Evaporative CO$_2$ microchannel cooling for the LHCb VELO pixel upgrade

The LHCb Vertex Detector (VELO) will be upgraded in 2018 to a lightweight pixel detector capable of 40 MHz readout and operation in very close proximity to the LHC beams. The thermal management of the system will be provided by evaporative CO$_2$ circulating in microchannels embedded within thin silicon plates. This solution has been selected due to the excellent thermal efficiency, the absence of thermal expansion mismatch with silicon ASICs and sensors, the radiation hardness of CO$_2$, and very low contribution to the material budget. Although microchannel cooling is gaining considerable attention for applications related to microelectronics, it is still a novel technology for particle physics experiments, in particular when combined with evaporative CO$_2$ cooling. The R&D effort for LHCb is focused on the design and layout of the channels together with a fluidic connector and its attachment which must withstand pressures up to 170 bar. Even distribution of the coolant is ensured by means of the use of restrictions implemented before the entrance to a race track like layout of the main cooling channels. The coolant flow and pressure drop have been simulated as well as the thermal performance of the device. This proceeding describes the design and optimization of the cooling system for the VELO upgrade and the latest prototyping results.