Recycling Compatibilizers: Polymer Blend Domain Size (2D Cross-Section)

Blend Process

Compatibilizer φ_c 0.0 wt%

Shear rate γ̇ 40 s⁻¹

Viscosity ratio p = η_d/η_m 1.0

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Interfacial tension Γ

— mN/m

Capillary number Ca

—

Mean domain d₃₂

— µm

Droplet count

—

How it works

Two immiscible polymers (e.g. recycled PE + PP) forced through a mixer form a matrix with a dispersed minority phase. Whether that dispersed phase ends up as coarse, weak globules or a fine, strong dispersion is set by a competition between droplet breakup and droplet coalescence, both controlled by the interfacial tension Γ between the phases. This view is a 2D cross-section (top-down slice) through the sheared melt — the same competition, seen in plane.

Capillary number:  Ca = η_m · γ̇ · R / Γ
Breakup occurs when Ca > Ca_crit(p), p = η_d / η_m  (Grace curve)
Equilibrium radius:  R_eq ≈ Ca_crit(p) · Γ / (η_m · γ̇)

A block-copolymer compatibilizer migrates to the PE/PP interface, where its two blocks anchor into each phase. This does two things: it lowers Γ (so R_eq shrinks — finer dispersion), and it sterically shields droplet surfaces so they resist coalescing on contact — modelled here as an added interfacial-elasticity term:

Γ(φc)      = Γ0 · exp(−k1 · φc)              (interfacial tension drops)
P_coalesce = exp(−k2 · φc) · exp(−|Ca|/Ca_crit) (merge probability drops)

Compatibilizer φc — raise it to shrink Γ and suppress coalescence: droplets get smaller and stop coarsening.
Shear rate γ̇ — faster mixing raises Ca, forcing more droplets past Ca_crit and splitting them in two.
Viscosity ratio p — Ca_crit(p) has a minimum near p≈1 (easiest to break up) and rises sharply for very viscous or very fluid dispersed phases, matching the classic Grace/Taylor breakup curve.

Real-world relevance: this is exactly why mixed-plastic recycling streams need compatibilizers — without one, PE and PP separate into coarse domains that crack under load; with a well-chosen block copolymer, the recyclate approaches the toughness of the virgin resin.

Dispersed-phase droplets Matrix boundary

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