• The velocity model of abrasive particles in the radial direction is modified. • Abrasive air-jet (AAJ) direct-writing of PDMS at 15° is presented. • Cryogenic abrasive air-jet (CAAJ) direct-writing of PDMS is presented. • CFD models of AAJ and CAAJ direct-writing are established. • "U"-shaped micro-channels are obtained by CAAJ and compared against AAJ at 15°. Cryogenic abrasive air-jet (CAAJ) machining technology is performed simultaneously with the occurrence of the glass transition for PDMS material. However, the mask material is also cooled with cryogenic PDMS cooling. Then, they both show significant brittle characteristics. Therefore, this leads to very poor selectivity between the mask and the PDMS. To solve this problem, CAAJ direct-write machining under unmasking conditions are proposed based on the modified velocity model of abrasive particles in the radial direction. This technique was used to direct-write machined the PDMS materials under small SOD. Then, the effect of cryogenic conditions on machining characteristics of PDMS micro-channels was studied by comparing the abrasive air-jet direct-write machining at oblique angles and CAAJ direct-write machining technologies through a series of experimental studies and CFD simulations. The results show that the material removal mode is transformed to a semi-brittle one, which greatly improves erosion removal efficiency, aspect ratio and bottom surface roughness of the micro-channel. On the other hand, the change in the viscosity of the jet medium has a crucial influence on the geometry of the micro-channel. The rebound direction of abrasive particles changes, and the sidewall of micro-channels is secondarily eroded due to an increase in jet medium viscosity in CAAJ. This, in turn, leads to a micro-channel with "U"-shaped profile. In addition, during CAAJ direct-write machining, sliding, scratching, and rolling of abrasive particles caused by bubble bursting can effectively reduce the bottom surface roughness of the micro-channel.