Modeling Interfacial Viscous Fingering Instabilities during Continuous Melt Fractionation of Degraded Polymers

Interface

Continuous fractionation channels separate degraded polymer melts into discrete molecular weight cuts through controlled viscosity gradients. In these channels, a less viscous scissored polymer fraction displaces a higher-viscosity un-degraded fraction or extraction fluid. This displacement triggers fluid dynamic instability along the moving boundary between the two polymer cuts, mirroring classical Saffman-Taylor behavior in porous media and narrow gaps.

Non-Newtonian melt rheology complicates boundary dynamics because local shear rates vary across the flow profile, where shear thinning decreases local fluid viscosity near channel walls and accelerates perturbation growth at specific wave numbers.

When thermally degraded polyolefins undergo continuous melt fractionation, chain scission yields a lower weight-average molecular mass fraction with elevated melt flow rates. Pumping this degraded fraction against a viscous virgin or high-molecular-weight carrier melt creates a mobility ratio M defined as the ratio of displacing fluid mobility to displaced fluid mobility. Mobility ratios exceeding unity render the moving liquid boundary unstable to infinitesimal spatial perturbations.

Linear stability analysis shows that perturbation growth rates depend on viscosity contrast, interfacial tension between polymer phases, channel wall drag, and fluid viscoelasticity.

Viscous Penetration in Degraded Melt Streams

Low molecular weight polymer chains migrate faster under pressure gradients, forming thin low-resistance channels that concentrate fluid flow and reduce local shear viscosity in non-Newtonian polyolefin melts. As fluid enters these primary channels, shear rate spikes, driving local zero-shear viscosity down according to Carreau-Yasuda rheological models. This localized shear thinning creates a feedback loop where finger growth accelerates along the flow axis while suppressive capillary forces struggle to restore flat boundary symmetry.

Saffman Taylor Criterion for Non Newtonian Fluids

Viscosity ratios exceeding unity across moving liquid-liquid boundaries spark spatial perturbations. Modified Saffman-Taylor equations account for the power-law exponent of non-Newtonian polymer melts, where lower power-law index values represent stronger shear thinning that shifts maximum growth rates toward higher spatial wave numbers. High-frequency fingers form across the fluid boundary, producing fine interpenetrating polymer filaments rather than single broad channels, while wall slip further alters finger growth.

Viscosity ratios above 4.2 across polyolefin phase boundaries at 210 °C under a shear rate of 50 s⁻¹ trigger finger initiation within 0.3 seconds.

The interaction between shear-dependent viscosity and normal stress differences determines whether initial perturbations widen into broad lobes or split into secondary branches. In linear viscoelastic fluids, the first normal stress difference generates elastic tension along streamline contours, resisting interfacial deformation and delaying finger initiation up to a critical Weissenberg number. Beyond this elastic threshold, second normal stress differences induce secondary circulations in the cross-sectional plane, compounding finger distortion across the separation channel.

How do non-isothermal temperature fields near channel walls alter the critical wavenumber spectrum when the displacing polymer stream contains volatile thermal degradation byproducts?

Slit

Flow channel dimensions govern the spatial amplitude of non-Newtonian melt perturbations. Slit dies and narrow annular channels used in continuous melt fractionation equipment enforce geometric constraints on moving polymer phase boundaries. Capillary pressure across the curved liquid boundary scales inversely with channel height, so narrow gap geometries enhance the stabilizing effect of surface and interfacial tension, suppressing long-wavelength instabilities while forcing short-wavelength perturbations into higher modes.

Shear stress distributions inside narrow rectangular channels peak at the solid boundary walls and drop to zero along the central neutral axis. When a degraded polymer melt flows through a narrow channel gap, spatial variation in shear rate creates a viscosity profile across the channel depth: the center retains higher zero-shear viscosity while regions near the walls undergo shear thinning. This structural velocity variation distorts finger profiles into three-dimensional shapes, where fluid fingers advance faster along the center plane than near wall surfaces.

Capillary Pressure and Channel Gap Geometry

Fluid boundary stability depends on the balance between wall drag and normal stress differences. Laplace pressure across an advancing finger tip depends on the effective interfacial tension between immiscible or partially miscible degraded melt cuts. In polyolefin melt separation, interfacial tension values remain low, typically ranging between 0.5 and 3.0 mN/m.

