Melt Fracture

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In polymer processing and rheology, melt fracture (also extrudate distortion) is a collective term for a family of flow instabilities that arise during the extrusion of polymer melts through dies at rates exceeding a critical throughput, manifesting as periodic or chaotic surface and/or volumetric distortions of the emerging extrudate. The limiting factor in the extrusion rate of polymeric fluids is the onset of these low-Reynolds number instabilities, which may range from mild surface roughness affecting product clarity to severe three-dimensional chaos that destroys the structural integrity of the extrudate entirely.

Melt fracture is of substantial industrial importance: during industrial extrusion processes, melt instabilities represent a critical factor limiting maximum throughput, because they alter the properties of the extrudate. The phenomenon has been known to rubber technologists since the earliest days of polymer extrusion, and its modern understanding has been shaped principally by Ramamurthy (1986), Kalika and Denn (1987), Hatzikiriakos and Dealy (1991–1992), and Migler and collaborators at NIST.

Classification of instability types

Visual observations range from smooth-glossy extrudates (no distortions), over extrudates showing degrees of surface irregularities defined as matt, loss of gloss, orange peel, sharkskin, wavy, and screw thread, to extrudates which are volumetrically distorted as a consequence of their oscillating emergence from the die (spurt) or their very irregular, chaotic shape. Five principal regimes are distinguished in order of increasing wall shear stress:

Regime	Common name	Critical stress (LLDPE)	Origin	Extrudate character
I	Smooth	${\tau }_w<{\tau }_{c1}$	—	Smooth, glossy
II	Sharkskin	${\tau }_w\approx 0.1\text{–}0.18\mathrm{M}\mathrm{P}\mathrm{a}$	Die exit; extensional failure	Fine periodic surface ridges
III	Stick–slip / spurt	${\tau }_w\approx 0.2\text{–}0.3\mathrm{M}\mathrm{P}\mathrm{a}$	Die land; wall slip oscillation	Alternating smooth and rough bands; pressure oscillations
IV	Wavy / oscillating	intermediate–high	Upstream entry vortex	Long-wavelength helical distortion
V	Gross melt fracture	${\tau }_w>{\tau }_{c,\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{s}\mathrm{s}}$	Upstream entry; bulk elastic failure	Chaotic, three-dimensional distortion

Not all melt instabilities occur for a specific polymer. Some polymers might only show sharkskin, whereas others only show stick–slip. Sharkskin typically occurs at lower shear rates than stick–slip.

Governing equations

Fully developed capillary flow

Consider isothermal, fully developed flow of a compressible viscoelastic melt in a cylindrical capillary of radius $R$ and length $L$, driven by upstream pressure $P_0$ against atmospheric pressure $P_L=0$. The momentum equation in the axial direction is

$\frac{1}{r}\frac{\partial }{\partial r}(r{\tau }_{rz})=\frac{\partial p}{\partial z}=-\frac{\mathrm{\Delta }P}{L}$

giving the radial shear stress distribution

${\tau }_{rz}(r)=-\frac{\mathrm{\Delta }P}{2L}r,{\tau }_w=\frac{\mathrm{\Delta }PR}{2L}$

For a generalized Newtonian fluid with the Carreau–Yasuda model,

$\eta (\dot{\gamma })={\eta }_{\mathrm{\infty }}+({\eta }_0-{\eta }_{\mathrm{\infty }}){[1+({\lambda }_C\dot{\gamma }{)}^a]}^{(n-1)/a}$

where ${\eta }_0$ is the zero-shear viscosity, ${\eta }_{\mathrm{\infty }}$ is the infinite-shear plateau viscosity, ${\lambda }_C$ is the Carreau time constant, $a$ is the Yasuda index, and $n$ is the power-law index. The apparent wall shear rate (Newtonian equivalent) is

${\dot{\gamma }}_{\mathrm{a}\mathrm{p}\mathrm{p}}=\frac{4Q}{\pi R^3}$

and the true wall shear rate, after the Weissenberg–Rabinowitsch correction, is

${\dot{\gamma }}_w=\frac{3n^{\prime }+1}{4n^{\prime }}{\dot{\gamma }}_{\mathrm{a}\mathrm{p}\mathrm{p}},n^{\prime }=\frac{\mathrm{d}\ln {\tau }_w}{\mathrm{d}\ln {\dot{\gamma }}_{\mathrm{a}\mathrm{p}\mathrm{p}}}$

