Cosmetic composition (I), for impregnating an absorbent support, comprises magnesium aluminum silicate and sodium carboxymethyl cellulose, where (I) has an apparent viscosity of greater than 80 (preferably 200) centipoises. Independent claims are included for: (1) an article for cleaning/care comprising (I); and (2) a process for manufacturing the article comprising a step for impregnating several absorbent supports arranged in stack by application under constraint of a rheofluidifying and thixotropic viscous composition on the support laid on the top of the stack.