= Polymer erosion front speed
\b[Polymer erosion front speed] is the rate at which a surface-localized degradation boundary advances into a specimen. In the IUPAC sense of <polymer erosion>, the process progresses from the surface inward. A decrease in specimen mass alone does not establish that such a front exists.<Terminology for biorelated polymers and applications (IUPAC Recommendations 2012) by Michel Vert and others>[entry 70, erosion, printed p. 391; Gold Book entry 13906]{ref}
For an original spherical model, let $R(t)$ be the radius of the surviving uniform material, assume constant density $\rho$ and define positive inward speed $v=-dR/dt$. Then
$$
M=\frac{4\pi\rho R^3}{3},\qquad
-\frac{dM}{dt}=4\pi\rho R^2v.
$$
The local speed is therefore $v=-M'/(4\pi\rho R^2)$. A declining mass-loss rate can arise from shrinking surface area even at constant front speed; it need not mean the surface reaction slowed.
Writing the retained mass fraction as $f=M/M_0$ gives, under these assumptions,
$$
R=R_0f^{1/3},\qquad
v=-\frac{R_0}{3}f^{-2/3}\frac{df}{dt}.
$$
<Geometry-dependent erosion-rate inference> matters: for a sheet attacked on two faces of fixed area $A$, the corresponding relation is $-M'=2\rho Av$ before the fronts meet. Substituting the spherical relation for a sheet would misassign the same observed mass rate.
An original radius measurement finds $R_1=1.00\,\mathrm{mm}$ and $R_2=0.94\,\mathrm{mm}$ six days apart. The average inward speed is $(R_1-R_2)/6=0.01\,\mathrm{mm\,day^{-1}}$. Independent standard uncertainties of 0.005 mm in the radii give speed uncertainty about $0.00118\,\mathrm{mm\,day^{-1}}$ when timing uncertainty is negligible. A shared additive radius offset cancels from the difference, but a shared scale error does not generally cancel from the speed. <Uncertainty propagation> must retain that distinction.<Guide to the expression of uncertainty in measurement by JCGM>[§5.2, correlated inputs]{ref}
To test the front interpretation, pair dimensional or cross-sectional measurements with mass and chemical observations. Swelling, nonuniform density, fragment detachment and a broad reaction zone violate parts of the sharp-front model. Numerical differentiation of noisy mass measurements can also magnify scatter.
A manufacturer's timed water-exposure test for <polyglycolic acid> weighs filtered dry residue.<Kuredux Polyglycolic Acid Resin technical brochure by Kureha>[PDF p. 3, Degradability test method]{ref} It supplies a retained-mass observable, not by itself a measured front position. Report a front speed only with the spatial evidence and geometric assumptions needed to give that speed a physical meaning.
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