arXiv subjects

Masao Iwamatsu

Publications and source records attributed to Masao Iwamatsu.

At least 19 recordsLinked to original sources

arXiv2024

A hydrodynamic model of capillary flow in an axially symmetric tube with a non-slowly-varying cross section and a boundary slip

The capillary flow of a Newtonian and incompressible fluid in an axially symmetric horizontal tube with a non-slowly-varying cross section and a boundary slip is considered theoretically under the assumption that the Reynolds number is small enough for the Stokes approximation to be valid. Combining the Stokes equation with the hydrodynamic model assuming the Hagen-Poiseulle flow, a general formula for the capillary flow in a non-slowly-varying tube is derived. Using the newly derived formula, the capillary imbibition and the time evolution of meniscus in tubes with non-uniform cross sections such as a conical tube, a power-law-shaped diverging tube, and a power-law-shaped converging tube are reconsidered. The perturbation parameters and the corrections due to the non-slowly-varying effects are elucidated and the new scaling formulas for the time evolution of the meniscus of these specific examples are derived. Our study could be useful for understanding various natural fluidic systems and for designing functional fluidic devices such as a diode and a switch.

physics.flu-dyn↗

arXiv2023

Thermodynamics of imbibition in capillaries of double conical structures-Hourglass, diamond, and sawtooth shaped capillaries-

Thermodynamics of imbibition (intrusion and extrusion) in capillaries of double conical structures is theoretically studied using the classical capillary model. By extending the knowledge of the thermodynamics of a single conical capillary, not only the nature of spontaneous imbibition but that of forced imbibition under applied external pressure are clarified. Spontaneous imbibition in capillaries of double conical structure can be predicted from the Laplace pressure in a single conical capillary. To understand the forced imbibition process, the free energy landscape along the imbibition pathway is calculated. This landscape shows either a maximum or a minimum. The former acts as the energy barrier and the latter acts as the trap for the liquid-vapor meniscus so that the imbibition process can be either abrupt with a pressure hysteresis or gradual and continuous. The landscape also predicts a completely filled, a half-filled and a completely empty state as the thermodynamically stable state. Furthermore, it also predicts a completely filled and a half-filled state of metastable liquid which can be prepared by the combination of the intrusion and the extrusion process. Our study could be useful for understanding various natural fluidic systems and for designing functional fluidic devices such as a diode, a switch etc.

cond-mat.soft↗

arXiv2022

Free-energy landscapes of intrusion and extrusion of liquid in truncated and inverted truncated conical pores: implications to the Cassie-Baxter to Wenzel transition

As the simplest model of transition between the superhydrophobic Cassie-Baxter (CB) and Wenzel (W) states of a macroscopic droplet sitting on a microscopically rough or corrugated substrate, a substrate whose surface is covered by identical truncated or inverted truncated conical pores is considered. The free energy landscapes of the intrusion and extrusion processes of a liquid into single pore are analyzed when the liquid is compressed or stretched so that the liquid phase is either stable or metastable relative to the vapor phase. Therefore, this model is also relevant to the stability of the superhydrophobic submerged substrates. In this study, the macroscopic classical capillary theory is adopted. Even within this simplified model, two simple geometries of truncated and inverted truncated cones lead to completely different free-energy landscapes. A simple criterion for the stability of the CB state based on Laplace pressure is shown not to be sufficient to understand the destruction and recovery of the CB state. The free-energy landscapes indicate that a gradual and an abrupt destruction of CB state is possible, which depends on the orientation of the conical pore and whether the liquid is compressed or stretched. The extensions of these theoretical results to more complex geometries are briefly discussed.

cond-mat.soft↗

arXiv2022

Thermodynamics and hydrodynamics of spontaneous and forced imbibition in conical capillaries: A theoretical study of conical liquid diode

