Recent environmental chamber studies suggest that acid-catalyzed reactions between alcohols and aldehydes in the condensed phase lead to the formation of hemiacetals and acetals, enhancing secondary organic aerosol (SOA) growth. We report measurements of heterogeneous uptake of butanol and decanol on liquid H2SO4 in the range of 62-84 wt% and between 273 and 296 K. Both alcohols exhibit two distinct types of uptake behaviors (partially irreversible vs totally irreversible uptake), depending on the acid concentration and temperature. For the partially irreversible uptake, a fraction of the alcohol was physically absorbed while the other fraction underwent irreversible reaction. For the totally irreversible uptake, the alcohols were completely lost onto the sulfuric acid. The Henry's law solubility constant (H*) was determined from the time-dependent uptake, while the reactive uptake coefficients were calculated from the time-independent irreversible loss. Coexistence of butanol or decanol with octanal or decanal did not show enhanced uptake of the aldehydes in the sulfuric acid. Protonation and dissolution likely account for the reversible uptake, while formation of alkyl sulfate or dialkyl sulfate explains irreversible uptake of the alcohols. The results suggest that heterogeneous uptake of larger alcohols is unlikely of significant importance in the lower atmosphere except in the case of freshly nucleated aerosols that may have high acid concentrations.