arXiv subjects

Koji Hasegawa

Publications and source records attributed to Koji Hasegawa.

13 recordsLinked to original sources

arXiv2026

Airborne liquid marble: Evaporation dynamics of liquid marble in acoustic levitation

Liquid marbles (LMs), droplets encapsulated by hydrophobic particles, allow for non-wetting manipulation and containerless handling, making them well-suited for applications such as microreactors. When integrated with acoustic levitation, the LMs serve as contact-free reaction platforms. However, the complex behaviours associated with acoustic fields, including deformation, internal flow, and evaporation, remain insufficiently understood. This study investigates the evaporation dynamics of acoustically levitated LMs. Simultaneous visualisation of the droplet morphology and surrounding vapour concentration fields was achieved using backlighting and the Background-oriented Schlieren (BOS) method. At intermediate relative humidity (RH = 40%), the evaporation rates and vapour distributions of LMs closely resembled those of pure water droplets, indicating that the particle shell exerts minimal influence under these conditions. Conversely, significant differences were observed at high- and low-humidity, attributable to the evaporation resistance and interfacial properties introduced by the hydrophobic particle layers. Furthermore, although pure water droplets maintained a quasi-spherical shape, LMs demonstrated progressive flattening over time, suggesting mechanical constraints imposed by the particle shell. These findings provide new insights into the coupled evaporation and deformation behaviours of LMs in acoustic fields, informing the design of contamination-free microfluidic and microreactor systems.

physics.flu-dyn↗

arXiv2026

Retraction dynamics of polymer-laden droplets impacting a smooth solid surface

Hypothesis: The presence of a polymer in a droplet plays a significant role in contact line dynamics following droplet impact onto a solid substrate. We hypothesize that the polymer concentration modifies the post-impact wetting behavior. Experiments: In our experiments, we visualize the contact line dynamics of polymer-laden droplets impacting onto a flat sapphire substrate. Using high-speed side and bottom-view imaging, we analyze droplet spreading and retraction over a broad range of Weber numbers (10-700) and polyethylene oxide (PEO) concentrations (0-400 ppm). To systematically characterize the contact line dynamics, we used image processing to quantify the maximum spreading factor, receding velocity, and receding contact angle. Findings: The effect of the polymer on the spreading phase is negligible, as the maximum spreading factor follows classical inertial-capillary scaling, showing that polymer addition produces no measurable change in the maximum spreading under the present conditions. In contrast, the receding phase exhibits a strong dependence on the polymer concentration: increasing the PEO content leads to a significant reduction in the receding velocity and dynamic contact angle, while the spreading dynamics remain water-like. These results are consistent with an additional resistance associated with the receding contact-line region, while the microscopic origin of this resistance remains unresolved. To capture this behavior, we propose a scaling model that relates the normalized retraction velocity to the receding contact angle and impact conditions. The model effectively collapses the experimental data across all investigated concentrations and Weber numbers.

physics.flu-dyn↗

arXiv2026

Non-stationary difference equation and affine Laumon space III : Generalization to $\widehat{\mathfrak{gl}}_N$

In a series of papers we have considered a non-stationary difference equation which was originally discovered for the deformed Virasoro conformal block. The equation involves mass parameters and, when they are tuned appropriately, the equation is regarded as a quantum KZ equation for $U_q(A_{1}^{(1)})$. We introduce a $\widehat{\mathfrak{gl}}_N$ generalization of the non-stationary difference equation. The Hamiltonian is expressed in terms of $q$-commuting variables and allows both factorized forms and a normal ordered form. By specializing the mass parameters appropriately, the Hamiltonian can be identified with the $R$-matrix of the symmetric tensor representation of $U_q(A_{N-1}^{(1)})$, which in turn comes from the 3D (tetrahedron) $R$-matrix. We conjecture that the affine Laumon partition function of type $A_{N-1}^{(1)}$ gives a solution to our $\widehat{\mathfrak{gl}}_N$ non-stationary difference equation. As a check of our conjecture, we work out the four dimensional limit and find that the non-stationary difference equation reduces to the Fuji-Suzuki-Tsuda system.

