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--- en:berechnungen:wandgleitende_materialien [2025/05/28 10:04] – neelest
+++ en:berechnungen:wandgleitende_materialien [2026/07/14 09:55] (aktuell) – cschall
@@ Zeile 1: / Zeile 1: @@
-======Wall-slipping materials======
+======Wall-slipping Materials ======
-The content is currently being processed and will be made available shortly. Please be patient.
+When considering flow processes in rheometers, but also in practical components such as dies, plasticizing units, and between roll gaps, it is usually assumed that the flowing melt adheres to the wall. In the case of polymer melts, experience shows that this applies to the majority of materials. However, there are some materials, including high-viscosity polyethylenes or polyvinyl chloride (PVC, often provided with external lubricants for gentler processing), which tend to exhibit wall-slip effects at high shear stresses or high shear rates.
-When considering the flow processes in rheometers but also in practical modules
+When the transition from wall adhesion to wall slip occurs, most equations used to calculate a flow are no longer valid. Since this is a very complex phenomenon that depends on viscosity, shear rate, shear stress, temperature, and pressure, a simple and stable empirical model is used.
-such as dies, plasticating units and between gaps, the flowing melt is presumed to be
-wall adhering. In polymer melting this is true for the majority of the materials.
-However, there are some materials, among which the ultrahigh molecular
-polyethylene of high density (HDPE) and the economically important polyvinylchloride
-(PVC, frequently provided with outward lubricants for a gentle processing), which are
-wall slipping under certain conditions.
-In order to calculate the plastisicating process with the simulation programs **REX** and
+Due to the complex relationships involved, the influence on the pressure-throughput behavior is neglected; instead, only the reduction in shear dissipation is taken into account in the temperature calculation.
-**PSI**, the option “wall slipping” has been added in the software. For this, critical shear stress values must be entered in the rheological material data as explained in the
-Chapter Rheological Material Data.
-When choosing the menu item Wall slipping, **REX/PSI** considers that wall slipping
+In REX/PSI, wall slip occurs above a critical shear stress. [[..:materialdaten:rheologische_materialdaten|This can be specified as a linear equation as a function of temperature]]. REX/PSI therefore requires the input of two pairs of values for the critical shear stress and the corresponding temperature.
-occurs above the critical wall shear stress. For this, the shear stresses at the barrel
-wall and the root surface are evaluated and limited to a value whose maximum is
-equal to the critical shear stress at the wall.
-$$τ_ {WH,S} > τ_{krit} ⇒ τ_S = τ_{krit}$$
+For the dissipation calculation, the following applies:
-This limitation has an effect on the flow profile in the screw channel and reduces the local pressure gradient. This reduces the pressure build-up capacity, but also the pressure consumption of
+$$ \tau_0 = \eta_0 \cdot \dot{\gamma} $$
-screw zones that are passed over.
+$$ if $$
+$$ \tau_0 > \tau_{crit}(T) $$
+$$ then $$
+$$ \Delta \tau = \tau_0 - \tau_{crit}(T) $$
+$$ \tau_{target} = \tau_{crit}(T) + \Delta \tau \cdot k_{mat} $$
+$$ with $$
+$$ 0 < k_{mat} \leq 1 $$
+$$ it~follows~that $$
+$$ \eta_{wall~slipping} = \frac{\tau_{target}}{\dot{\gamma}} $$
-If a wall-sliding material is to be calculated with **REX/PSI**, two pairs of values consisting of a test temperature and the critical wall shear stress determined at this test temperature must be entered in addition to the characterisation of the flow law using the Carreau or Arrhenius parameters.
+If the local shear stress is greater than the critical shear stress, the shear stress is reduced by means of the factor $k_{mat}$. A value of $0$ corresponds to a hard limit at $\tau_{krit}$, while a value of $1$ would mean no wall slip. Due to the reduced shear stress, a reduced representative viscosity can in turn be calculated, which is used for calculating dissipation. Wall slip therefore leads to a reduction in temperature.
-In addition, the material parameter $k_{mat}$ can be used to describe the increase in the dimensionless sliding velocity $V_{sl}^*$ as a function of the dimensionless shear stress $τ^*$. The required material data, such as the sliding velocity $v_{sl}$ as a function of the wall shear stress $τ$, is determined during the viscosity measurement (e.g. with a high-pressure capillary rheometer).
+**Important:**
-During the measurement of the pressure as a function of the volume flow, discontinuities occur in the double logarithmic diagram for wall-sliding melts in contrast to wall-adhering melts.
+If wall slip is checked in the material data, the values entered there are used. If wall slip is unchecked there, wall slip is still calculated using predefined values, since experience has shown that, especially for high-viscosity polymers with correspondingly high shear stresses, an excessively high temperature would otherwise be calculated. The default values used in this case are a critical shear stress of $\tau_{krit}=100 kPa$ and $k_{mat}=0,25$
-{{ :materialdaten:abb_krit_wandschubspannung_en.svg?nolink&700 |}}
-From the critical pressure $Δp_{krit}$ at which this discontinuity occurs, the critical wall shear stress $τ_{krit}$ can be calculated for a rectangular capillary using the following formula:
-\[τ_{krit} = \frac{\Delta p_{krit}}{2} \frac{h}{l}\]
-These critical shear stresses can be approximated as a straight line equation depending on the temperature. Therefore, **REX/PSI** requires the input of two pairs of values for the critical shear stress and the corresponding temperature.
 ===Further topics===