The flow of a suspension through a bifurcating channel is studied experimentally and by computational methods. The geometry considered is an ‘asymmetric T’, as flow in the entering branch divides to either continue straight or to make a right angle turn. All branches are of the same square cross-section of side length $D$ , with inlet and outlet section lengths $L$ yielding $L/D=58$ in the experiments. The suspensions are composed of neutrally buoyant spherical particles in a Newtonian liquid, with mean particle diameters of $d=250~\unicode[STIX]{x03BC}\text{m}$ and $480~\unicode[STIX]{x03BC}\text{m}$ resulting in $d/D\approx 0.1$ to $d/D\approx 0.2$ for $D=2.4~\text{mm}$ . The flow rate ratio $\unicode[STIX]{x1D6FD}=Q_{\Vert }/Q_{0}$ , defined for the bulk, fluid and particles, is used to characterize the flow behaviour; here $Q_{\Vert }$ and $Q_{0}$ are volumetric flow rates in the straight outlet branch and inlet branch, respectively. The channel Reynolds number $Re=(\unicode[STIX]{x1D70C}DU)/\unicode[STIX]{x1D702}$ was varied over $0<Re<900$ , with $\unicode[STIX]{x1D70C}$ and $\unicode[STIX]{x1D702}$ the fluid density and viscosity, respectively, and $U$ the mean velocity in the inlet channel; the inlet particle volume fraction was $0.05\leqslant \unicode[STIX]{x1D719}_{0}\leqslant 0.30$ . Experimental and numerical results for single-phase Newtonian fluid both show $\unicode[STIX]{x1D6FD}$ increasing with $Re$ , implying more material tending toward the straight branch as the inertia of the flow increases. In suspension flow at small $\unicode[STIX]{x1D719}_{0}$ , inertial migration of particles in the inlet branch affects the flow rate ratio for particles ( $\unicode[STIX]{x1D6FD}_{\mathit{particle}}$ ) and suspension ( $\unicode[STIX]{x1D6FD}_{\mathit{suspension}}$ ). The flow split for the bulk suspension satisfies $\unicode[STIX]{x1D6FD}>0.5$ for $\unicode[STIX]{x1D719}_{0}<0.16$ while $\unicode[STIX]{x1D719}_{0}=0.16$ crosses from $\unicode[STIX]{x1D6FD}\approx 0.5$ to $\unicode[STIX]{x1D6FD}>0.5$ at $Re\approx 100$ . For $\unicode[STIX]{x1D719}_{0}\geqslant 0.2$ , $\unicode[STIX]{x1D6FD}<0.5$ at all $Re$ studied. A complex dependence of the mean solid fraction in the downstream branches upon inlet fraction $\unicode[STIX]{x1D719}_{0}$ and $Re$ is observed: for $\unicode[STIX]{x1D719}_{0}<0.1$ , the solid fraction in the straight downstream branch initially decreases with $Re$ , before increasing to surpass the inlet fraction at large $Re$ ( $Re\approx 500$ for $\unicode[STIX]{x1D719}_{0}=0.05$ ). At $\unicode[STIX]{x1D719}_{0}>0.1$ , the solid fraction in the straight branch satisfies $\unicode[STIX]{x1D719}_{\Vert }/\unicode[STIX]{x1D719}_{0}>1$ , and this ratio grows with $Re$ . Discrete-particle simulations employing immersed boundary and lattice-Boltzmann techniques are used to analyse these phenomena, allowing rationalization of aspects of this complex behaviour as being due to particle migration in the inlet branch.