The disturbing of ultrafine particles on carrying phase is usually ignored in studies on dilute ultrafine particle systems. In a dense fractal-like agglomerate system, however, the effect of particle phase on carrier phase should be considered due to its unique heat and mass transfer while the corresponding mathematical model for this problem has not been established. By taking the agglomerate-laden suspension as a single pseudo fluid, we propose a two-way coupling model in which the developed governing equations for suspension and particle general dynamic equation (PGDE) for particle coagulation and breakage due to turbulence are simultaneously solved. The Taylor-expansion moment method has been applied to solve fractal-like aggregate process and dilute gas-to-particle conversion, and in this study it is further extended to close the PGDE equation by invoking fractal theory. The newly coupling model is not limited in dilute particle system, and thus it is expected to play important roles in studying dense fractal-like agglomerate synthesis or other particulate industrial applications.

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