Due to the importance of interfacial tension (IFT) in many industrial processes and daily activities, different methods have been developed to obtain IFT information for better process design and quality control in a variety of chemical systems. Compared with experimental measurements, model calculation is faster and lower-cost, allowing interpolation and extrapolation of data. Among many other models, density gradient theory (DGT) has gained popularity for simple functional form and accurate IFT predictions. Through more than a century of history, DGT has been developed and successfully implemented in IFT calculations of many pure and mixed systems. The strengths of the conventional DGT model have been well studied, while several major limitations are identified in our implementations, which restrict the model from being applied to a broader range of systems. These limitations include:

• The established reference fluid algorithm for DGT equations needs the preselection of a component with a monotonic density profile, and there is no clear strategy for this selection. Furthermore, the algorithm does not allow any extensions to the current DGT functional form.

• The conventional DGT model built for open systems fails to describe the IFT on spherical interfaces, since no stable droplets form when the system is allowed to have mass exchange with the ambient environment. A closed system with conserved mass would stabilize the droplet, but applications of DGT to closed systems are lacking in literature.

• The conventional DGT model assumes that each molecule occupies a single position in space regardless of its molecular structure. This assumption prevents accurate application of DGT for surfactant molecules with amphiphilic chain structures.

In addition to the model limitations, we also identify several potential applications of the DGT model that are highly needed in this field: • A quick and accurate surface energy model for DGT that defines the wetting boundary conditions for a 2D or 3D fluid model.

• Software with different DGT models that can be easily used by engineers with relatively little background.

In this thesis, we present a multistage work that addresses these challenges and needs. Firstly, we develop a novel and robust algorithm, which handles DGT equations smoothly and serves as a powerful tool to support the next-step model developments. Secondly, we construct a mass-conserved DGT model for closed systems, which can be used to study the IFT of droplets during the nucleation process. Thirdly, a modified DGT model for surfactant molecules is developed by introducing a chain formation term in the free energy expression. Fourthly, a surface free energy model is derived to define solid-fluid interactions. Finally, we develop a MATLAB based software, which integrates different DGT models and numerical algorithms into an user-friendly interface.

With systematic extensions of the DGT model, we have shaped the model to meet IFT calculation requirements in different scenarios. These model development progresses also unveil the great potential of DGT as an interface model for broader academic and industrial applications in the future.