= Geometry-dependent erosion-rate inference
\b[Geometry-dependent erosion-rate inference] converts a measured <polymer> mass-loss rate into a <polymer erosion front speed> using an explicit model of specimen shape, exposed surfaces and <density>. The conversion is justified only if an inward-moving boundary actually describes the specimen. IUPAC's definition of <polymer erosion> concerns degradation progressing from the surface inward; loss of mass alone does not establish that spatial mechanism.<Terminology for biorelated polymers and applications (IUPAC Recommendations 2012) by Michel Vert and others>[entry 70, erosion, printed p. 391]{ref}
An original constant-density calculation shows the geometric dependence. Write $q=-M'/M$ for positive relative mass-loss rate and $v$ for positive inward boundary speed. For a <sphere> of radius $R$, a long <cylinder> of radius $R$ whose ends are protected, and a sheet of full thickness $h$ attacked on both large faces with negligible edge effects, respectively,
$$
q=\frac{3v}{R},\qquad q=\frac{2v}{R},\qquad q=\frac{2v}{h}.
$$
These follow by differentiating $M=4\pi\rho R^3/3$, $M=\pi\rho R^2\ell$ with fixed length $\ell$, and $M=\rho Ah$ with fixed face area $A$. The radial boundaries obey $R'=-v$; the two sheet boundaries give $h'=-2v$. Exposing the cylinder ends or the sheet edges requires including their motion as well.
For stipulated $q=0.03\,\mathrm{day^{-1}}$ and current $R=1\,\mathrm{mm}$, the <sphere> implies $v=0.01\,\mathrm{mm\,day^{-1}}$, whereas the end-protected <cylinder> implies $0.015\,\mathrm{mm\,day^{-1}}$. A sheet with current $h=1\,\mathrm{mm}$ gives the latter speed under its two-face assumption. The identical relative mass slope therefore does not identify a unique front speed without geometry.
The retained mass fraction $f=M/M_0$ similarly implies
$$
\frac{R}{R_0}=f^{1/3}\quad\text{for the sphere},\qquad
\frac{R}{R_0}=f^{1/2}\quad\text{for the end-protected cylinder}.
$$
For $f=0.729$, the respective radius ratios are 0.900 and approximately 0.854. These are original model predictions, not measurements of a particular <polymer>. A fit to retained mass cannot by itself select between the shapes or demonstrate a sharp front.
Even the relation between <mass> and volume needs checking. If a specimen remains spatially uniform but its <density> changes with time, $M=\rho V$ gives
$$
-\frac{M'}M=-\frac{V'}V-\frac{\rho'}\rho.
$$
A density change contributes to the inferred relative mass slope independently of boundary motion. <Nonuniform-density erosion inference> requires the further spatial information hidden by this uniform-density equation. Swelling, fragment detachment and an extended reaction zone also challenge a sharp-front interpretation.
A discriminating experiment combines timed dry-mass measurements with radius or thickness measurements, imaging of cut specimens and chemical observations at different depths. Specify which faces were exposed, how drying was performed and whether dimensions were measured wet or dry. Kureha's <polyglycolic acid> test holds material in water, then filters and dries it before measuring retained solids.<Kuredux Polyglycolic Acid Resin technical brochure by Kureha>[March 2022 brochure, PDF p. 3, Degradability test method]{ref} That apparatus supplies a retained-mass curve; direct front or dimensional observations would be an additional measurement, rather than information already contained in that curve.
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