math.QA↗

arXiv2025

Evaporation-induced freezing dynamics of droplets levitated in acoustic field

This paper presents the evaporation-induced freezing dynamics of pure cyclohexane droplets levitated via acoustic levitation. Acoustic levitation has attracted considerable attention across various fields owing to its potential to create lab-in-a-drop systems. While droplet evaporation is a fundamental physicochemical process in such a platform, the freezing of droplets induced by evaporation has been sparsely explored experimentally. For pure cyclohexane, the rapid evaporation of levitated droplets initiated freezing at the droplet surface. To better understand this evaporation-induced freezing process, the evaporation behavior of the levitated cyclohexane droplets was visualized and quantified using a high-speed camera and an infrared camera. According to the obtained experimental data, the evaporative heat transfer characteristics of the droplets were identified with theoretical models. Using the derived heat transfer coefficient, a mathematical prediction method for the onset of freezing was proposed and validated with the experimental data. These experimental findings offer valuable insights into the phase transition process and its potential physicochemical applications in a containerless environment.

physics.flu-dyn↗

arXiv2024

Non-Stationary Difference Equation and Affine Laumon Space II: Quantum Knizhnik-Zamolodchikov Equation

We show that Shakirov's non-stationary difference equation, when it is truncated, implies the quantum Knizhnik-Zamolodchikov ($q$-KZ) equation for $U_{\mathsf v}\bigl(A_1^{(1)}\bigr)$ with generic spins. Namely, we can tune mass parameters so that the Hamiltonian acts on the space of finite Laurent polynomials. Then the representation matrix of the Hamiltonian agrees with the $R$-matrix, or the quantum $6j$ symbols. On the other hand, we prove that the $K$ theoretic Nekrasov partition function from the affine Laumon space is identified with the well-studied Jackson integral solution to the $q$-KZ equation. Combining these results, we establish that the affine Laumon partition function gives a solution to Shakirov's equation, which was a conjecture in our previous paper. We also work out the base-fiber duality and four-dimensional limit in relation with the $q$-KZ equation.

math.QA↗

arXiv2023

Airborne Ouzo: Evaporation-induced emulsification and phase separation dynamics of ternary droplets in acoustic levitation

We experimentally investigated the evaporation dynamics of acoustically levitated Ouzo droplets (a mixture of ethanol, water, and anise oil). Acoustic levitation has gained significant attention in various fields due to its potential to create a lab-in-a-drop. Although evaporation is a key process in nature and industry, many studies have focused on single and binary components, and ternary droplets in acoustic levitation have rarely been experimentally investigated. In this study, the evaporation-induced spontaneous emulsification (the Ouzo effect) and phase separation process at 40-90 vol% ethanol were visualized. We estimated the concentration change by evaporation of each component in the levitated ternary droplets based on the evaporation model to identify the experimental results. Our experimental results revealed four distinct stages of evaporation in levitated Ouzo droplets: (1) preferential evaporation of the volatile component (ethanol), (2) spontaneous emulsification (myriad micro-oil droplets generation), (3) phase separation forming a core-shell droplet, and (4) water evaporation completion resulting in remaining an oil droplet. Finally, we analyzed the emulsification process by a spacetime diagram. These findings suggest that acoustic levitation is suitable for physicochemical manipulation in mid-air.

physics.flu-dyn↗

arXiv2023

Non-Stationary Difference Equation and Affine Laumon Space: Quantization of Discrete Painlevé Equation