Thermodynamics and hydrodynamics of spontaneous and forced imbibition of liquid into conical capillaries are studied to assess the feasibility of a conical liquid diode. The analytical formulas for the Laplace pressure and the critical Young's contact angle of the capillary for the onset of spontaneous imbibition are derived using the classical capillary model of thermodynamics. The critical contact angle below which the spontaneous imbibition can occur belongs to the hydrophilic region for the capillary with a diverging radius while it belongs to the hydrophobic region for the capillary with a converging radius. Thus, by choosing Young's contact angle between these two critical contact angles, only the spontaneous imbibition toward the converging radius occurs. Therefore, the capillary with a converging radius acts as the forward direction and that with a diverging radius as the reverse direction of diode. Even under the external applied pressure, the free-energy landscape implies that the forced imbibition occurs only to the forward direction by tuning the applied pressure. Furthermore, the scaling rule of the time scale of imbibition is derived by assuming Hagen-Poiseuille steady flow. Again, the time scale of the forward direction is advantageous compared to the reverse direction when the imbibition to both direction is possible. Therefore, our theoretical analysis shows that a conical capillary acts as a liquid diode.

cond-mat.soft↗

arXiv2019

Effect of line tension on axisymmetric nanoscale capillary bridges at the liquid-vapor equilibrium

The effect of line tension on the axisymmetric nanoscale capillary bridge between two identical substrates with convex, concave and flat geometry at the liquid-vapor equilibrium is theoretically studied. The modified Young's equation for the contact angle, which takes into account the effect of line tension is derived on a general axisymmetric curved surface using the variational method. Even without the effect of line tension, the parameter space where the bridge can exist is limited simply by the geometry of substrates. The modified Young's equation further restricts the space where the bridge can exist when the line tension is positive because the equilibrium contact angle always remain finite and the wetting state near the zero contact angle cannot be realized. It is shown that the interplay of the geometry and the positive line tension restricts the formation of capillary bridge.

cond-mat.soft↗

arXiv2018

Four stages of droplet spreading on a spherical substrate and in a spherical cavity -Surface tension vs line tension and viscous dissipation vs frictional dissipation-

The spreading of a cap-shaped spherical droplet of non-Newtonian power-law liquids on a completely wettable spherical substrate is theoretically studied. Both convex spherical substrates and concave spherical cavities with smooth or rough surfaces are considered. The droplet on a rough substrate is modeled by either the Wenzel or the Cassie-Baxter model. The two sources of driving force of spreading by the surface-tension and the line tension are considered. Also, the two channels of energy dissipation by the viscous dissipation within the bulk and the frictional dissipation at the contact line are considered. A combined theory of spreading on a spherical substrate is constructed by including those four factors. The spreading process is divided into four stages, each of which is governed by one of two driving forces and one of two dissipations. It is found that the dynamic contact angle $θ$ has a characteristic time ($t$) dependence at each stage. It does not necessarily follow the standard power law $θ\sim t^{-α}$. Instead, the relaxation can be a power-law with the exponent $α$ different from that on a flat substrate, or it can be exponential or it can finish within a finite time. Therefore, various spreading scenarios on a spherical substrate and in a spherical cavity are predicted.

cond-mat.soft↗

arXiv2018

A generalized Young's equation to bridge a gap between the experimentally measured and the theoretically calculated line tensions

A generalized Young's equation, which takes into account two corrections to the line tension by the curvature dependence of the liquid-vapor surface tension and by the contact angle dependence of the intrinsic line tension, is derived from the thermodynamic free-energy minimization. The correction from the curvature dependence can be qualitatively estimated using Tolman's formula. The correction from the contact angle dependence can be estimated for nanometer-scale droplets for which the analytical formula for the intrinsic line tension determined from the van der Waals interaction is available. The two corrections to the apparent line tension of this van der Waals nano-droplets are as small as nN, and lead to either a positive or a negative apparent line tension. The gravitational line tension for millimeter-scale droplets by the gravitational acceleration is also considered. The gravitational line tension is of the order of $μ$N so that the correction from the curvature dependence can be neglected. Yet, the contact angle dependence is so large that the apparent line tension becomes always negative though the intrinsic line tension without the correction is always positive. These two examples demonstrate clear distinction between the theoretical calculated intrinsic line tension and the experimentally determined apparent line tension which includes these two corrections. Naive comparison of the experimentally determined and the theoretically calculated line tension is not always possible.

