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Abstract In this article, we use the Nehari manifold and the eigenvalue problem for the negative Laplacian with Dirichlet boundary condition to analytically study the minimizers for the de Gennes–Cahn–Hilliard energy with quartic double‐well potential and Dirichlet boundary condition on the bounded domain. Our analysis reveals a bifurcation phenomenon determined by the boundary value and a bifurcation parameter that describes the thickness of the transition layer that segregates the binary mixture's two phases. Specifically, when the boundary value aligns precisely with the average of the pure phases, and the bifurcation parameter surpasses or equals a critical threshold, the minimizer assumes a unique form, representing the homogeneous state. Conversely, when the bifurcation parameter falls below this critical value, two symmetric minimizers emerge. Should the boundary value be larger or smaller from the average of the pure phases, symmetry breaks, resulting in a unique minimizer. Furthermore, we derive bounds of these minimizers, incorporating boundary conditions and features of the de Gennes–Cahn–Hilliard energy. 

Smart emulsions are both versatile additives to smart materials and functional smart materials themselves, acting as active components and structural elements driving innovative development. Emulsions offer versatility, ease of manipulation, and stability to smart materials. This review explores the multifaceted roles of emulsions, examining their formulation methods, applications, and role as building blocks in smart materials. The significance of emulsions in smart materials is discussed for applications such as drug delivery and adaptive coatings, as well as their role in stimuli‐responsive colloidal systems and nanocomposites. The smart emulsions reviewed encompass all manner of material types, including fluid and solid/polymerized smart materials. These include both emulsions with dynamic properties and emulsions used in the process of synthesizing other materials. Smart emulsions are categorized by application into shape memory, self‐healing, biological, and stimuli‐responsive, with analysis of formulation methods, metrics, and methods of final incorporation. Smart emulsions can be found initially as fluid systems and some react into solid polymers, tailored to meet functional needs. A comparative analysis reveals emerging trends such as coupling coating self‐healing/corrosion inhibition and use of waterborne polyurethanes. The discussion of smart emulsions concludes by outlining challenges and future directions for leveraging smart emulsions.