arXiv subjects

Masao Doi

Publications and source records attributed to Masao Doi.

At least 37 records · Page 2Linked to original sources

arXiv2021

Contact Angle of an Evaporating Droplet of Binary Solution on a Super Wetting Surface

We study the dynamics of contact angle of a droplet of binary solution evaporating on a super wetting surface. Recent experiments show that although equilibrium contact angle of such droplet is zero, the contract angle can show complex time dependence before reaching the equilibrium value. We analyse such phenomena by extending our previous theory for the dynamics of an evaporating single component droplet to double component droplet. We show that the time dependence of the contact angle can be quite complex. Typically, it first decreases slightly, and then increases and finally decreases again. Under certain conditions, we find that the contact angle remains constant over a certain period of time during evaporation. We study how the plateau or peak contact angle depends on the initial composition and the humidity. The theory explains experimental results reported previously.

cond-mat.soft↗

arXiv2021

Swelling Dynamics of a Disk-Shaped Gel

When a gel absorbs solvent from surrounding, stress field is created in the gel, and this causes complex dynamics of the swelling behavior. Here we study this effect for disk-shaped gel by rigorously solving the diffusio-mechanical coupling equation. We show that (a) while the macroscopic thickness and the radius of the gel increases monotonically in time, the gel is compressed near the mid-plane, and that (b) while the swelling time depends on the shear modulus $G$ of the gel, its dependence is weak, and the time is mainly determined by the friction constant of the gel network and the osmotic bulk modulus of the gel. We also show that these characteristic features are reproduced accurately by a simple variational calculation for the gel deformation. An analytical expression is given for the swelling time.

cond-mat.soft↗

arXiv2021

Elastic Response of Wire Frame Glasses. I. Two Dimensional Model

We study the elastic response of concentrated suspensions of rigid wire frame particles to a step strain. These particles are constructed from infinitely thin, rigid rods of length $L$. We specifically compare straight rod-like particles to bent and branched wire frames. In dense suspensions the wire frames are frozen in a disordered state by the topological entanglements between their arms. We present a simple, geometric method to find the scaling of the elastic stress with concentration in these glassy systems. We apply this method to a simple 2D model system where a test particle is placed on a plane and constrained by a random distribution of points with number density $ν$. Two striking differences between wire frame and rod suspensions are found: 1) The linear elasticity per particle for wire frames is very large, scaling like $ν^2 L^4$, whereas for rods it much smaller and independent of concentration. 2) Rods always shear thin but wire frames shear harden for densities less than $\sim \sqrt{K/k_B T L^4}$, where $K$ is the bending modulus of the particles. The deformation of wire frames is found to be important even for small strains, with the proportion of deformed particles at a particular strain, $γ$, being given by $(νL^2)^2 γ^2$. Our results agree well with a simple simulation of the 2D system.

cond-mat.soft↗

arXiv2021

Elastic Response of Wire Frame Glasses. II. Three Dimensional Systems

We study the elastic response of rigid, wire frame particles in concentrated, glassy suspensions to a step strain by applying the simple, geometric methods developed in part I. The wire frame particles are comprised of thin, rigid rods of length $L$ and their number density, $ρ$, is such that $ρL^3 \gg 1$. We specifically compare rigid rods to L-shapes made of two equal length rods joined at right angles. The behaviour of wire frames is found to be strikingly different from that of rods. The linear elasticity scales like $ρ^3 L^6$ for L-shaped particles, whereas it scales proportional to $ρ$ for rods and the non-linear response shows a transition from shear hardening to shear softening at a critical density $ρ_c \sim \sqrt{K / k_B T L^6}$, where $K$ is the bending modulus of the particles. For realistic particles made of double stranded DNA, this transition occurs at densities of about $ρL^3 \sim 10$. The reason for these differences is that wire frames can be forced to bend by the entanglements with their surroundings, whereas rods always remain straight. This is found to be very important even for small strains, with most particles being bent above a critical strain $γ_c \sim (ρL^3)^{-1}$.

cond-mat.soft↗

arXiv2020

Wetting equilibrium in a rectangular channel

When a capillary channel with corners is wetted by a fluid, there are regions where the fluid fills the whole cross-section and regions where only the corners are filled by the fluid. The fluid fraction of the partially-filled region, $s^*$, is an important quantity related to the capillary pressure. We calculate the value of $s^*$ for channels with a cross-section slightly deviated from a rectangle: the height is larger in the center than those on the two short sides. We find that a small change in the cross-section geometry leads to a huge change of $s^*$. This result is consistent with experimental observations.