Deborah and Weissenberg numbers

The onset of all melt fracture types is governed fundamentally by the ratio of elastic to viscous forces, characterized by the Deborah number

$\mathrm{D}\mathrm{e}=\frac{{\lambda }_r}{{𝒯}}=\frac{{\lambda }_{r}U}{L}$

and the Weissenberg number

$\mathrm{W}\mathrm{i}={\lambda }_r{\dot{\gamma }}_w$

where ${\lambda }_r$ is the terminal relaxation time of the melt and $U=Q/(\pi R^2)$ is the mean axial velocity. Instabilities generally emerge when $\mathrm{W}\mathrm{i}$ exceeds a critical value ${\mathrm{W}\mathrm{i}}_c$ that depends on the instability type and geometry. The ratio $\mathrm{W}\mathrm{i}/\mathrm{D}\mathrm{e}={\dot{\gamma }}_{w}L/U={\dot{\gamma }}_w\pi R^{2}L/Q$ measures the importance of residence time in the die relative to the relaxation time.

Sharkskin instability

Phenomenology

Sharkskin melt fracture refers to a fine surface distortion found on extrudates of certain polymers at shear stress levels around 0.1 MPa. It can limit the productivity of extrusion lines. The instability is most severe in narrow-molecular-weight-distribution linear polyethylenes (LLDPE, metallocene PE) and is characterized by a regular, periodic surface roughness whose wavelength and amplitude increase with throughput. The driving force behind attempts to understand sharkskin is that linear chain polyethylenes of narrow molecular weight distribution are particularly susceptible to this instability, and because it occurs at relatively low extrusion rates, it is troublesome.

Mechanism: exit extensional failure

The sharkskin instability originates at the die exit. As the melt accelerates from the plug-like die-flow velocity profile to the unconfined free-surface state, a strong extensional deformation field develops in a thin surface layer. The onset of extrudate distortion (sharkskin) in linear low-density polyethylene coincides with the failure of adhesion at the polymer/metal interface.

The extensional stress in the surface layer at the die exit scales as

${\sigma }_E\sim {\eta }_E{\dot{\epsilon }}_{\mathrm{e}\mathrm{x}\mathrm{i}\mathrm{t}}\sim {\eta }_E\frac{U_{\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{e}}-U_{\mathrm{d}\mathrm{i}\mathrm{e}}}{R}$

where ${\eta }_E=3{\eta }_0$ is the Trouton extensional viscosity (Newtonian limit) and ${\dot{\epsilon }}_{\mathrm{e}\mathrm{x}\mathrm{i}\mathrm{t}}$ is the exit extensional strain rate. The surface layer fractures cohesively when the extensional stress exceeds the cohesive strength ${\sigma }_c$ of the entangled melt network:

${\sigma }_E\ge {\sigma }_c\approx G_N^0$

where $G_N^0$ is the plateau modulus. Since $G_N^0\sim \rho R_{g}T/M_e$, materials with low entanglement molecular weight $M_e$ (higher $G_N^0$) are more resistant to sharkskin.

Pearson–Petrie stability criterion

The onset of sharkskin can be estimated from the linear stability analysis of Pearson and Petrie (1965) applied to the free-surface jet emerging from the die. For a viscoelastic jet of radius $R_j$ moving at velocity $U_j$, a surface perturbation of wavenumber $k$ and amplitude $\epsilon e^{i(kz-\omega t)}$ grows when the temporal growth rate ${\omega }_i=\mathrm{I}\mathrm{m}(\omega )$ is positive:

${\omega }_i>0\iff {\mathrm{W}\mathrm{i}}_{\mathrm{e}\mathrm{x}\mathrm{i}\mathrm{t}}>{\mathrm{W}\mathrm{i}}_c^{\mathrm{S}\mathrm{S}}$

The onset of sharkskin is in agreement with a calculation based on the stability theory of Pearson and Petrie. The critical Weissenberg number for sharkskin has been estimated as ${\mathrm{W}\mathrm{i}}_c^{\mathrm{S}\mathrm{S}}\approx 1\text{–}3$ depending on the constitutive model employed.

Stick–slip (spurt) instability

Phenomenology and pressure oscillations

At shear stresses above the sharkskin threshold, the flow becomes unsteady and the extrudate alternates between sharkskinned and smooth segments; this is commonly called slip-stick or spurt flow. At still higher stress levels, sometimes after a second region of spurt flow, the flow becomes steady with a long-wavelength distortion, but gross distortions occur at higher stresses — this regime is commonly called wavy or gross melt fracture.

