“…With the MB size distribution known, the MB shell stiffness ( S p in N/m) and shell friction ( S f in kg/s) are estimated by fitting a linearized encapsulated MB model proposed by de Jong et al , to the measured attenuation curves. The linearized model has been used extensively in previous literature studies; ,− it neglects multiple scattering effects and assumes low amplitude bubble oscillations (both of which are reasonable considering the high MB dilution ratios and low acoustic pressure employed in our experiments). For more information about the model, one can refer to previously published literature. , The size distribution of MBs is directly used to obtain the estimated attenuation per unit distance using the following equation α normale normals normalt normali normalm normala normalt normale normald ( r , f ) = 10 ln ( 10 ) ∑ r n ( r ) σ s ( r , f ) δ normalt normalo normalt ( r , f ) δ normalr normala normald ( r , f ) Here, n is the MB number density from measurements obtained using Coulter counter, σ s is the scattering cross sections of the MBs, and δ tot is the total damping which is the sum of the radiation (δ rad ), viscous (δ vis ), and shell friction (δ sh ) terms.…”