cond-mat.soft↗

arXiv2020

Theoretical analysis for flattening of a rising bubble in a Hele-Shaw cell

We calculate the shape and the velocity of a bubble rising in an infinitely large and closed Hele-Shaw cell using Park and Homsy's boundary condition which accounts for the change of the three dimensional structure in the perimeter zone. We first formulate the problem in the form of a variational problem, and discuss the shape change assuming that the bubble takes elliptic shape. We calculate the shape and the velocity of the bubble as a function of the bubble size, gap distance and the inclination angle of the cell. We show that the bubble is flattened as it rises. This result is in agreement with experiments for large Hele-Shaw cells.

physics.flu-dyn↗

arXiv2020

Drying Pathways of an Evaporating Soft Matter Droplet

Micro-droplets of soft matter solutions have different morphologies upon drying, and can finally become wrinkled, buckled or cavitated particles. We investigate the morphology evolution of a drying soft matter droplet in this work: at the early stage of drying, wrinkling or cavitation instability can occur in the droplet, depending on the comparison between the critical wrinkling and cavitation pressure; at a later stage of drying, no wrinkle will appear if cavitation happens first, while there can still be cavitation if wrinkling happens first. A three-dimensional phase diagram in the space of elastic length, gel layer thickness and weight loss is provided for illustrating these drying pathways of a soft matter droplet, which can guide future fabrications of micro-particles with desired morphologies.

cond-mat.soft↗

arXiv2020

Dynamics of a viscoelastic liquid filament connected to two mobile droplets

A filament of liquid is usually unstable and breaks up into small droplets, while a filament of polymer solution is known to be quite stable against such instability, and they form a stable configuration of filament connecting two spherical droplets. If the droplets are fixed in space, the liquid flows from the filament region to the droplet region to reduce the surface energy and the filament gets thinner. If the whole liquid is placed in another viscous fluid, the droplets approach each other, and the filament can get thicker. Here we study the dynamics of such system. We derive time evolution equations for the radius and the length of the filament taking into account the fluid flux from filament to droplets and the motion of the droplets. We will show that (a) if the centers of the droplets are fixed, the filament thins following the classical prediction of Entov and Hinch, and that (b) if the droplets are mobile (subject to the Stokes drag in the viscous medium), the thinning of the filament is suppressed, and under certain conditions, the filament thickens. This theory explains the phenomena observed by Yang and Xu [Phys. Fluids 20, 043101 (2008)] in four-roller mill device.

cond-mat.soft↗

arXiv2019

Particle shapes leading to Newtonian dilute suspensions

It is well known that suspensions of particles in a viscous fluid can affect the rheology significantly, producing a pronounced non-Newtonian response even in dilute suspension. However, it is unclear a priori which particle shapes lead to this behaviour. We present two simple symmetry conditions on the shape which are sufficient for a dilute suspension to be Newtonian for all strain sizes and one sufficient for Newtonian behavior for small strains. We also construct a class of shapes out of thin, rigid rods not found by the symmetry argument which share this property for small strains.

cond-mat.soft↗

arXiv2019

Defect removal by solvent vapor annealing in thin films of lamellar diblock copolymers

Solvent vapor annealing (SVA) is known to be a simple, low-cost and highly efficient technique to produce defect-free diblock copolymer (BCP) thin films. Not only can the solvent weaken the BCP segmental interactions, but it can vary the characteristic spacing of the BCP microstructures. We carry out systematic theoretical studies on the effect of adding solvent into lamellar BCP thin films on the defect removal close to the BCP order-disorder transition. We find that the increase of the lamellar spacing, as is induced by addition of solvent, facilitates more efficient removal of defects. The stability of a particular defect in a lamellar BCP thin film is given in terms of two key controllable parameters: the amount of BCP swelling and solvent evaporation rate. Our results highlight the SVA mechanism for obtaining defect-free BCP thin films, as is highly desired in nanolithography and other industrial applications.

cond-mat.soft↗

arXiv2019

Application of Onsager Machlup integral in solving dynamic equations in non-equilibrium systems

