We use a multi-fluid model to describe the dynamic behavior of electrons, ions, and neutrals in a weakly ionized three-component plasma and investigate the differentially rotational instability. Charged species and neutrals are supposed to have the same angular velocity to eliminate the equilibrium current and collisions in the unperturbed state. By taking into account collisions between electrons/ions and neutrals, we derive the analytical expression of the general local dispersion relation and examine the collision effect on the rotational instability in different limiting cases. Collisions on neutrals are neglected in the first case to obtain a simplified dispersion, in which collisions play an important role in the instability criteria. In the low-frequency region, the previous result in the magnetohydrodynamic model is reproduced. The collision effect in the high-frequency case for non-magnetized electrons is found to be similar to the low-frequency region, but can induce instability for both the negative and positive radial derivative of rotational frequency.
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