During stick–slip flow in a capillary of length $L$ and radius $R$ connected to a reservoir of compliance ${𝒞}$ (volume per unit pressure), the pressure $P(t)$ and flow rate $Q(t)$ oscillate. The pressure balance on the upstream reservoir gives

${𝒞}\frac{\mathrm{d}P}{\mathrm{d}t}=Q_{\mathrm{p}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{n}}-Q(P,v_s)$

where $Q_{\mathrm{p}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{n}}$ is the constant piston-imposed volumetric flow rate and

$Q(P,v_s)=\frac{\pi R^4{\tau }_w^3}{8{\eta }_{\mathrm{e}\mathrm{f}\mathrm{f}}L{\tau }_w^3}\underset{0}{\overset{{\tau }_w}{\int }}\dot{\gamma }(\tau ){\tau }^2\mathrm{d}\tau +\pi R^2{v}_s({\tau }_w)$

This system exhibits a limit cycle when the steady-state $Q({\tau }_w)$ curve is non-monotone (S-shaped), with a region of negative slope:

$\frac{\mathrm{d}Q}{\mathrm{d}{\tau }_w}<0\Rightarrow \text{mechanically unstable branch}$

The system jumps between the lower stable branch (stick, no-slip, $v_s\approx 0$) and the upper stable branch (slip, large $v_s$), producing the observed oscillatory extrudate morphology. There is a distinct flattening of the flow curve, the shear stress versus shear rate plot, indicating a region where multiple flow rates are possible for the same wall shear stress.

Non-monotone constitutive behavior: the Johnson–Segalman model

An alternative (or complementary) explanation for stick–slip involves a non-monotone intrinsic constitutive law, independent of wall slip, arising from chain stretch and retraction dynamics. The Johnson–Segalman model is a differential viscoelastic model with slip between the affine and non-affine deformation of the polymer network, governed by a slip parameter $a\in [0,1]$:

$\mathit{\tau }+{\lambda }_r\stackrel{{\mathrm{\nabla }}_a}{\mathit{\tau }}=2{\eta }_p\mathbf{𝐃}$

where the generalized upper-convected derivative is

$\stackrel{{\mathrm{\nabla }}_a}{\mathit{\tau }}=\frac{\partial \mathit{\tau }}{\partial t}+\mathbf{𝐯}\cdot \mathrm{\nabla }\mathit{\tau }-\frac{1-a}{2}(\mathrm{\Omega }\cdot \mathit{\tau }-\mathit{\tau }\cdot \mathrm{\Omega })-\frac{1+a}{2}(\mathbf{𝐃}\cdot \mathit{\tau }+\mathit{\tau }\cdot \mathbf{𝐃})$

with $\mathbf{𝐃}=\frac{1}{2}[\mathrm{\nabla }\mathbf{𝐯}+(\mathrm{\nabla }\mathbf{𝐯}{)}^T]$ the rate-of-strain tensor and $\mathrm{\Omega }=\frac{1}{2}[\mathrm{\nabla }\mathbf{𝐯}-(\mathrm{\nabla }\mathbf{𝐯}{)}^T]$ the vorticity tensor. For $a\ne \pm 1$, the steady-state shear stress ${\tau }_{12}(\dot{\gamma })$ is non-monotone — it rises to a maximum, decreases, and then rises again — producing a constitutive S-curve that intrinsically supports spurt without invoking wall slip:

${\tau }_{12}=\frac{{\eta }_p\dot{\gamma }}{1+(1-a^2){\lambda }_r^2{\dot{\gamma }}^2}+{\eta }_s\dot{\gamma }$

where ${\eta }_s$ is the solvent (Newtonian) viscosity contribution. The maximum in ${\tau }_{12}(\dot{\gamma })$ occurs at

${\dot{\gamma }}_{\max }=\frac{1}{{\lambda }_r\sqrt{1-a^2}}$

Beyond this point the constitutive curve has negative slope, corresponding to the mechanically unstable region that triggers spurt.

Gross melt fracture

Origin in upstream entry flow

Gross melt fracture is a volumetric instability originating in the upstream convergent entry region of the die, not at the exit. Volume instabilities, including gross melt fracture, are instabilities that originate in the upstream region of the extrusion. As the melt converges from the barrel into the die land, it undergoes strong biaxial extensional deformation. Vortex recirculation patterns develop in the corners of the contraction, storing elastic energy. When the stored elastic energy per unit volume exceeds a critical threshold, these vortices become unstable and release periodically, sending pressure waves downstream that distort the entire extrudate cross-section.

