You may use gravity differences between CNTs and alumina powders. Put them into a column container to spin. You may be able to use centrifuges to do so.
Al2O3 is amphoteric and will be dissolved with warm (50 C) NaOH at pH > 12 or warm (50 C) HCl (at pH < 2). Take care with the former as NaOH dissolves glass (so do it in a plastic beaker). Wear eye and face protection. Your material will need extensive washing with DI water after the dissolution of the alumina.
Ethireddy Radhika If you use WC balls then your material will be contaminated with WC... You'll not see it with CNT's though.... Try using WC to mill Al2O3 (which is white) - then you'll see your product turn grey and then black...
Alan F Rawle sir, what you said is right sir, i tried with another white colour chemical it is contaminated and turned to grey and then black, but for aluminium nitride it is good, when i tried in alumina, and zirconia balls it contaminated, so i thought if alumina is contaminating for any material we can use tungsten carbide, but finally i came to know that its dependent on characteristic of particular material.