= Hydration versus production in nail mass balance
\b[Hydration versus production in nail mass balance] distinguishes changes in retained <water> from changes in structural <nail plate> material. A wet <mass>, a thickness reading and a marked displacement measure different properties. They cannot be converted into a common production rate without a model of composition and geometry.
Write an original two-inventory balance as
$$
M_{\rm wet}=M_s+W,\qquad
\frac{dM_s}{dt}=P_s-L_s,\qquad
\frac{dW}{dt}=J_{w,\rm in}-J_{w,\rm out}.
$$
Here $M_s$ is structural <mass>, $W$ retained <water>, and $P_s,L_s$ structural production and loss. Wet-mass gain can occur with $P_s=0$ when water inflow exceeds outflow. For an isolated clipping, there is no continuing supply from the <nail matrix> even though water exchange can continue.
A primary <ellipsometry> study measured changes in human fingernail <complex refractive index> during water uptake and loss, reporting characteristic time domains of approximately 4, 150 and 3,200 minutes. Its model distinguished more weakly and more tightly associated water in <keratin>.<Hydration dynamics of human fingernails: An ellipsometric study by B. Schulz and others>[Abstract, measured optical response and interpretation, DOI 10.1103/PhysRevE.65.061913]{ref} Those observations concern material conditioning; they are not measurements of matrix cell production or universal time constants for every nail.
For a simple illustrative one-pool relaxation, $W(t)=W_\infty+(W_0-W_\infty)e^{-t/\tau}$. Choose fixed $M_s=10$ mg, $W_0=4$ mg, $W_\infty=2$ mg and $\tau=60$ minutes. Wet <mass> falls from 14 towards 12 mg, reaching approximately 12.736 mg after one hour, despite unchanged structural material. These values are constructed examples rather than fitted parameters from the cited study.
<Water-denominator effects in nail concentration measurements> follow even if a retained marker amount is unchanged. A stipulated 100 ng marker in those samples would increase from $100/14\approx7.14$ to $100/12\approx8.33\,\mathrm{ng\,mg^{-1}}$ when expressed per wet <mass>, a 16.7% increase without added marker. Actual retention must be checked rather than assumed.
A useful experiment records conditioning, weighs the sample over time and independently measures geometry or optical response. Structural production, water exchange and clipping removal belong to separate terms. Specify whether a reported concentration is normalized to wet material or a separately characterized structural amount before comparing measurements.
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