In 1931, Onsager proposed a variational principle which has become the base of many kinetic equations for non-equilibrium systems. We have been showing that this principle is useful in obtaining approximate solutions for the kinetic equations, but our previous method has a weakness that it can be justified, strictly speaking, only for small incremental time. Here we propose an improved method which does not have this drawback. The new method utilizes the integral proposed by Onsager and Machlup in 1953, and can tell us which of the approximate solutions is the best solution without knowing the exact solution. The new method has an advantage that it allows us to determine the steady state in non-equilibrium system by a variational calculus. We demonstrate this using three examples, (a) simple diffusion problem, (b) capillary problem in a tube with corners, and (c) free boundary problem in liquid coating, for which the kinetic equations are written in second or fourth order partial differential equations.

cond-mat.soft↗

arXiv2019

Dynamics of Taylor Rising

We study the dynamics of liquid climbing in a narrow and tilting corner, inspired by recent work on liquid transportation on the peristome surface of Nepenthes alata. Considering the balance of gravity, interfacial tension and viscous force, we derive a partial differential equation for the meniscus profile, and numerically study the behavior of the solution for various tilting angle $β$. We show that the liquid height $h(t)$ at time $t$ satisfy the same scaling law found for vertical corner, i.e., $h(t) \propto t^{1/3}$ for large $t$, but the coefficient depends on the tilting angle $β$. The coefficient can be calculated approximately by Onsager principle, and the result agrees well with that obtained by numerical calculation. Our model can be applied for a weakly curved corner and may provide guidance to the design of biomimetic surfaces for liquid transportation.

cond-mat.soft↗

arXiv2018

Directional freezing of binary colloidal suspensions: A model for size fractionation of graphene oxide

The performance of graphene oxide(GO)-based materials strongly depends on the lateral size and size distribution of GO nanosheets. Various methods are employed to prepare GO nanosheets with a narrow size distribution. One of the promising method was proposed recently by directionally freezing of a GO aqueous dispersion at a controlled growth rate of the freezing front. We develop a theoretic model of binary colloids suspension, incorporating both the moving freezing boundary and the preferential adsorption of colloidal particles to the ice phase. We numerically solve the coupled diffusion equations and present state diagrams of size fractionation. Selective trapping of colloids according to their size can be achieved by a suitable choice of the experimental parameters, such as the adsorption rates and the freezing speed.

cond-mat.soft↗

arXiv2018

Capillary imbibition in a square tube

When a square tube is brought in contact with bulk liquid, the liquid wets the corners of the tube, and creates finger-like wetted region. 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 the 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 the liquid imbibition in both parts and show that (a) the length of each part, $h_0$ and $h_1$, both increases in time $t$ following the Lucas-Washburn's law, $h_0 \sim t^{1/2}$ and $h_1 \sim t^{1/2}$, but that (b) the coefficients are different from those obtained in the previous analysis which ignored the coupling.

cond-mat.soft↗

arXiv2018

Dynamics of Viscoelastic Filaments Based on Onsager Principle

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 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)].

cond-mat.soft↗

arXiv2018

Multi-Ring Deposition Pattern of Drying Droplets

We propose a theory for the multi-ring pattern of the deposits that are formed when droplets of suspension are dried on a substrate. Assuming a standard model for the stick-slip motion of the contact line, we show that as droplets evaporate, many concentric rings of deposits are formed, but are taken over by a solid-circle pattern in the final stage of drying. An analytical expression is given to indicate when ring-pattern changes to solid-circle pattern during an evaporation process. The results are in qualitative agreement with existing experiments, and the other predictions on how the evaporation rate, droplet radius and receding contact angle affect the pattern are all subject to experimental test.

cond-mat.soft↗

arXiv2018

Capillary filling in closed-end nanotubes

Capillary filling in small length scale is an important process in nanotechnology and microfabrication. When one end of the tube or channel is sealed, it is important to consider the escape of the trapped gas. We develop a dynamic model on capillary filling in closed-end tubes, based on the diffusion-convection equation and Henry's law of gas dissolution. We systematically investigate the filling dynamics for various sets of parameters, and compare the results with a previous model which assumes a linear density profile of dissolved gas and neglect the convective term.

cond-mat.soft↗

arXiv2017

Structure Formation in Soft Matter Solutions Induced by Solvent Evaporation

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

cond-mat.soft↗