This weak interfacial tension allows high-wavenumber perturbations to grow rapidly, producing complex finger branching inside narrow separation gaps unless stabilization tactics intervene.

Where Does Interfacial Breakdown Initiate under Shear?

Distortions emerge near die boundaries where fluid displacement rates reach peak values. High shear rates near channel walls depress local melt viscosity, allowing the lower-viscosity degraded melt to punch through the stagnant boundary layer. This localized penetration alters channel pressure distribution, pulling adjacent fluid into the primary flow path and establishing a stable finger geometry.

• Saffman-Taylor finger widening causes broad low-viscosity channels that bypass high-molecular weight fractions during extraction.
• Tip splitting instability breaks primary fingers into secondary branch filaments under high capillary pressure gradients.
• Side-branching distortion produces lateral viscous leaks that contaminate adjacent pure fraction streams.
• Localized melt breakup generates micro-droplet emulsions when shear rates exceed critical elasticity thresholds.

Channel gap height reductions stabilize moving polymer liquid boundaries when shear thinning dominates normal stress differences.

Modifying channel geometry from a uniform parallel slit to a tapered or convergent gap alters local pressure gradients along the flow path. Tapered channels impose an accelerating pressure gradient that compresses advancing finger fronts, increasing effective drag on finger tips and narrowing the unstable wavenumber spectrum. Process operators utilize gap tapering to limit finger propagation, preserving discrete boundary layers across continuous melt fractionation beds.

Controlling channel geometry alone cannot fully suppress instability when incoming feedstocks exhibit wide shifts in molecular weight distribution.

Broadening

Repeated thermal cycles in reprocessing extruders break polymer chains into wider mass distribution bands. Post-consumer and post-industrial plastic feedstocks contain varying ratios of chain-scissored low-molecular fractions and cross-linked high-molecular species. This structural heterogeneity widens the polydispersity index ~ defined as the ratio of weight-average molecular mass to number-average molecular mass ~ from pristine values around 2.5 to post-degradation values exceeding 8.0, altering the rheological contrast between fractionated streams during continuous melt separation.

As polydispersity expands, the shear-rate dependence of melt viscosity becomes less steep but extends across a wider shear-rate spectrum. High-molecular weight tails contribute to strong normal stress differences at low shear rates, while low-molecular-weight tails promote rapid shear thinning at moderate shear rates. During fractionation, low-molecular species concentrate rapidly into the displacing phase, lowering its zero-shear viscosity and elevating the overall mobility ratio across the boundary.

Polydispersity Shifts in Post Consumer Feedstocks

Thermal history variations alter the ratio between weight-average and number-average molecular mass. Industrial regrind lots containing degraded polypropylene exhibit significant melt flow rate jumps, increasing from a nominal 4.0 g/10min at 230 °C under 2.16 kg load to over 35.0 g/10min, where melt fracture ruins optical clarity. This change in flow rate reflects a reduction in zero-shear viscosity by more than one order of magnitude.

When processed in continuous fractionation equipment, these high-MFR fractions form aggressive viscous fingers that penetrate high-molecular fraction beds, reducing separation purity.

Molecular Weight Distribution Splitting in Extruders

Chain scission reactions during melt conveying reduce long-chain entanglement density, which lowers the fundamental relaxation time spectrum of the melt. In continuous fractionation channels, short relaxation times suppress elastic stress build-up at advancing finger interfaces, removing the primary fluid mechanism that opposes tip-splitting. The absence of strong elastic forces allows fingers to split into fine micro-channels, producing an uncontrolled mixing zone across the melt interface.

1. Melt flow verification establishes baseline viscosity profiles under standard ASTM D1238 test conditions before process entry.
2. High-temperature size exclusion chromatography measures true polydispersity index to predict spatial finger growth rates.
3. Differential scanning calorimetry analysis flags thermal history variations that alter local crystallization behavior.
4. Rotational rheometry sweep records first normal stress differences across target shear rate spectra.

Uncontrolled polydispersity expansion in incoming raw material leads directly to variable separation yields, higher energy consumption per kilogram of recovered fraction, and off-specification melt flow rates in finished pellet lots.

