An after-treatment (AT) system for a flow of exhaust gas of an internal combustion engine includes a first AT device and a second AT device in fluid communication with and positioned in the exhaust gas flow downstream of the first AT device. The AT system also includes an exhaust passage configured to carry the exhaust gas flow from the first AT device to the second AT device. The AT system additionally includes an injector configured to introduce a reductant into the exhaust passage. The second AT device includes an inlet cone having a volute defining a spiral primary path for the exhaust gas flow into the second AT device and configured to generate a swirling motion of and turbulence in the exhaust gas flow. A vehicle employing the AT system is also disclosed.