The drying of liquid droplets is a common daily life phenomenon that has long held a special interest in scientific research. When the droplet includes nonvolatile solutes, the evaporation of the solvent induces rich deposition patterns of solutes on the substrate. Understanding the formation mechanism of these patterns has important ramifications for technical applications, ranging from coating to inkjet printing to disease detection. This topical review addresses the development of physical understanding of tailoring the specific ring-like deposition patterns of drying droplets. We start with a brief introduction of the experimental techniques that are developed to control these patterns of sessile droplets. We then summarize the development of the corresponding theory. Particular attention herein is focused on advances and issues related to applying the Onsager variational principle (OVP) theory to the study of the deposition patterns of drying droplets. The main obstacle to conventional theory is the requirement of complex numerical solutions, but fortunately there has been recent groundbreaking progress due to the OVP theory. The advantage of the OVP theory is that it can be used as an approximation tool to reduce the high-order conventional hydrodynamic equations to first-order evolution equations, facilitating the analysis of soft matter dynamic problems. As such, OVP theory is now well poised to become a theory of choice for predicting deposition patterns of drying droplets.
A thin gel sheet bends as liquid penetrates from one side of the surface. We develop a diffusio-mechanical theory for the phenomena and calculate the time dependence of the bending behaviors for two types of gels, (a) a free gel that can swell in all directions freely and (b) a bound gel with its bottom surface adhered to a plastic film that can bend but cannot stretch. The theory shows that the bending behaviors of the two gels are distinctively different. The free gel bends as the liquid penetrates, takes a maximum curvature, and then slowly bends back to take the original flat shape. On the other hand, the bound gel keeps bending and gets an equilibrium state in a bent configuration. Analytical expressions are given for the maximum curvature, the equilibrium curvature, and the time at which the gel takes its maximum curvature.
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