In continuous compounding of an ethylene-vinyl acetate foam soling formulation containing 18–28 wt% vinyl acetate, an activated azodicarbonamide blowing agent at 4.0 phr, zinc oxide at 1.2 phr, zinc stearate at 0.6 phr, and calcium carbonate at 10–20 phr, the terminal melt temperature at the screw tip of a 90 mm single-screw extruder with L/D 30:1, a barrier section, and a Maddock mixing section commonly reaches 138–146°C even though the barrel set points remain between 105°C and 120°C. The local viscous heat generation is the controlling variable rather than the barrel heating capacity, because the activated azodicarbonamide decomposition onset in the continuous phase is observed as an exotherm starting at 150–170°C by differential scanning calorimetry at 10°C/min under nitrogen. A practical processing window of ±5°C around a die melt set point of 128°C therefore becomes critical: if the screw-tip temperature exceeds 145°C, premature gas evolution produces surface blowholes, irregular cell size, and a density spread that widens from ±0.02 g/cm³ to ±0.06 g/cm³. Split tear strength under ASTM D624-00(2020) in such over-sheared batches typically falls below 2.5 N/mm, and the foam soling surface exhibits localized collapse because the gas-loss zone in the metering section has been initiated before the die entry. On the same production line, the screw speed is usually limited to 45–55 min⁻¹; raising the speed to 65 min⁻¹ raises the screw-tip melt temperature by an additional 8–12°C at constant barrel settings. This thermal offset is not eliminated by lowering the barrel temperature alone, because the heat generation term scales with the square of the local shear rate.

The issue is compounded by the rheological profile of EVA foam compounds. At a melt temperature near 130°C, the apparent viscosity can range from 900 Pa·s to 1500 Pa·s at shear rates of 50–100 s⁻¹, producing a viscous dissipation term of sufficient magnitude to override the thermal boundary condition imposed by the barrel cooling circuit. The screw geometry determines where the limiting temperature occurs: the metering channel depth and flight clearance create two distinct shear regimes, with the shallow flight clearance contributing disproportionately to local heating even though its volume fraction is small. Because the activated azodicarbonamide decomposition is kinetic, a short residence-time excursion above the onset temperature may initiate gas release that cannot be reversed by downstream cooling. This explains why production-scale single-screw foam extrusion facilities often operate with tempered screw cores, oil-based barrel cooling units rated to 180°C, and water-cooled feed throats at 40–60°C. Under these conditions, the observed melt temperature at the screw tip can remain 15–30°C above the barrel set point without necessarily causing decomposition, provided the residence time does not exceed approximately 35–45 s. Published data for this specific configuration is limited, but the general relationship between screw speed and melt-temperature rise is well established in industrial extrusion practice.

How Does Flight Clearance and Screw Speed Set the Shear Heating Ceiling in Single-Screw Extrusion?

For a single-screw extruder, the dominant shear rate in the screw channel is approximated by the drag flow expression γ̇_c = π D N / 60 h, where D is the screw diameter in metres, N is the screw speed in revolutions per minute, and h is the metering channel depth in metres. The shear rate in the flight clearance is given by the same tip-speed relationship divided by the clearance width δ. For a 90 mm screw running at 55 min⁻¹ with a metering depth of 4.2 mm and a flight clearance of 0.15 mm, the channel shear rate is approximately 62 s⁻¹, while the flight-clearance shear rate approaches 1730 s⁻¹. The local viscous dissipation is Φ = η γ̇², so the flight-clearance region generates energy at roughly 3.6×10⁹ W/m³ when the viscosity is 1200 Pa·s, compared with 4.6×10⁶ W/m³ in the channel. In adiabatic terms, the channel contribution over a 35 s residence time would correspond to a temperature rise of approximately 75–85°C for a melt density of 930 kg/m³ and a heat capacity of 2300 J/(kg·K), but industrial barrel cooling removes much of this energy. The actual screw-tip melt temperature above the barrel set point is therefore a balance between the square-law shear heating term and the heat-transfer coefficient of the barrel-cooling circuit, which for water-cooled steel barrels typically falls in the range 50–150 W/(m²·K).

The practical consequence for footwear soling compounds is that screw speed limits are not arbitrary. In a compound with a 5°C decomposition-processing window, the allowable speed is calculated from the terminal melt-temperature limit rather than from throughput demand. Because Φ scales with N², a 20% increase in screw speed from 50 min⁻¹ to 60 min⁻¹ can increase the local heat generation by approximately 44% if the melt viscosity remains unchanged. Shear thinning partially offsets this effect, but the reduction in viscosity with temperature and rate does not fully compensate. Production records on 90 mm single-screw machines with L/D 30:1 indicate that when the terminal melt temperature is held at 143°C, the screw speed tolerance may be as narrow as ±3 min⁻¹ for sensitive EVA foam formulations. Because the clearance region repeatedly subjects the melt to high shear, slight wear in the screw flights from 0.15 mm to 0.30 mm can reduce the clearance shear-rate peak but also increase leakage flow, changing the thermal profile and shifting the melt-temperature limit. This failure mode is often detected only after an increase in scrap rate, because barrel pressure and motor load may remain within normal limits.

