Zeta potential - pH titration.  Alternatively you may be able to use color indicators along the lines of methyl orange, litmus, or phenolphthalein.

Dear Dr Xiaoen Wang,

Al2O3 is usually amphoteric in nature with its isoelectric point around pH 7-8 .But again the acidic or basic properties of these metal oxides is influenced by the method of preparation, phase composition and the capping agent or surfactant present on its surface.

Since the zeta potential is  pH sensitive and it may behave as acidic and basic oxide at different pH. As suggested by Dr. Alan a study of Zeta potential Vs pH is one of the best way to study the surface chemistry of it.

In recommendation to Dr. Alan and  Bikaah Sir,  To investigate the surface chemistry of Al2O3 NPs,  you should prefer zeta potential measurements . 

Hi 

By measuring the zeta potential, you can access the surface charge of nanoparticles and with the surface charge being determined, you can find the type of nanoparticles  interaction in the solution you are looking for.

I worked in this area, I think my work is useful for you.