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The phrase "as a function of volume fraction" is correct and usable in written English.
It is typically used in scientific or mathematical contexts to describe how one variable changes in relation to the volume fraction of a substance or component.
Example: "The viscosity of the mixture varies as a function of volume fraction, indicating how the concentration of each component affects the overall flow behavior."
Alternatives: "in relation to volume fraction" or "depending on volume fraction".
Exact(32)
We study the settling velocity and the average orientation of the ellipsoids as a function of volume fraction.
Figure 5 The normalized thermal conductivity as a function of volume fraction for the Cu, CuO, and MWNT nanofluids.
Fig. 3 Thermal conductivity enhancements of silicone composites with different fillers as a function of volume fraction.
Figure 6 Enhancement of viscosity increase for alumina nanofluids as a function of volume fraction of nanoparticles.
Wear (w) and coefficient of friction are expressed as a function of volume fraction of the ingredients selected as w= k0V1k1V2k2…Vpkp and μ= m0V1m1V2m2…Vpmp.
Results also showed that there was no direct correlation between hardness and wear resistance as a function of volume fraction and Rs/Ms ratio.
Similar(28)
The rheology of the dispersions as a function of the volume fraction of the particles was monitored and the viscosity and shear-thinning increased as volume fraction increased.
At high ethanol volume fractions, the measured partition coefficients displayed an approximate linear relationship when plotted on semi-log scale as a function of ethanol volume fraction.
The values of α as a function of filler volume fraction are provided in Figure 10.
These properties exhibit a nonlinear variation as a function of filler volume fraction.
Figure 6 Thermal conductivity ratio as a function of CuO volume fraction at 25°C.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com