On injection molding machines with clamping forces between 1500 kN and 2400 kN, polyester TPU soling compounds of 85–90 Shore A hardness per ASTM D2240 require a nozzle melt-temperature limit of 195–205°C because hydrolysis above 210°C causes irreversible molecular-weight reduction. Pre-drying in a desiccant dryer at 95°C for 3 h to a moisture content below 0.02% is mandatory when regression of tensile strength per ISO 37 exceeds 10%. The shear heating contribution during plasticization can push the melt temperature from the barrel set point of 185°C to a nozzle value of 205–215°C if back pressure is set above 5 MPa hydraulic and screw speed exceeds 80 min⁻¹. The resulting surface defects appear as silver streaks, delamination at the gate, and occasional black specks, while the internal degradation is better quantified by a reduction in melt viscosity or a drop in tensile strength after molding. In shoe-sole production, the shot-to-shot cushion temperature variation has been observed to reach 18–38°C above the nozzle set point when the screw decompression stroke is excessive or when the nonreturn valve is worn. These thermal excursions are particularly damaging for polyester TPU because the ester linkages are hydrolytically unstable at processing temperatures, and the presence of residual moisture converts the high shear zone into a localized reactor for chain scission.

For polyether TPU soling compounds, the practical melt-temperature ceiling is lower, generally near 190–200°C, because oxidative degradation and discoloration begin to compete with hydrolysis. The shear heating constraint in TPU injection molding is therefore tied to the water content of the feedstock, the L/D ratio of the screw, and the back pressure setting. A screw with L/D 22:1 and a compression ratio of 2.0–2.5:1 generates less shear than a high-work L/D 25:1 barrier screw, but the lower shear design may not provide adequate melt homogeneity for thin-wall outsole sections. The operating limit is often determined by a differential scanning calorimetry scan of the molded part: if the first heating endotherm shows a melting peak shift greater than 2–3°C or a new low-temperature shoulder, the material has undergone sufficient shear-induced molecular-weight loss to alter its crystallization behavior. The same effect is detected in injection-molded soling by a reduction in ASTM D412 tensile strength and an increase in ISO 815 compression set beyond the specification limit for the part.

Thermal Degradation Pathways in PVC and PVC/NBR Soling Blends at the Screw Tip

The upper screw-tip temperature for PVC and PVC/NBR soling compounds is commonly held below 190°C because dehydrochlorination initiated at 180–190°C produces hydrogen chloride and conjugated polyene sequences. In a single-screw extruder with L/D 20:1 and a compression ratio of 2.0–2.5:1, the barrel profile is typically set to 150/160/170°C from feed to metering, with the screw-tip melt temperature not exceeding 185°C for stabilized compounds. The thermal stability measured by conductivity per ISO 182-3 for plasticized PVC soling formulations falls below the required value when the melt is held at 190°C for more than 30–45 min, and the effect is accelerated in the high-shear zone between the screw flight and barrel wall. Shear heating can therefore negate the stabilization package even when the barrel temperature is below the degradation threshold. In PVC/NBR blends, the nitrile rubber phase has a lower thermal conductivity than the PVC matrix and can develop internal hot spots during dispersive mixing, especially when the compound contains sulfur or accelerator residues. The failure signature is a pink-to-brown discoloration at the die lip and a pungent acidic odour, followed by a measurable increase in the compound's melt viscosity as crosslinking occurs. The use of a cooled screw core with water at 80–90°C is often specified for PVC soling extrusion because it removes heat from the highest shear zone without raising the barrel wall temperature.

Because PVC decomposition is autocatalytic, a single shear-heating event that produces hydrochloric acid can accelerate subsequent degradation throughout the remainder of the run. This is a production-bottleneck failure mode: a batch that passes the ISO 182-3 stability test before extrusion may still fail during processing if the screw-tip temperature exceeds 190°C for a short interval. Practical countermeasures include reducing screw speed to below 35 min⁻¹ for highly plasticized compounds, maintaining a melt pressure below 15 MPa at the die, and avoiding excessively long barrel residence times. The shear heating ceiling is therefore set not by the onset of dehydrochlorination alone, but by the kinetic interaction between local temperature, residence time, and stabilizer consumption. For PVC/NBR soling materials, the use of a two-stage screw with a vent section reduces the thermal load, but the vent cannot remove the localized heat generated in the transition section where the compound undergoes rapid compression. Published data for this specific configuration is limited, but industrial practice consistently maintains the screw-tip temperature 10–15°C below the laboratory thermal-stability limit to account for shear-induced overheating.

