering angle of the kneading discs | $\pi_{p,Ele}$ | Dimensionless pressure gradient in a pair of elements |
| $\beta$ | Temperature shift factor (Arrhenius law) | $\pi_{p,ei}$ | Dimensionless pressure gradient in the intermeshing region |
| $\dot{\gamma}$ | Shear rate | $\pi_{p,fr}$ | Dimensionless pressure gradient in the free channels |
| $\dot{\gamma}_{min}$ | Minimum shear rate | $\pi^{\dot{V}}$ | Dimensionless flow rate |
| $\dot{\gamma}_{max}$ | Maximum shear rate | $\pi^{\dot{m}}$ | Dimensionless mass flow rate |
| $\overline{\delta}$ | Average thickness of the melt film | $\pi^{\dot{V}}_{Kanal}$ | Dimensionless flow rate in the screw channel |
| $d$ | Thickness of the melt film | $\pi^{\dot{V}}_x$ | Dimensionless flow rate in x-direction |
| $\overline{\delta_0}$ | Average initial thickness of the melt film | $\pi^{\dot{V}}_{Spalt}$ | Dimensionless flow rate in the radial clearance |
| $\delta_0$ | Initial thickness of the melt film | $\pi^{\dot{V}}_z$ | Dimensionless flow rate in z-direction |
| $\varepsilon$ | Accuracy | $\pi^{\dot{V}}_{Ele}$ | Dimensionless flow rate in a pair of screw elements |
| $z$ | Dimensionless z-coordinate | $\pi^{\dot{V}}_{ei}$ | Dimensionless flow rate in the intermeshing region |
| $\eta$ | Melt viscosity | $\pi^{\dot{V}}_{fr}$ | Dimensionless flow rate in the free channels |
| $\overline{\eta}$ | Average effectivity | $\rho_0$ | Density at reference temperature (melt regime) |
| $\eta_{Ge}$ | Effectivity of the gear box | $\rho_m$ | Slope of the density at reference temperature (melt regime) |
| $\eta_{Mo}$ | Effectivity of the motor | $\rho, \rho_S$ | Density, bulk density |
| $\Theta$ | Polar coordinates | $\rho_{Schütti}$ | Bulk density at the element i |
| $\overline{\Theta}$ | Average dimensionless residence time | $\sigma^2$ | Variance of the residence time distribution |
| $\Theta$ | Dimensionless residence time | $\sigma_M$ | Axial mixing coefficient |
| $\Theta$ | Dimensionless temperature | $\overline{\sigma_M}$ | Average axial mixing coefficient |
| $\Theta_0$ | Initial temperature | $\tau$ | Shear stress |
| $\Theta_1$ | Minimum dimensionless residence time | $\overline{\tau}$ | Average shear stress |
| $\Theta_B$ | Dimensionless width of the residence time distribution | $\overline{\tau_W}$ | Average wall shear stress |
| $\Theta_S$ | Self cleaning number | $\tau_{0x}$ | Wall shear stress in x-direction |
| $\lambda_0$ | Thermal conductivity at $T_0$ (melt regime) | $\tau_{0z}$ | Wall shear stress in z-direction |
| $\lambda_1$ | Slope of the linearized thermal conductivity | $\tau_{yi,j}$ | Shear stress |
| $\lambda$ | Thermal conductivity | $\Phi,\phi$ | Flight angle |
| $\xi$ | Dimensionless coordinate in y-direction | $\Psi$ | Standardised melt film thickness |
| $\pi_{0,1}$ | Dimensionless number | $\omega$ | Angular velocity |
| $\pi_{geo}$ | Dimensionless geometrical number | $\Omega$ | Intermeshing angle |
| $\pi_p$ | Dimensionless pressure gradient | $\phi_{1A},\phi_{2A},\phi_{1F},\phi_{2F},\phi_1,\phi_2,\phi_{1z},\phi_{2z}$ | Constants for the linearized throughput equation |
| $\pi_{pKanal}$ | Dimensionless pressure gradient in the channel | $\varphi$ | Lead angle |
| $\pi_{px}$ | Dimensionless pressure gradient in x-direction | $\varphi_S$ | Lead angle at the outer screw diameter |
| $\pi_{pSpalt}$ | Dimensionless pressure gradient in the radial clearance | $\varphi_{S,Kn}$ | Characteristic lead angle of kneading blocks |
| $\pi_{pz}$ | Dimensionless pressure gradient in z-direction | $\overline{\Psi}$ | Standardised thickness of the melt film |
| $\pi_{p,ges}$ | Dimensionless overall pressure gradient | $\overline{\Psi_S}$ | To $\delta_0$ standardized radial clearance |
| $\Psi_S$ | To $\delta_0$ standardized radial clearance | ||
| $\Psi_{1,2}$ | Standardised thickness of the melt film |
| Symbol | Meaning |
|---|---|
| $Br$ | Brinkmann Number |
| $Gz$ | Graetz Number |
| Symbol | Meaning | Symbol | Meaning |
|---|---|---|---|
| A, B, C | Corner points | ber. | Calculated |
| Ele | Element, pair of elements | ei. | Value in the intermeshing region |
| ESE | Single screw extruder | exp. | Experimentally determined |
| Kanal | Channel section | fr. | Value in the free channel section |
| Ma | Machine | i, j | Counter variable |
| Spalt | Radial clearance | min, max | Minimum, maximum |
| Ve | Processing unit | r., l. | Right, left |
| Zw | Intermeshing region |