. 2019 Dec 17;16(24):5159. doi: 10.3390/ijerph16245159

Table 4.

Accumulative release model of heavy metals.

Treatment		First-Order Kinetic Model		Modified Elovich Model		Double-Constant Model		Hyperbolic Diffusion Model
Treatment		lny = a + bx	R²	y = alnx + b	R²	lny = alnx + b	R²	y = ax^0.5 + b	R²
Cu	Control treatment	lny = 0.2381x − 0.1348	0.6964	y = 0.6879lnx − 1.2099	0.9811	lny = 0.5206lnx − 0.0941	0.9458	y = 1.0246x^0.5 − 0.1459	0.9239
	SSS treatment	lny = 0.2263x − 0.2398	0.6889	y = 0.5749lnx − 1.0682	0.9801	lny = 0.4963lnx − 0.0233	0.9422	y = 0.8538x^0.5 − 0.1828	0.9170
	USS treatment	lny = 0.1933x − 0.4609	0.6634	y = 0.3703lnx − 0.8112	0.9649	lny = 0.4282lnx − 0.2792	0.9289	y = 0.5447x^0.5 − 0.2491	0.8840
Cr	Control treatment	lny = 0.2996x − 3.0445	0.6832	y = 0.5133lnx − 0.0740	0.9911	lny = 0.6581lnx − 2.7587	0.9378	y = 0.0796x^0.5 − 0.0089	0.9470
	SSS treatment	lny = 0.2201x − 3.0824	0.6133	y = 0.0319lnx − 0.0621	0.9686	lny = 0.4969lnx − 2.8825	0.8986	y = 0.0468x^0.5 − 0.0139	0.8788
	USS treatment	lny = 0.1032x − 3.5910	0.4747	y = 0.0075lnx − 0.0310	0.8502	lny = 0.2464lnx − 3.5074	0.7999	y = 0.0105x^0.5 − 0.0204	0.6946
Zn	Control treatment	lny = 0.3624x − 0.1496	0.7339	y = 1.3790lnx − 1.4965	0.9746	lny = 0.7795lnx − 0.2087	0.9595	y = 2.0498x^0.5 − 0.6526	0.9595
	SSS treatment	lny = 0.3593x − 0.3164	0.7420	y = 1.1286lnx − 1.2558	0.9635	lny = 0.7695lnx − 0.0413	0.9604	y = 1.7157^0.5 − 0.5431	0.9489
	USS treatment	lny = 0.1803x − 0.3950	0.5509	y = 0.3573x − 0.8556	0.9281	lny = 0.4173lnx − 0.2388	0.8572	y = 0.5136x^0.5 − 0.3316	0.8068