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The dissolution process was controlled by the bulk diffusion through the product layer crystals.

The linear relationship between JH2 and ln(p′H2/p′′H2) indicates that hydrogen permeation occurs via the ambipolar diffusion of proton and electron in ESC asymmetrical membrane and is controlled by the bulk diffusion of proton.

The hydrogen transport rate is controlled by the bulk diffusion although the pressure dependence of the H2 flux deviates slightly from Sieverts' law.

According to classic theories, at high supersaturation, the Gibbs Thomson effect is weak, and crystal growth is usually dominated by the bulk diffusion process in which small crystals grow at a higher rate than large ones so that the particle size distribution is focused [13, 21, 22].

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Nitrogen plays the key role in compartment generation by the formation of pentagons in addition to hexagons [40] and also by increasing the bulk diffusion of carbon and nitrogen species in catalyst nanoparticles [41].

During the first stage, the growth of CdSe QDs was dominated by bulk diffusion, whereas, neither the bulk diffusion process nor the surface reaction process could be neglected during the later stage.

We denote the bulk diffusion timescale by (t_{d}) and the surface dissolution timescale by (t_{s}).

Several studies have documented that the bulk diffusion properties of deformed materials can be enhanced by several orders of magnitude over volume diffusion in a pristine lattice [28, 31, 55 57].

Finally, swapping is a process in which molecules exchange position, accounting for the bulk diffusion.

In this regime, both the fine-grained microstructure and Al3Sc particles exhibit third order coarsening kinetics with dR/dt ∝ dr/dt which indicates that grain coarsening is controlled by the rate of particle growth with the latter controlled by bulk diffusion of scandium in the Al matrix.

CNT shell that is created by the diffusion of Rs species to the peripheral surface is followed by bulk diffusion of the RS species through the droplet.

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