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Boundary-density calibration for erosion fronts determines the local density needed to convert a surface mass-loss rate into a polymer erosion front speed. The relevant density is that of the material crossing the boundary, conditioned consistently with the mass and dimensional measurements. Whole-specimen mass divided by whole-specimen volume gives an average, not automatically the required boundary value.

For a spherical, inward-moving boundary of radius $R$, negligible interior density change givesThe local-density requirement follows from nonuniform-density erosion inference. NIST defines mass density as mass divided by volume; the experimental volume and sampled region must therefore be specified.^[ref]

An original calibration construction removes or samples a shell of thickness $\delta$. Its mean density isA finite shell measures a weighted layer average. For a smooth radial profile, expansion gives ${\rho }_{\delta }=\rho (R)-{\rho }^{\prime }(R)\delta /2+O({\delta }^2)$. Thus a thinner shell approaches the boundary value, but finite-layer bias depends on the density gradient. Finite-shell bias in boundary-density calibration is distinct from random weighing error.

For the stipulated profile $\rho (r)={\rho }_0[1+(r/R_0{)}^2]$ at current radius $R=R_0$, a shell with $\delta =0.1R_0$ giveswhereas the actual boundary density is $2{\rho }_0$. Substituting the shell average into the instantaneous speed conversion overestimates speed by about 4.9%. These are original profile calculations, not measured material properties.

Very thin layers have their own uncertainty cost. For measured layer mass $m$ and volume $V$, first-order propagation givesShrinking the layer can increase relative mass and thickness uncertainty. Shared dimensional corrections can correlate volumes and successive layer estimates; the GUM requires relevant covariance terms.^[ref] A smaller sampling thickness therefore trades spatial averaging against measurement uncertainty.

A proposed experiment uses matched specimens or recorded sequential sectioning, measures removed material and layer geometry, and compares several layer thicknesses. Distinguish wet, dried, porous-envelope and solid-material volumes. Cutting, drying or extracting a layer can change its composition, so independent spatial observations should test whether the sampled material represents the original boundary.

Kureha's polyglycolic acid degradation test filters and dries residual solids after water exposure.^[ref] It supplies retained dry mass; it does not supply local boundary density or prove the existence of a sharp erosion front. The additional calibration construction above makes those missing measurements explicit.

The layer-thickness tradeoff in erosion-density sampling balances spatial averaging bias against uncertainty in the small mass and volume of a sampled surface layer. A thinner layer can better represent boundary density while being harder to measure precisely. The preferred thickness depends on the measurement model and the required inference, rather than being a material constant.

In an original locally planar model, layer density is estimated as $\hat{\rho }=\Delta M/(A\delta )$, with area $A$ and thickness $\delta$. For boundary density ${\rho }_s$ and outward density gradient $g$, finite-shell bias in boundary-density calibration gives leading bias $-g\delta /2$. Suppose the standard uncertainties $u_M$ and $u_{\delta }$ are independent and approximately constant over the tested thickness range. First-order propagation givesThe final term assumes independent area uncertainty; correlations require additional terms. The GUM supplies the general correlated-input propagation rule.^[ref]

Write $b^2=(u_M/A{)}^2+({\rho }_s{u}_{\delta }{)}^2$ and $c^2={\rho }_s^2{u}_A^2/A^2$. The resulting squared-error planning objective isFor nonzero $g,b$, differentiation gives ${\delta }_{\ast }=(4b^2/g^2{)}^{1/4}=\sqrt{2b/|g|}$. The area term raises the error floor in this approximation without changing the optimum; thickness uncertainty changes the optimum through $b$.

For stipulated $A=1\mathrm{c}{\mathrm{m}}^2$, ${\rho }_s=1\mathrm{g}\mathrm{c}{\mathrm{m}}^{-3}$, $|g|=0.2\mathrm{g}\mathrm{c}{\mathrm{m}}^{-4}$ and $u_M=0.0001$ g, neglecting thickness uncertainty gives ${\delta }_{\ast }\approx 0.316$ mm. Including $u_{\delta }=0.0001$ cm, or 1 micrometre, gives $b=\sqrt{2}\times 10^{-4}\mathrm{g}\mathrm{c}{\mathrm{m}}^{-2}$ and ${\delta }_{\ast }\approx 0.376$ mm. These are original planning examples, not prescribed section thicknesses.

Thickness-uncertainty limit in erosion-density sampling becomes important when small layers approach the dimensional readout's resolution. If the feasible interval excludes the calculated optimum, optimize over the actual interval and test whether the local-gradient and planar approximations remain adequate. If $g=0$, this simplified model has no finite interior optimum; other constraints determine the usable thickness.

A proposed experiment uses matched conditioning, several layer thicknesses and recorded mass-difference correlations. Sectioning damage or density changes during drying can invalidate the assumed error model. Kureha's polyglycolic acid experiment measures filtered, dried retained solids after water exposure.^[ref] Local density sampling is an additional measurement, and its tradeoff should be assessed separately from the retained-mass curve.