Ultrasonic cleaning in the membrane process: From phenomenon to mechanism and mathematical model

•A new model was proposed to describe the flux variation rate (FRR) for ultrasonic cleaning.•Suspended layer observed in ultrasonication had inhibition effect on FRR (10%-20%)•This model considered bubble dynamics, nonuniform cake structure and inhibition effect.•A novel determining the cleaning efficiency of ultrasonic cleaning was proposed.•Energy conservation of about 70% was obtained in periodical ultrasonic cleaning.