Numerical design of magnetic-field-gradient-guided branch targeting of Au/Ni-SiO2 Janus microrobots in a bifurcating microchannel.

The controllable branch guidance of magnetic Janus microrobots in bifurcating microchannels is governed by the coupled effects of background advection, magnetophoretic migration and particle structure. Here, a three-dimensional numerical framework was developed to investigate the magnetically controlled transport of Au/Ni-SiO2 Janus microrobots in an idealised low-Reynolds-number bifurcating microchannel. An equivalent three-axis Helmholtz-Maxwell coil model was used to reconstruct an oblique magnetic-field gradient directed towards the target branch, and the resulting electromagnetic field was coupled with particle tracking. Over 0.5-7.0 T m-1, the reconstructed gradients closely reproduced the prescribed values, whilst the magnetic flux density remained above the adopted near-saturation criterion for Ni. For the baseline microrobot with a 120 nm Ni layer, the target-branch transport efficiency increased from 42.67% at 1.5 T m-1 to 100% at 7.0 T m-1. Increasing the inlet velocity from 0.25 to 1.50 mm s-1 shifted the guidance response towards higher gradients, reflecting stronger competition between axial advection and lateral magnetophoretic migration. Increasing the Ni-layer thickness from 150 to 390 nm raised the magnetic Ni volume fraction from 8.45% to 20.74% and reduced the minimum tested gradient for complete target-branch transport from 5.5 to 2.5 T m-1, a reduction of approximately 54.5%. Mechanistic analysis showed that the increase in magnetic moment substantially exceeded the increase in hydrodynamic resistance, and the transport data for different Ni-layer thicknesses were largely represented by a common response using a dimensionless magnetic-guidance parameter. These results provide a quantitative basis for co-optimising microrobot magnetic structure, background flow and external magnetic actuation.