When a droplet containing a nonvolatile component is dried on a substrate, it leaves a ringlike deposit on the substrate. We propose a theory that predicts the deposit distribution based on a model of fluid flow and the contact line motion of the droplet. It is shown that the deposition pattern changes continuously from a coffee ring to volcanolike and to mountainlike depending on the mobility of the contact line and the evaporation rate. An analytical expression is given for the peak position of the distribution of the deposit left on the substrate.

When a liquid film of a colloidal solution consisting of particles of different sizes is dried on a substrate, the colloids often stratify, where smaller colloids are laid upon larger colloids. This phenomenon is counterintuitive because larger colloids which have a smaller diffusion constant, are expected to remain near the surface during the drying process, leaving a layer of larger colloids on top of smaller colloids. Here we show that the phenomenon is caused by the interaction between the colloids, and can be explained by a diffusion model accounting for the interaction between the colloids. By studying the evolution equations both numerically and analytically, we derive the condition at which the stratified structures are obtained.

Solvent evaporation in soft‐matter solutions (solutions of colloidal particles, polymers, and their mixtures) is an important process in material making and in the printing and coating industries. The solvent‐evaporation process determines the structure of materials and strongly affects their performance. Solvent evaporation involves many physicochemical processes: flow, diffusion, crystallization, gelation, glass transition, etc. and is quite complex. Here, recent progress in this important process is reported, with a special focus on theoretical and simulation studies.

Evaporating droplets are known to show complex motion that has conventionally been explained by the Marangoni effect (flow induced by the gradient of surface tension). Here, we show that the droplet motion can be induced even in the absence of the Marangoni effect due to the gradient of the evaporation rate. We derive an equation for the velocity of a droplet subject to the nonuniform evaporation rate and nonuniform surface tension placed on an inert substrate, where the wettability is uniform and unchanged. The equation explains the previously observed attraction-repulsion-chasing behaviors of evaporating droplets.

When a polymer solution is uniaxially stretched and held fixed at both ends, the solution quickly separates into droplets connected by strings and takes the beads-on-string structure. The string then becomes thinner by capillary forces. Here we develop a theoretical framework on viscoelastic fluids based on the Onsager principle and apply it to the dynamics of viscoelastic filaments. We show that the beads-on-string structure is a thermodynamic quasi-equilibrium state and derive an equation for the coexistence condition in the pseudo-equilibrium state. Using the condition, we solve the evolution equation analytically and show that the string radius and the tensile stress vary exponentially as predicted by the classical theory of Entov and Hinch [ J. Non-Newtonian Fluid Mech. 72, 31 (1997)], but the prefactor for the tensile stress is different from their theory and agrees with the numerical solutions of Clasen et al. [ J. Fluid Mech. 556, 283 (2006)].

When a square tube is brought in contact with bulk liquid, the liquid wets the corners of the tube and creates finger-like wetted regions. The wetting of the liquid then takes place with the growth of two parts, the bulk part where the cross section is entirely filled with the liquid and the finger part where the cross section of the tube is partially filled. In previous works, the growth of these two parts has been discussed separately. Here we conduct the analysis by explicitly accounting for the coupling of the two parts. We propose coupled equations for liquid imbibition in both parts and show that (a) the length of each part, h₀ and h₁, both increases in time t following Lucas–Washburn's law, h₀ ∼ t^1/2 and h₁ ∼ t^1/2, but that (b) the coefficients are different from those obtained in the previous analysis which ignored the coupling.