Particle–bubble interaction energies for particles with physical and chemical heterogeneities

•Physical and chemical heterogeneities were considered in bubble−particle interaction.•Surface roughness decreased the energy barrier (EB) in a quadratic−type manner.•Charge heterogeneity (CH) decreased the EB in an exponential−type manner.•Contact angle heterogeneity (CAH) increased the EB in an exponential−type manner.•CH had the strongest influence while CAH had the least.