Numerical simulations are performed of a compressible oxidizer gas laden with fuel droplets. The carrier phase is considered in the Eulerian context and is simulated via direct numerical simulation (DNS). The fuel droplets are tracked in the Lagrangian frame and interactions between the two phases are taken into account in a realistic two-way coupled formulation. It is assumed that combustion takes place in the vapour phase, resulting in a ‘homogeneous’ reaction described by fuel + oxidizer → products + energy. Several simulations are performed within the configuration of low-Mach-number homogeneous shear turbulence to investigate the effects of the mass loading ratio, the droplet time constant, the Damköhler number, and the heat release coefficient. Initial mass loading ratios up to 0.8 and initial Stokes numbers (based on the Kolmogorov time scale) of 1.23 and 2.46 are considered. The results of these simulations along with those from non-reacting cases are utilized to analyse the droplet size distribution, the fuel vapour, the oxidizer, and the reaction rate and zone. An analysis of the statistics of the two-phase flow indicates that various fields are accurately resolved and the assumptions invoked in the formulation of the problem are satisfied. The mean evaporation rate (normalized with the initial mass of the droplets) decreases with the increase of either the mass loading ratio or the droplet time constant. It is shown that the droplet size distribution can be reasonably approximated by a Gaussian probability density function (p.d.f.) for all of the cases. The joint p.d.f. of the fuel vapour and the oxidizer mass fractions exhibits the features of a premixed reaction. The values of the Taylor microscale of the fuel vapour and the oxidizer are closer in the presence of the chemical reaction than in the evaporating but non-reacting case. The reaction rate exhibits higher values in the regions of the flow containing the droplets while experiencing moderate increase in the high-strain-rate regions. The evaporation rate (per mass of the droplet) is smaller for larger droplets but an opposite trend is observed for the reaction rate. The reaction zone tends to align with the streamwise direction due to the effects of the mean flow on the droplets. The alignment is enhanced with either the increase of the mass loading ratio or the decrease of the droplet time constant, or the decrease of the Damköhler number. The alignment of the fuel vapour and the oxidizer with the mean flow direction decreases and increases, respectively, as a result of the chemical reaction.