Dampening

Thermal gradients imposed across flow channels stabilize moving fluid fronts. Lowering die wall temperatures increases local viscosity of the polymer melt adjacent to solid boundary surfaces, offsetting shear thinning effects. Maintaining a temperature difference of 10 °C to 25 °C between the channel wall and the central fluid core raises outer layer viscosity, creating a high-viscosity fluid jacket that contains advancing low-viscosity fingers within the central flow axis.

Process adjustments also rely on viscoelastic stress control to suppress perturbation growth. Operating continuous fractionation equipment within shear rate regimes that maximize the first normal stress difference enhances interfacial elasticity. Elastic normal stresses create extra tension along deformed phase boundaries, acting like an artificial interfacial tension that dampens short-wavelength Saffman-Taylor modes.

Thermal Gradient Modulation across Flow Channels

Active cooling at die surfaces increases local fluid resistance along outer flow boundaries. Channel wall cooling alters the spatial temperature distribution inside the melt, shifting local relaxation times according to the Williams-Landel-Ferry relationship. Raising outer fluid viscosity reduces the local mobility ratio M along the wall boundary, preventing finger breakthrough along die surfaces so that flow remains centered within the warmer inner core.

1. Set die wall temperatures 15 °C below central melt temperature to increase wall fluid viscosity.
2. Adjust pump feed rates until channel shear rates remain inside the linear viscoelastic fluid regime.
3. Introduce low-molecular-weight compatibilizer additives at 0.5 percent by weight to lower interfacial tension.
4. Monitor downstream differential pressure sensors to detect perturbation growth prior to stream contamination.

Viscoelasticity and Normal Stress Suppression

First normal stress differences generate elastic forces that oppose finger development. Increasing the Weissenberg number Wi by tuning extrusion screw speed elevates elastic stress storage within high-molecular polymer chains. Beyond a critical Weissenberg threshold of approximately 1.5, elastic tension along streamline paths forces advancing finger tips to flatten, suppressing tip-splitting behavior.

Dosing minor fractions of high-molecular-weight branched polyolefins into the feed stream raises elastic stress storage without significantly elevating zero-shear viscosity.

Purchase contracts specifying ISO 1133 MFR tolerance within plus or minus 0.5 grams per 10 minutes allow rejection of thermally unstable lots before fractionation processing.

Lot-to-lot MFR variations frequently stem from thermal history shifts within standard commercial production allowances. Downstream fingering breakdown can likewise originate from extruder temperature fluctuations rather than feedstock polydispersity drift.

Split

Separation efficiency dictates the commercial pricing structure of purified recyclate streams. Continuous melt fractionation converts variable degraded polyolefin scrap into discrete, high-value resin grades with narrow molecular weight distributions, though yield loss erodes processing margins. Viscous fingering instability causes cross-stream contamination between fractions, lowering target MFR precision and forcing re-processing through compounder lines.

Landed resin costs depend on energy expenditure per metric tonne, fraction purity, and overall process yield. Continuous melt separation routes bypass solvent recovery systems, reducing operating costs compared to solution-based fractionation systems. Uncontrolled interfacial fingering reduces fraction purity from a target 98 percent down to less than 82 percent, destroying the market premium commanded by narrow-MWD recycled grades.

Economic Yields of Fractionated Recyclate

Melt fractionation processing costs scale directly with heating requirements and dwell times. High processing dwell times accelerate secondary oxidative degradation, requiring higher antioxidant additive dosing during post-fractionation compounding, while recyclate pricing tracks virgin naphtha. When interfacial fingering contaminates high-molecular-weight streams with low-viscosity fractions, the resulting compound fails performance standards for virgin-replacement engineering applications.

Specification Lines for High Purity Recycled Resins

Target melt flow rates require strict variance caps on constituent molecular weight fractions. Procurement agreements for fractionated recycled resins incorporate precise testing requirements to verify lot uniformity. Specifications define maximum allowable polydispersity index bounds alongside standard melt flow rate targets, ensuring incoming resin lots process predictably during injection molding or film extrusion.

Fractionation yields dropping below 82 percent invert the economic advantage of melt separation over solvent purification routes.

Quality guarantees in supply contracts state that fractionated pellet shipments must maintain an MFR variance within plus or minus 8 percent across a 20-tonne shipment under ISO 1133 test conditions at 230 °C under 2.16 kg load, failing which the buyer retains full right of lot rejection at seller cost.