What is the actual mechanism of Fenton reaction?
The Fenton reaction

The oxidation of organic substrates by iron(II) and hydrogen peroxide ($\ce{H2O2}$ ) is called the Fenton Reaction. It was first described by Henry John Horstman Fenton in 1894 who first observed the oxidation of tartaric acid by $\ce{H2O2}$ in the presence of $\ce{Fe^{2+}}$ ions [1]. After more than 100 years, the mechanism of the reaction is still unsettled. The recent review by Dunford (2002) stated that:


  The mechanism of reaction of hexaquo iron(II) with hydrogen peroxide has been unresolved for 70 years. Most scientists, perhaps by default, have accepted the free radical chain mechanism of Barb et al. (1957)[3]. However an earlier proposal involved formation of the ferryl ion, $\ce{FeO2+}$ [4]. Recent work has favored a mechanism involving $\ce{FeO2+}$ and $\ce{FeOFe^{5+}}$ species. Similarly there are differences of opinion on the mechanism of reaction of iron(III), both hexaquo and chelated, with hydrogen peroxide. These differences have fostered a recent burst of activity, with claims on one hand that hydroxyl radicals play a key role, and on the other, that there is a non-free radical mechanism. In contrast, the mechanism of reaction of the heme-containing peroxidase and catalase enzymes with hydrogen peroxide, orders of magnitude faster than reactions of iron(II)/(III), now appears to be well established. 


According to the free radical chain mechanism [3], the formation of radicals $\ce{HO^.}$ and $\ce{HO2^.}$ have been proposed. Although, this mechanism has some flaws, it has still been used to explain result in current research as recently as 2014 [5]. The proposed mechanism was depicted in Figure 1, which is followed by several other well received mechanisms for the reaction discussed in reviews sighted.

Mechanism of the redox reaction involved in the Fenton’s reagent (Figure 1)[5]:



Basic reactions and intermediates involved in the classic Fenton and the metal centered Fenton reactions (Figure 2)[6]:



Proposed non-radical mechanism for the Fenton reaction (Figure 3)[6]:


Possible reaction pathways for the Fenton reaction in absence of organic substrates (Figure 4)[6]:



Requirements of the reaction:

$\mathrm{pH}$ should be adjusted to 3-5: if the $\mathrm{pH}$ is too high the iron precipitate in $\ce{Fe(OH)3}$ and will decompose the $\ce{H2O2}$ to oxygen. Basically, the optimal $\mathrm{pH}$ occurs between $3$ and $6$. It's really important to pay attention to the double $\mathrm{pH}$ drop due to the addition of $\ce{FeSO4}$ ($\ce{Fe^{2+}}$ source) and $\ce{H2O2}$. Indeed, $\ce{FeSO4}$ catalyst which contains residual $\ce{H2SO4}$ and the $\ce{H2O2}$ addition is responsible for the fragmentation of organic material into organic acids. Thus, the iron catalyst should be added as a solution of $\ce{FeSO4}$ with slow addition of $\ce{H2O2}$, you may able to control the suddern variation of $\mathrm{pH}$ and the temperature during the reaction. It's better to complete the reaction step by step with a continuous adjustment of these factors.

References:

[1] LXXIII.—Oxidation of tartaric acid in presence of iron: H. J. H. Fenton, J. Chem. Soc., Trans., 1894, 65, 899–910 (DOI: 10.1039/CT8946500899).

[2] Oxidations of iron(II)/(III) by hydrogen peroxide: from aquo to enzyme: H.Brian Dunford, Coordination Chemistry Reviews, 2002, 233–234, 311-318 (https://doi.org/10.1016/S0010-8545(02)00024-3).

[3] Reactions of ferrous and ferric ions with hydrogen peroxide. Part I.—The ferrous ion reaction: W. G. Barb,  J. H. Baxendale,  P. George,  and  K. R. Hargrave, Trans. Faraday Soc., 1951, 47, 462-500 (http://dx.doi.org/10.1039/TF9514700462).

[4] Ferryl ion, a compound of tetravalent iron: William C. Bray, and M. H. Gorin, Journal of American Chemical Society, 1932, 54(5), 2124-2125 (DOI: 10.1021/ja01344a505).

[5] Design Polysaccharides of Marine Origin: Chemical Modifications to Reach Advanced Versatile Compounds: Nathalie Chopin, Xavier Guillory, Pierre Weiss, Jean Le Bideau, and Sylvia Colliec-Jouault, Current Organic Chemistry, 2014, 18(7), 867-895 (DOI: 10.2174/138527281807140515152334).

[6] Fenton reaction - Controversy concerning the chemistry: Krzysztof Barbusinski, Ecological Chemistry and Engineering S, 2009, 16(3), 347-358.