Experimental Study on Fracture Structure of Sumi-Wari

TL;DR

The study investigates how localized surface-tension perturbations drive fracture patterns in a sumi film floating on a viscous subphase. It combines controlled experiments that vary subphase viscosity, atomic force microscopy stiffness measurements, and a coarse-grained overdamped network model with breakable springs initialized from Voronoi-relaxed positions to capture dynamics. The results show that the spike count $n$ increases with subphase viscosity and that the film becomes flatter and softer as glycerol content rises, with a model that reproduces both morphology and growth dynamics by varying the effective stiffness parameter $k$. This work reveals that pattern formation in interfacial fractures is governed by the interplay between surface tension gradients, subphase rheology, and film mechanics, providing a minimal framework for understanding two-dimensional brittle fracture in fluid-supported films.

Abstract

Local variations in surface tension can induce complex fracture dynamics in thin interfacial films. Here, we investigate the fracture patterns that emerge when a localized surface-tension perturbation is applied to a sumi film supported on a water-glycerol subphase. Sumi is a traditional Japanese carbon black ink, and this process, referred to as sumi-wari, produces aesthetically pleasing, star-shaped crack patterns with multiple spikes radiating from the perturbation site. The number of crack spikes increases with the viscosity of the subphase, controlled here by the addition of glycerol. Atomic force microscopy measurements reveal that the effective stiffness of the sumi f ilm decreases as glycerol concentration increases. This suggests a strong coupling between the subphase properties and the mechanics of the sumi film. To capture the dynamics of sumi-wari, a phenomenological model is outlined, based on an overdamped equation of motion for particles connected by breakable springs. Numerical simulations reproduce both the morphology and the experimental trends of sumi-wari: the number of cracks and their temporal evolution depend on the spring stiffness, mirroring the behavior observed for subphases with different viscosities. These findings demonstrate how the interplay between surface-tension gradients, subphase properties, and film mechanics governs local fracture and pattern formation in fluid-supported thin films

Figures (14)

• Figure 1: Sumi-wari. Sumi ink contains hydrophobic carbon particles that can be easily spread into a thin, floating film. Sumi-wari is made by breaking this film with a surfactant-laden needle, creating a star-shaped or sunburst crack pattern. Solid line in the image is a scale bar of 2.0 cm.
• Figure 2: Schematic of the experimental setup.
• Figure 3: Sumi-wari patterns observed in experiments with subphase viscositiy $\eta =1.0 ~{\rm mPa}\cdot{\rm s}$ ($c = 0 ~\%$) at (a) $t=0.1~{\rm s}$, (b) $0.3~{\rm s}$, (c) $0.6~{\rm s}$, (d) $1.0~{\rm s}$, (e) $1.5~{\rm s}$ and (f) $2.0~{\rm s}$. The solid lines below these images are scale bars of $2.0~{\rm cm}$.
• Figure 4: Sumi-wari patterns observed in experiments of several different subphase viscosities, with (a) $\eta =1.0 ~{\rm mPa}\cdot{\rm s}$ ($c = 0 ~\%$) at $t=2.7~{\rm s}$, (b) $1.5~{\rm mPa}\cdot{\rm s}$ ($c = 15~\%$) at $t=2.0~{\rm s}$, (c) $2.4~{\rm mPa}\cdot{\rm s}$ ($c = 30~\%$) at $t=2.5~{\rm s}$ and (d) $3.1~{\rm mPa}\cdot{\rm s}$ ($c = 35~\%$) at $t=2.8~{\rm s}$. Here, $t=0$ is a time when the surfactant-laden toothpick was inserted. The solid lines below these images are scale bars of $3.0~{\rm cm}$.
• Figure 5: Relationship between the viscosity $\eta$ of the solution under the film and the number $n$ of spikes of the sumi-wari patterns. Each value of $n$ is the average from at least seven independent experimental trials. The error bars show the standard deviation.