In this work the development and validation of an interfacial tension model for single droplets in liquid-liquid systems using the CFD-software DROPS is presented. Due to the relative motion between the droplet and the continuous phase, a concentration gradient of surface-active impurities is present on the liquid-liquid interface. As a result, an interfacial-tension gradient is established, that induces a force that opposes the continuous phase flow and influences the droplet internal circulation. The model developed in this work simulates this state by defining an interfacial-tension gradient with the help of adjustable parameters that describe the width, steepness and position of the interfacial-tension gradient on the droplet surface. The model does not make any assumptions concerning the extent of the interfacial stagnation. The internal droplet circulation is calculated based on the force balance at the interface. In addition, no assumption is made concerning the value of the interfacial tension at any point of the droplet surface and the droplet shape is calculated with the help of the level-set function. The parameters of the interfacial-tension model were fitted by quantitatively comparing the simulated velocities of the internal droplet flow to data measured using NMR-velocimetry. The parameter fitting was performed for a toluene droplet with a diameter of 4 mm levitated in an aqueous counter-current. For evaluating the overall behavior of the model, n-butanol and toluene droplets with a diameter of 2 mm were also simulated with various parameter values. The fitting procedure was initialized using a droplet simulation without any interfacial stagnation. The model parameters were subsequently adjusted so that the qualitative and quantitative discrepancies in comparison to the experiment were reduced. For this purpose, an NMR-imaging function was used, that transforms the velocity vector data of both the simulation and the experiment into signal transpositions. The measuring technique is thus applied to the simulation results for calculating the objective function. The experimental data and the simulation results at the end of the fitting procedure were in good agreement. The present work is the first to obtain an experimentally validated interfacial tension gradient on the droplet surface using a numerical model and high-resolution velocimetry data obtained with a non-invasive technique. The CFD-software DROPS was validated based on simulations of single n-butanol droplets freely sedimenting in an aqueous continuum. The study was performed in the diameter range from 1 to 4 mm that includes spherical, deformed and oscillating droplets. The droplet terminal velocity was obtained from the transient simulation results and compared to a semi-empirical sedimentation model from the literature that was fitted to experimental data. The influence of the mesh size, the simulation timestep, the droplet initial velocity, and the distance of the droplet interface to the walls of the computational domain was investigated and eliminated from the final results. Two different discretization methods were also compared, namely the conventional finite-element technique and the "extended finite-element" (XFEM) method, that improves the calculation of the pressure jump across the interface. It was found that the DROPS-XFEM version provides the most accurate results. The simulation results, the semi-empirical model and the experimental data were found to be in good agreement.
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