What are micelles? Discuss the mechanism of micelle formation and cleaning active of soap

Micelle : The colloidal sized. Particle formed in water by the association of simple molecules
each having a hydrophilic end and hydrophobic end is called micelle.
→ Soap is sodium stearate $\left[{\mathrm{C}}_{17}{\mathrm{H}}_{35}\mathrm{COONa}\right]$ , in water soap gives the ions stearate anion and sodium ion ${\mathrm{C}}_{17}{\mathrm{H}}_{35}\mathrm{COONa}\to {\mathrm{C}}_{17}{\mathrm{H}}_{35}{\mathrm{COO}}^{-}+{\mathrm{Na}}^{+}$
In stearate anion, COO^– group as affinity for water is called hydrophilic group [head of anion]
– C₁₇H₃₅ as not affinity for water is called hydrophobic end [tail of the anion]
– The tail part dissolves the grease and forms micelle, removed by washing with water.
– For this a critical concentration of soap solution is required.