Assume constant current flows through the wires. I feel that at the junction, electrons suddenly gain or lose velocity. This is a result of $I=n_e\cdot e\cdot A \cdot v_d$ with $v_d$ (drift velocity) and that the current is a scalar quantity.
I want to know what is the reason behind this, or where does the force which changes direction and magnitude of drift velocity come from, since battery's emf only accelerates them along the direction of wire, and thus whenever wire is curved or junction is present, I encounter this problem.