The elastic energy density stored in the vortex region scales with the first normal stress difference $N_1$:

${{ℰ}}_{\mathrm{e}\mathrm{l}}\sim \frac{N_1^2}{2G^{\prime }({\omega }^{*})}$

where $G^{\prime }({\omega }^{*})$ is the storage modulus evaluated at an angular frequency ${\omega }^{*}=1/{\lambda }_r$ characteristic of the dominant relaxation mode. The onset of gross melt fracture occurs when

${\mathrm{W}\mathrm{i}}_{\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{y}}={\lambda }_r{\dot{\epsilon }}_{\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{y}}>{\mathrm{W}\mathrm{i}}_c^{\mathrm{G}\mathrm{M}\mathrm{F}}\approx O(1)$

where the entry extensional strain rate is estimated as

${\dot{\epsilon }}_{\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{y}}\approx \frac{U_{\mathrm{d}\mathrm{i}\mathrm{e}}-U_{\mathrm{b}\mathrm{a}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{l}}}{L_{\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{y}}}\approx \frac{Q}{\pi R^3}[{\left(\frac{R_{\mathrm{b}\mathrm{a}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{l}}}{R}\right)}^2-1]\frac{R}{L_{\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{y}}}$

For an abrupt (zero-length) contraction, $L_{\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{y}}\to 0$ and the entry strain rate diverges, making abrupt contractions more prone to gross melt fracture than tapered dies, a well-established experimental observation.

Bagley entry pressure and the Cogswell analysis

The entry pressure loss $\mathrm{\Delta }{P}_{\mathrm{e}\mathrm{n}\mathrm{t}}$ (extracted from the Bagley plot) encodes the extensional rheology of the entry flow. Cogswell's analysis (1972) relates $\mathrm{\Delta }{P}_{\mathrm{e}\mathrm{n}\mathrm{t}}$ to the apparent extensional viscosity ${\eta }_E$:

${\eta }_E({\dot{\epsilon }}_{\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{y}})=\frac{3(n^{\prime }+1)}{8}\frac{\mathrm{\Delta }{P}_{\mathrm{e}\mathrm{n}\mathrm{t}}}{{\dot{\gamma }}_{\mathrm{a}\mathrm{p}\mathrm{p}}}$

${\dot{\epsilon }}_{\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{y}}=\frac{{\dot{\gamma }}_{\mathrm{a}\mathrm{p}\mathrm{p}}^2{\tau }_w}{3\mathrm{\Delta }{P}_{\mathrm{e}\mathrm{n}\mathrm{t}}}\cdot \frac{(n^{\prime }+1)}{2}$

These equations together provide a means of extracting the extensional viscosity function ${\eta }_E(\dot{\epsilon })$ from simple capillary rheometry data, a powerful tool because true uniaxial extensional rheometry of polymer melts is experimentally challenging.

Non-monotone flow curve and the spurt criterion

The key mathematical condition unifying all spurt-type instabilities is the non-monotonicity of the steady-state capillary flow curve $Q({\tau }_w)$ or equivalently ${\tau }_w({\dot{\gamma }}_{\mathrm{a}\mathrm{p}\mathrm{p}})$. In the Mooney-plot framework for Wall Slip the true flow curve ${\dot{\gamma }}_{\mathrm{t}\mathrm{r}\mathrm{u}\mathrm{e}}({\tau }_w)$ and the slip contribution $4v_s({\tau }_w)/R$ add to give the apparent shear rate. If $v_s({\tau }_w)$ is a rapidly increasing function of ${\tau }_w$ (as it is near ${\tau }_{c2}$), the apparent flow curve becomes non-monotone even if the true bulk flow curve is monotone.

Formally, the spurt criterion from the combined slip-compressibility model is

$\frac{\mathrm{d}}{\mathrm{d}{\tau }_w}[{\dot{\gamma }}_{\mathrm{t}\mathrm{r}\mathrm{u}\mathrm{e}}({\tau }_w)+\frac{4v_s({\tau }_w)}{R}]<0$

which, after differentiation, gives

$\frac{\mathrm{d}{v}_s}{\mathrm{d}{\tau }_w}>\frac{R}{4}\frac{\mathrm{d}{\dot{\gamma }}_{\mathrm{t}\mathrm{r}\mathrm{u}\mathrm{e}}}{\mathrm{d}{\tau }_w}$

The non-monotone regime spans a stress interval $[{\tau }_w^{-},{\tau }_w^{+}]$ on the flow curve, and all steady operating points in this interval are unstable; the system must jump discontinuously between the lower branch ${\tau }_w<{\tau }_w^{-}$ (stick) and the upper branch ${\tau }_w>{\tau }_w^{+}$ (slip), producing the stick–slip oscillation.

