The mechanism of dimerization is now clear, Thanks to Mathew Mahindratne.
Ref.Yoshihisa, et.al
There are two different isomers of Cholestadiene present, namely 3,5 Cholestadiene [ I ], and 2,4 cholestdiene [ IV ]. The plausible mechanism of their formation is shown below. They can undergo dimerization to yield [ II ] & [III].
Dimer [ II ] was formed from two pathways, which were the conversion of the dimer [ III ] and the dimerization of [I] (3,5-cholestadiene).
The dimer [ III ] was formed from [ IV ] (2,4-cholestadiene).
The mechanism of their formation is shown below.
The formation of the dimer [ II ] and/or the dimer [ III ] varies with the kind of acids employed.
Using a Bronsted acid medium results in the formation of [ II ].
For eg: In presence of Trichloroacetic acid and hydrochloric acid (10:1 ratio), dimer [ II ] was obtained.
Using a Lewis acid results in the formation of [ III ]. For eg: Zinc chloride and Acetyl chloride (Tschugaeff reaction),
Antimony trichloride and Acetyl chloride,
Ferric chloride and Sulfuric acid (Zak-Henly reaction),
Ferric chloride, Perchloric acid, and Phosphoric acid results in the formation of [ III ].
If the solution contains both Bronsted and Lewis acids, then a mixture of products is formed.
Eg: Both [ II ] and [ III ] are formed from the reactions with
Sulfuric acid and Acetic anhydride (Liebermann-Burchard reaction)
sulfuric acid (Salkowski reaction)
Trichloroacetic acid-SbCl3
Since sulfuric acid, having both Bronsted and Lewis acid character is used in our reaction, a mixture of products will be formed.
Ps: All Bronsted acids are Lewis acids, but not vice versa.
However, the third step (Sulfonation) needs further explanation.