Dear Aditya,

as an inorganic chemist I'm not an expert in this particular field of research, but I assume that the answer lies in the acidic or basic character of common dyes. Many dyes have e.g. sulfonate or amino functionsal groups which direct their solubility in acids or bases. This means that basic dyes are better soluble and desorbed when using an acid. For a typical literature reference about this issue please have a look at the following potentially useful article which might help ypu in your analysis:

Acid Dye Removal from Aqueous Solution by Using Neodymium(III) Oxide Nanoadsorbents

This article has been published Open Access so that the full text is freely available on the internet (please see attached pdf file).

Good luck with your research!

Thanks sir for your suggestions.

Desorption of dyes from the nanoparticles involves the cleavage of metal-dye bond for that purpose , you need acid or base catalyst.