Production-scale two-stage mixing of sulfur-curable SBR/NR soling compounds in a 270 L intermeshing internal mixer shows that rotor speed and ram pressure influence the dump temperature as strongly as the heat-transfer oil set point. A masterbatch containing 45 phr N330 carbon black and 8 phr naphthenic oil is dumped at 142–148°C after a ram-pressure cycle at 0.6 MPa and a rotor speed of 32 min⁻¹. The Mooney viscosity ML(1+4) 100°C per ASTM D1646-19a for such a masterbatch is usually between 50 and 80 MU. Raising the rotor speed from 32 min⁻¹ to 40 min⁻¹ can raise the dump temperature by 8–12°C at constant batch weight, which narrows the scorch safety margin. In the second mixing stage, sulfur and accelerators are added below 95°C on a two-roll mill, and the mill rolls are maintained at 70–80°C because the residence time on the mill is sufficient to initiate vulcanization if the stock temperature exceeds 100°C. The practical shear heating limit is therefore defined by the scorch time at 121°C measured as t₅ under ASTM D1646-19a; if the t₅ value falls below 4 min, the compound may still pass the rheometer cure test but will exhibit premature crosslinking during extrusion or injection molding.

The internal mixer bottleneck arises from the interaction between the rotor tip clearance and the non-Newtonian viscosity of the carbon-black-filled rubber. At the rotor tip, the local shear rate can exceed 200 s⁻¹ at 32 min⁻¹, producing heat generation rates that are high enough to dominate the heat-transfer capacity of the mixer jacket. The resulting dump temperature is non-uniform: the chamber thermocouple may read 142°C at the wall while the stock near the rotor tip is temporarily 10–15°C hotter. This is the reason for the two-stage mixing sequence. If the full sulfur cure system is added in the first stage, the compound scorches within seconds in the hot tip region, causing a rise in motor power and a characteristic lumpy discharge. In production, the shear heating limit is therefore expressed as a maximum dump temperature for the masterbatch, a maximum second-stage mill temperature for sulfur addition, and a minimum Mooney scorch time before the soling compound is approved for extrusion or molding.

When Blowing Agents Are Pre-Dispersed in Closed-Rotor Mixers with Short Cycle Times

A 75 L laboratory internal mixer operating at 35 min⁻¹ with a heat-transfer oil temperature of 80–90°C can generate localized in-chamber temperatures of 110–125°C when a pre-dispersed activated azodicarbonamide masterbatch is being compounded into an EVA carrier. The rotor tip clearance of 0.5–0.8 mm creates a narrow high-shear zone where the local temperature may be 10–20°C above the batch thermocouple reading. Because activated azodicarbonamide decomposition begins near 150–170°C by DSC, this is not necessarily sufficient to cause widespread gas evolution, but it can consume part of the activation system and reduce the available blowing efficiency during subsequent expansion. For this reason, pre-dispersed blowing-agent batches are regularly discharged at or below 110°C rather than at the 130–140°C dump temperatures used for EVA compounding without the blowing agent. The short cycle time in a closed-rotor mixer is an advantage for dispersion but a disadvantage for thermal control because the ram does not allow the removal of gases and the heat-transfer area is fixed. If the discharge temperature exceeds 115°C, the next processing stage may show a lower gas yield per unit mass of blowing agent, a coarser cell structure after expansion, and an increase in foam density of 0.02–0.04 g/cm³.

The same constraint applies to twin-screw extrusion of blowing-agent masterbatches. A co-rotating twin-screw extruder with 50 mm diameter screws and L/D 40:1, using kneading blocks with 45° stagger angles at 300 min⁻¹, can raise the melt temperature by 25–35°C over the barrel set point. The specific mechanical energy input under such conditions commonly ranges from 0.18 kWh/kg to 0.24 kWh/kg, and the die pressure may fluctuate from 6.0 MPa to 8.5 MPa as the blowing agent decomposes partially or as the melt viscosity changes. The masterbatch must therefore be processed with a barrel profile that starts below 80°C in the feed zone and does not exceed 105°C at the die, while the screw speed is limited to 200–250 min⁻¹ to keep the melt temperature below 110°C. This is a narrower window than the same twin-screw extruder would use for a filled EVA compound without blowing agent, where melt temperatures of 130–145°C are acceptable. The consequence of exceeding the 110°C limit in the masterbatch is not necessarily immediate gas evolution but a partial decomposition that reduces the effective blowing-agent concentration in the final soling compound, requiring a correction in dosing that adds additional thermal load downstream.