cond-mat.soft↗

arXiv2017

Topography- and topology-driven spreading of non-Newtonian power-law liquids on a flat and a spherical substrate

The spreading of a cap-shaped spherical droplet of non-Newtonian power-law liquids on a flat and a spherical rough and textured substrate is theoretically studied in the capillary-controlled spreading regime. A droplet whose scale is much larger than that of the roughness of substrate is considered. The equilibrium contact angle on a rough substrate is modeled by the Wenzel and the Cassie-Baxter model. Only the viscous energy dissipation within the droplet volume is considered, and that within the texture of substrate by imbibition is neglected. Then, the energy balance approach is adopted to derive the evolution equation of the contact angle. When the equilibrium contact angle vanishes, the relaxation of dynamic contact angle $θ$ of a droplet obeys a power law decay $θ\sim t^{-α}$ except for the Newtonian and the non-Newtonian shear-thinning liquid of the Wenzel model on a spherical substrate. The spreading exponent $α$ of the non-Newtonian shear-thickening liquid of the Wenzel model on a spherical substrate is larger than others. The relaxation of the Newtonian liquid of the Wenzel model on a spherical substrate is even faster showing the exponential relaxation. The relaxation of the non-Newtonian shear-thinning liquid of Wenzel model on a spherical substrate is fastest and finishes within a finite time. Thus, the topography (roughness) and the topology (flat to spherical) of substrate accelerate the spreading of droplet.

cond-mat.soft↗

arXiv2017

Spreading law of non-Newtonian power-law liquids on a spherical substrate by energy balance approach

The spreading of a cap-shaped spherical droplet of non-Newtonian power-law liquids, both shear-thinning and shear-thinning liquids, that completely wet a spherical substrate is theoretically investigated in the capillary-controlled spreading regime. The crater-shaped droplet model with the wedge-shaped meniscus near the three-phase contact line is used to calculate the viscous dissipation near the contact line. Then the energy balance approach is adopted to derive the equation which governs the evolution of the contact line. The time evolution of the dynamic contact angle $θ$ of a droplet obeys a power law $θ\sim t^{-α}$ with the spreading exponent $α$, which is different from Tanner's law for Newtonian liquids and those for non-Newtonian liquids on a flat substrate. Furthermore, the line-tension dominated spreading, which could be realized on a spherical substrate for late-stage of spreading when the contact angle becomes low and the curvature of the contact line becomes large, is also investigated.

cond-mat.soft↗

arXiv2017

Spreading law on a completely wettable spherical substrate: The energy balance approach

The spreading of a cap-shaped spherical droplet on a completely wettable spherical substrate is studied. The non-equilibrium thermodynamic formulation is used to derive the thermodynamic driving force of spreading including the line-tension effect. Then the energy balance approach is adopted to derive the evolution equation of the spreading droplet. The time evolution of the contact angle $θ$ of a droplet obeys a power law $θ\sim t^{-α}$ with the exponent $α$, which is different from that derived from Tanner's law on a flat substrate. Furthermore, the line tension must be positive to promote complete wetting on a spherical substrate, while it must be negative on a flat substrate.

cond-mat.soft↗

arXiv2017

Nucleation and growth of a core-shell composite nucleus by diffusion

The critical radius of a core-shell-type nucleus grown by diffusion in a phase-separated solution is studied. A {\it kinetic} critical radius rather than the {\it thermodynamic} critical radius of standard classical nucleation theory can be defined from the diffusional growth equations. It is shown that there exist two kinetic critical radii for the core-shell-type nucleus, for which both the inner core radius and the outer shell radius will be stationary. Therefore, these two critical radii correspond to a single critical point of the nucleation path with a single energy barrier even though the nucleation looks like a two-step process. The two radii are given by formulas similar to that of classical nucleation theory if the Ostwald-Freundlich boundary condition is imposed at the surface of the inner nucleus and that of the outer shell. The subsequent growth of a core-shell-type post-critical nucleus follows the classical picture of Ostwald's step rule. Our result is consistent with some of the experimental and numerical results which suggest the core-shell-type critical nucleus.

