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This work presents a hybrid numerical framework for modelling solid-liquid flow with particle adhesion based on a coupled single-relaxation-time lattice Boltzmann method (LBM) and a discrete element method (DEM) for adhesive particles. The LBM is implemented with an improved immersed moving boundary (IMB) method for solving complex fluid-particle interactions using a fast linear approximation of partially intersected volume between a particle and a lattice cell. It is shown that the linear approximation of the solid fraction is very efficient with good accuracy. In order to model particle adhesion, the Johnson-Kendall-Roberts (JKR) adhesive contact mechanics is adopted with a novel implicit solution to obtain the particle-particle normal force in the DEM. The developed hybrid IMB-LBM-DEM numerical framework is verified with several benchmark tests. The results confirm that the hybrid numerical approach is capable of deriving more detailed flow field between dense particles with relatively low grid resolution, as well as effectively capturing the adhesive mechanics between microspheres.