Pressure oscillation period and amplitude

For the coupled piston–reservoir–die system, the oscillation period $T_{\mathrm{o}\mathrm{s}\mathrm{c}}$ of the stick–slip cycle is controlled by the reservoir compliance ${𝒞}$:

$T_{\mathrm{o}\mathrm{s}\mathrm{c}}\approx \frac{{𝒞}\mathrm{\Delta }{P}_{\mathrm{o}\mathrm{s}\mathrm{c}}}{Q_{\mathrm{p}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{n}}}$

where $\mathrm{\Delta }{P}_{\mathrm{o}\mathrm{s}\mathrm{c}}=P_{\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{k}}-P_{\mathrm{s}\mathrm{l}\mathrm{i}\mathrm{p}}$ is the pressure amplitude of the oscillation. More precisely, integrating the compliance equation over one cycle gives

$T_{\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{k}}=\frac{{𝒞}(P_{\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{k}}-P_{\mathrm{s}\mathrm{l}\mathrm{i}\mathrm{p}})}{Q_{\mathrm{p}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{n}}-Q_{\mathrm{s}\mathrm{l}\mathrm{i}\mathrm{p}}};T_{\mathrm{s}\mathrm{l}\mathrm{i}\mathrm{p}}=\frac{{𝒞}(P_{\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{k}}-P_{\mathrm{s}\mathrm{l}\mathrm{i}\mathrm{p}})}{Q_{\mathrm{s}\mathrm{l}\mathrm{i}\mathrm{p}}-Q_{\mathrm{p}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{n}}}$

where $Q_{\mathrm{s}\mathrm{l}\mathrm{i}\mathrm{p}}$ is the flow rate on the upper (slip) branch at pressure $P_{\mathrm{s}\mathrm{l}\mathrm{i}\mathrm{p}}$. The total period is $T_{\mathrm{o}\mathrm{s}\mathrm{c}}=T_{\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{k}}+T_{\mathrm{s}\mathrm{l}\mathrm{i}\mathrm{p}}$. Increasing the die compliance (softer reservoir) increases $T_{\mathrm{o}\mathrm{s}\mathrm{c}}$, consistent with experimental observations that stiff-barrel rheometers produce higher-frequency oscillations than compliant systems. If the L/D ratio of the die is increased, the magnitude of the pressure fluctuation increases.

Sharkskin wavelength and frequency

The wavelength $\mathrm{\Lambda }$ of the sharkskin surface ridges is determined by the ratio of the extrusion velocity to the sharkskin oscillation frequency $f_{\mathrm{S}\mathrm{S}}$:

$\mathrm{\Lambda }=\frac{U_j}{f_{\mathrm{S}\mathrm{S}}}$

The frequency $f_{\mathrm{S}\mathrm{S}}$ is set by the time required to accumulate sufficient extensional stress at the die exit to cause cohesive failure and then re-adhere. Scaling analysis gives

$f_{\mathrm{S}\mathrm{S}}\sim \frac{1}{{\lambda }_{\mathrm{e}\mathrm{x}\mathrm{t}}}\sim \frac{{\dot{\epsilon }}_{\mathrm{e}\mathrm{x}\mathrm{i}\mathrm{t}}}{{\epsilon }_c}$

where ${\lambda }_{\mathrm{e}\mathrm{x}\mathrm{t}}$ is the extensional relaxation time at the die exit and ${\epsilon }_c\approx \ln (R_j/R)\approx (B_s-1)$ is the critical Hencky strain at the exit ($B_s$ is the die-swell ratio). Observed sharkskin frequencies for LLDPE are typically in the range 10–300 Hz, with wavelengths of order 10–300 μm — in the range that causes loss of optical clarity.

Die swell and its relation to melt fracture

The free-surface extrudate swells radially upon exit from the die due to the elastic recovery of normal stresses accumulated during flow. The die-swell ratio $B_s=R_{\mathrm{e}\mathrm{x}\mathrm{t}\mathrm{r}\mathrm{u}\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{e}}/R$ is related to the first normal stress difference $N_1$ by the Tanner equation:

$B_s=0.1+{[1+\frac{1}{2}{\left(\frac{N_1}{2{\tau }_w}\right)}^2]}^{1/6}$

Die swell is thermodynamically consistent with sharkskin: the same elastic energy that drives die swell (elastic recoil) is the energy that, when released catastrophically and non-uniformly, drives the extensional failure at the die exit responsible for sharkskin. In other words, large die swell and early-onset sharkskin are both symptoms of high elastic energy storage.