A co-rotating twin-screw extruder with 50 mm diameter screws and L/D 40:1 used for high-hardness microcellular EVA soling compounds at 500 kg/h exhibits segmented screw-element shear heating that differs sharply from single-screw behavior. Kneading blocks with 45° stagger angles at 300 min⁻¹ can raise melt temperature by 25–35°C over the barrel set point; pressure at the die may fluctuate from 6.0 MPa to 8.5 MPa as filler-induced viscosity changes propagate through the screw. The compound often contains calcium carbonate at 30 phr, which raises the low-shear viscosity and increases the sensitivity of the melt temperature to screw speed. Under these conditions, the cell density measured per ISO 845 can shift from a nominal 0.25 g/cm³ to 0.31 g/cm³ if the melt temperature at the die rises by 8°C, because the solubility and diffusion of the gas are temperature-dependent. In addition, split tear values under ASTM D624 decline when the foam skin becomes too thick or the core cell walls are over-elongated. This production setup requires barrel cooling in the kneading-block zones, screw elements with reduced mixing intensity, and an oil-cooled die plate maintained at 115–125°C. The processing window for the melt temperature is frequently quoted as ±5°C around 128°C at the die entry, and the limiting temperature is therefore the same order as the EVA foam case, despite the use of a twin-screw extruder.

The use of a side-fed blowing-agent masterbatch can reduce the heat history of the blowing agent but does not eliminate the shear heating problem. When the side feeder is located after the main mixing zones, the blowing agent is exposed only to the final pumping elements, which generate less viscous dissipation than kneading blocks. However, the melt must be hot enough to accept the masterbatch without freezing, usually 120–130°C, and that already approaches the onset of activated azodicarbonamide decomposition. If the side feeder is not sealed, gas generated locally can escape into the feed port and create a pressure fluctuation that destabilizes the foam density. This is one reason why production lines for foam soling often prefer a single-stage compounding operation with very tight temperature control rather than a separate masterbatch letdown on the same machine. In either case, the shear heating limit is determined by the blowing-agent decomposition kinetics at the existing melt temperature and residence time, not by the barrel controller set point.

Rheometric and Calorimetric Characterization Criteria for Shear Heating Limits

The shear heating limit for a footwear soling compound is established from a combination of capillary rheometry, melt-flow testing, Mooney viscosity, and differential scanning calorimetry. Melt viscosity curves obtained under ASTM D3835-16 at temperatures from 110°C to 190°C provide the shear-rate dependence required to estimate the local viscous dissipation in a given screw geometry. The melt flow index under ISO 1133-1:2022 at 190°C and 2.16 kg is used as a lot-to-lot control for EVA and TPU soling compounds, but it is not sufficient to define the shear heating ceiling because it does not capture the high-shear-region viscosity that governs the flight-clearance heating. For rubber-containing compounds, the Mooney viscosity and Mooney scorch are measured under ASTM D1646-19a at 100°C and 121°C, respectively, providing a direct indication of whether the compound can survive the shear history of an internal mixer or a dump extruder. Differential scanning calorimetry under ASTM D3418-21 identifies the melting transitions, crystallization temperature, and thermal-degradation or blowing-agent decomposition exotherms that define the upper melt-temperature boundary. The limiting screw speed is then calculated by setting the no-flow melt-temperature limit from the decomposition or degradation onset and back-calculating the screw speed from the relationship ΔT ∝ N².

Calendered NR/BR soling sheets of gauge 0.8–1.2 mm run through a two-roll mill with a friction ratio of 1.15:1 are sensitive to roll-neck shear heating even though the stock temperature is usually set at 70–80°C. The roll-nip shear rate at a roll speed of 18–22 min⁻¹ and a nip gap of 0.4 mm is high enough to raise the mill-batch surface temperature by 5–10°C above the roll set point. For NR/BR soling compounds containing heat-sensitive accelerators, this local heating can initiate sulfur blooming and partial scorch if the sheet remains on the mill for more than 8–10 min. The detection method is a rise in mill power and a loss of tack, followed by surface matte defects on the calendered sheet. Because the mill is an open system, the heat-transfer coefficient to the air is low, and the shear heating is concentrated in the nip; this limits the practical sheet thickness and mill residence time for unfilled or lightly filled soling compounds. The shear heating limitation in this final shaping step is therefore expressed as a maximum mill-roll temperature of 80°C, a maximum batch residence time of 10 min, and a nip gap sufficient to avoid excessive shear without compromising the sheet gauge tolerance.