A theoretical study on the agglomeration kernel of bipolar charged particles in external fields is presented in order to investigate particle agglomeration under the combined effects of a direct-current (DC) electric field and an acoustic field, while taking into consideration particle collision efficiency. Three agglomeration kernels are considered in our model, namely Coulomb agglomeration, electric agglomeration, and acoustic agglomeration. The model performance is validated by comparing its predictions with the available exact solutions of peculiar cases. Our results indicate that the collision efficiency increases when an electric field is applied simultaneously with an acoustic field. The size of the total agglomeration kernel formed by the three processes listed above increases with the external electric field intensity and the sound pressure level (SPL). Based on this model which includes collision efficiency, the electric and acoustic agglomeration kernels both increase rapidly as the agglomeration nucleus particle size increases, eventually approaching saturation for large diameters. On the other hand, the total agglomeration kernel decreases as the sound frequency increases within the investigated range. The agglomeration kernels of particles with different relative dielectric constants, such as fly ash particles, solid carbon particles and water droplets, are investigated as well.