A microbial strain is cultured in a $100$ L stirred fermenter for secondary metabolite production. If the specific rate of oxygen uptake is $0.4 \: h^{-1}$ and the oxygen solubility in the broth is $8$ mg/L, then the volumetric mass transfer coefficient $(K_La)$ (in $s^{-1}$) of oxygen required to achieve a maximum cell concentration of $12$ g/L is (up to two decimal places) ___________