Effect of molecular architecture

Molecular weight and polydispersity

The critical wall shear stress for sharkskin onset scales approximately as

${\tau }_{c1}^{\mathrm{S}\mathrm{S}}\sim G_N^0\sim \frac{1}{M_e}$

independent of total molecular weight $M$, consistent with its identification as a cohesive failure of the entanglement network. In contrast, the critical stress for stick–slip scales with the disentanglement stress:

${\tau }_{c2}^{\mathrm{s}\mathrm{p}\mathrm{u}\mathrm{r}\mathrm{t}}\sim G_N^0$

The occurrence of different instabilities depends on molecular weight, polydispersity, and branching. Long-chain branching (as in LDPE) suppresses both sharkskin and stick–slip because branches entangle more effectively, raising $G_N^0$ and promoting strain hardening in extension, which stabilizes the exit flow. Narrow molecular weight distribution (metallocene PE) enhances sharkskin susceptibility because the sharp terminal relaxation spectrum produces a more abrupt stress response.

Polymer-processing additives (PPA)

Fluoropolymer processing aids work by depositing a low-surface-energy coating on the die wall. LDV velocity profiles provide direct evidence that slip occurs when the fluoropolymer additive is present; the experimental evidence suggests that additives can be effective in providing partial slip, thereby reducing both the magnitude and localization of velocity and stress concentrations. Mathematically, the PPA reduces the effective Navier slip coefficient from near-zero to a finite value ${\beta }_{N,\mathrm{P}\mathrm{P}\mathrm{A}}>0$, smoothing the velocity gradient at the die exit and reducing ${\dot{\epsilon }}_{\mathrm{e}\mathrm{x}\mathrm{i}\mathrm{t}}$ below the critical threshold.

Summary comparison of instabilities

Property	Sharkskin	Stick–slip / Spurt	Gross melt fracture
Location of origin	Die exit	Die land	Die entry (convergent zone)
Character	Surface only	Surface + pressure oscillation	Volumetric + surface
Critical stress (LLDPE)	~0.10–0.18 MPa	~0.20–0.30 MPa	>0.5 MPa
Mathematical criterion	${\mathrm{W}\mathrm{i}}_{\mathrm{e}\mathrm{x}\mathrm{i}\mathrm{t}}>{\mathrm{W}\mathrm{i}}_c$	$\frac{\mathrm{d}{v}_s}{\mathrm{d}{\tau }_w}>\frac{R}{4}\frac{\mathrm{d}\dot{\gamma }}{\mathrm{d}{\tau }_w}$	${\mathrm{W}\mathrm{i}}_{\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{y}}>{\mathrm{W}\mathrm{i}}_c^{\mathrm{G}\mathrm{M}\mathrm{F}}$
Key material property	$G_N^0$, ${\lambda }_r$	Slip law; compressibility	Extensional viscosity; entry vortex
Suppressed by	PPA; die exit taper; temperature gradient	PPA; fluoropolymer coating; die length reduction	Tapered entry; elevated temperature; branching

See also

• Wall slip
• Mooney–Rivlin solid
• Polymer melt
• Capillary rheometer
• Deborah number
• Weissenberg number
• Non-Newtonian fluid
• Polymer extrusion
• Viscoelasticity
• Die swell

Further reading

• Hatzikiriakos, S. G., and Migler, K. B. (eds.), 2005, Polymer Processing Instabilities: Control and Understanding, Marcel Dekker, New York.
• Denn, M. M., 2001, Extrusion instabilities and wall slip, Annual Review of Fluid Mechanics, 33, pp. 265–287.
• Agassant, J.-F. et al., 2006, Polymer processing extrusion instabilities and methods for their elimination or minimization, International Polymer Processing, 21(3), pp. 239–255.
• Larson, R. G., 1992, Instabilities in viscoelastic flows, Rheologica Acta, 31, pp. 213–263.
• Cogswell, F. N., 1972, Converging flow of polymer melts in extrusion dies, Polymer Engineering and Science, 12(1), pp. 64–73.
• Tanner, R. I., 1970, A theory of die-swell, Journal of Polymer Science Part A-2, 8(12), pp. 2067–2078.

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