We show the relation of the non-stationary difference equation proposed by one of the authors and the quantized discrete Painlevé VI equation. The five-dimensional Seiberg-Witten curve associated with the difference equation has a consistent four-dimensional limit. We also show that the original equation can be factorized as a coupled system for a pair of functions $\bigl(\mathcal{F}^{(1)},\mathcal{F}^{(2)}\bigr)$, which is a consequence of the identification of the Hamiltonian as a translation element in the extended affine Weyl group. We conjecture that the instanton partition function coming from the affine Laumon space provides a solution to the coupled system.

nlin.SI↗

arXiv2020

Diffusion enhancement in a levitated droplet via oscillatory deformation

Recent experimental results indicate that mixing is enhanced by a reciprocal flow induced inside a levitated droplet with an oscillatory deformation [T. Watanabe et al. Sci. Rep. 8, 10221 (2018)]. Generally, reciprocal flow cannot convect the solutes in time average, and agitation cannot take place. In the present paper, we focus on the diffusion process coupled with the reciprocal flow. We theoretically derive that the diffusion process can be enhanced by the reciprocal flow, and the results are confirmed via numerical calculation of the over-damped Langevin equation with a reciprocal flow.

nlin.PS↗

arXiv2015

Oscillation of a Rotating Levitated Droplet: Analysis with a Mechanical Model

A droplet of millimeter-to-centimeter scale can exhibit electrostatic levitation, and such levitated droplets can be used for the measurement of the surface tension of the liquids by observing the characteristic frequency of oscillatory deformation. In the present study, a simple mechanical model is proposed by considering a single mode of oscillation in the ellipsoidal deformation of a levitated rotating droplet. By measuring the oscillation frequency with respect to the rotational speed and oscillation amplitude, it is expected that the accuracy of the surface tension measurement could be improved. Using the proposed model, the dependences of the characteristic frequency of oscillatory deformation and the averaged aspect ratio are calculated with respect to the rotational angular velocity of a rotating droplet. These dependences are found to be consistent with the experimental observations.

nlin.PS↗

arXiv2012

Quantizing the discrete Painlevé VI equation : The Lax formalism

A discretization of Painlevé VI equation was obtained by Jimbo and Sakai in 1996. There are two ways to quantize it: 1) use the affine Weyl group symmetry (of $D_5^{(1)}$) (Hasegawa, 2011), 2) Lax formalism i.e. monodromy preserving point of view. It turns out that the second approach is also successful and gives the same quantization as in the first approach.

math.QA↗

arXiv2007

Quantizing the Bäcklund transformations of Painlevé equations and the quantum discrete Painlevé VI equation

Based on the works by Kajiwara, Noumi and Yamada, we propose a canonically quantized version of the rational Weyl group representation which originally arose as "symmetries" or the Bäcklund transformations in Painlevé equations. We thereby propose a quantization of the discrete Painlevé VI equation as a discrete Hamiltonian flow commuting with the action of $W(D_4^{(1)})$.

math.QA↗

arXiv1998

Commuting difference operators arising from the elliptic C_2^{(1)}-face model

We study a pair of commuting difference operators arising from the elliptic C_2^{(1)}-face model. The operators, whose coefficients are expressed in terms of the Jacobi's elliptic theta function, act on the space of meromorphic functions on the weight space of the C_2 type simple Lie algebra. We show that the space of functions spanned by the level one characters of the affine Lie algebra sp(4,C) is invariant under the action of the difference operators.

math.QA↗

arXiv1995

Ruijsenaars' commuting difference operators as commuting transfer matrices

For Belavin's elliptic quantum R-matrix, we construct an L-operator as a set of difference operators acting on functions on the type A weight space. According to the fundamental relation $RLL=LLR$, the trace of the L-operator gives a commuting difference operators. We show that for the above mentioned L-operator this approach gives Macdonald type operators with elliptic theta function coefficient, actually equivalent to Ruijsenaars' operators. The relationship between the difference L-operator and Krichever's Lax matrix as well as other approaches for the elliptic commuting system is given. We also study the invariant subspace for the system which is spanned by symmetric theta functions.

q-alg↗