We introduce a framework to efficiently parameterise the aerosol water uptake for mixtures of semi-volatile and non-volatile compounds, based on the coefficient, vi. This solute-specific coefficient was introduced in Metzger et al. (2012) to accurately parameterise the single solution hygroscopic growth, considering the Kelvin effect - accounting for the water uptake of concentrated nanometer-sized particles up to dilute solutions, i.e. from the compounds relative humidity of deliquescence (RHD) up to supersaturation (Köhler theory). Here we extend the vi parameterisation from single to mixed solutions. We evaluate our framework at various levels of complexity, by considering the full gas-liquid-solid partitioning for a comprehensive comparison with reference calculations using the E-AIM, EQUISOLV II and ISORROPIA II models as well as textbook examples. We apply our parameterisation in the EQuilibrium Simplified Aerosol Model V4 (EQSAM4clim) for climate simulations, implemented in a box model and in the global chemistry-climate model EMAC. Our results show (i) that the vi approach enables one to analytically solve the entire gas-liquid-solid partitioning and the mixed solution water uptake with sufficient accuracy, (ii) that ammonium sulfate mixtures can be solved with a simple method, e.g. pure ammonium nitrate and mixed ammonium nitrate and (iii) that the aerosol optical depth (AOD) simulations are in close agreement with remote sensing observations for the year 2005. Long-term evaluation of the EMAC results based on EQSAM4clim and ISORROPIA II will be presented separately. © Author(s) 2016.