Onset of Rayleigh-Bénard-Marangoni convection with time-dependent nonlinear concentration profiles

► We predict the onset of transient Rayleigh-Bénard-Marangoni convection. ► We examine the relations between the base profiles and disturbances. ► A spatial base-profile influenced frozen-time marginal state analysis developed. ► Calculated critical parameters are in good agreement with measured data. ► The new model solves unresolved difficulties in the previous techniques.