Mass continuity equation in the electromagnetic field

A theoretical method with the quaternion algebra was presented to derive the mass continuity equation from the linear momentum. It predicts that the strength of electromagnetic field and the velocity have the impact on the mass continuity equation. In the gravitational field and electromagnetic field, the mass continuity equation will change with the electromagnetic field strength, gravitational field strength, linear momentum, electric current, and the speed of light. The deduction can explain why the field strength has an influence on the anomalous transport about the mass continuity equation in the plasma and electrolytes etc.