cond-mat.stat-mech↗

arXiv2016

Size-dependent contact angle, and wetting and drying transition of a droplet adsorbed on to a spherical substrate: Line tension effect

The size-dependent contact angle and the drying and wetting morphological transition are studied with respect to the volume change for a spherical cap-shaped droplet placed on a spherical substrate. The line-tension effect is included using the rigorous formula for the Helmholtz free energy in the droplet capillary model. A morphological drying transition from a cap-shaped to a spherical droplet occurs when the substrate is hydrophobic and the droplet volume is small, similar to the transition predicted on a flat substrate. In addition, a morphological wetting transition from a cap-shaped to a wrapped spherical droplet occurs for a hydrophilic substrate and a large droplet volume. The contact angle depends on the droplet size: it decreases as the droplet volume increases when the line tension is positive, whereas it increases when the line tension is negative. The spherical droplets and wrapped droplets are stable when the line tension is positive and large.

cond-mat.soft↗

arXiv2016

Free-energy barrier of filling a spherical cavity in the presence of line tension: Implication to the energy barrier between the Cassie and Wenzel state on a superhydrophobic surface with spherical cavities

The free-energy barrier of filling a spherical cavity having an inner wall of various wettabiities is studied. The morphology and free energy of a lens-shaped droplet are determined from the minimum of the free energy. The effect of line tension on the free energy is also studied. Then, the equilibrium contact angle of the droplet is determined from the generalized Young's equation. By increasing the droplet volume within the spherical cavity, the droplet morphology changes from spherical with an equilibrium contact angle of $180^{\circ}$ to a lens with a convex meniscus, where the morphological complete drying transition occurs. By further increasing the droplet volume, the meniscus changes from convex to concave. Then, the lens-shaped droplet with concave meniscus spreads over the whole inner wall resulting in an equilibrium contact angle of $0^{\circ}$ to leave a spherical bubble, where the morphological complete wetting transition occurs. Finally, the whole cavity is filled with liquid. The free energy shows a barrier from complete drying to complete wetting as a function of droplet volume, which corresponds to the energy barrier between the Cassie and Wenzel state of the superhydrophobic surface with spherical cavities. The free-energy maximum occurs when the meniscus of the droplet becomes flat and it is given by an analytic formula. The effect of line tension is expressed by the scaled line tension, and this effect is largest at the free-energy maximum. The positive line tension increases the free-energy maximum, which thus, increases the stability of the Cassie superhydrophobic state, whereas the negative line tension destabilizes the superhydrophobic state.

cond-mat.soft↗

arXiv2016

Line tension and morphology of a droplet and a bubble attached to the inner wall of a spherical cavity

The effects of line tension on the morphology of a lens-shaped droplet and bubble placed on the inner wall of a spherical cavity are studied. The contact angle between the lens-shaped droplet and the concave spherical substrate is expressed by the generalized Young's formula. The equator of the spherical substrate is found to play a crucial role. Neither a droplet with its contact line on the upper hemisphere of the substrate nor one with its contact line on the lower hemisphere can transform into each other continuously. On a hydrophobic substrate, the contact angle jumps discontinuously to $180^{\circ}$, and the droplet is detached from the substrate to form a spherical droplet when the line tension is positive and large. This is similar to the drying transition on a flat substrate. On the other hand, on a hydrophilic substrate, the contact angle jumps discontinuously to $0^{\circ}$ when the line tension is positive and large. Then, the droplet spread over the whole inner wall to leave a spherical bubble. Therefore, not only the drying transition but also the wetting transition is induced by positive line tension on a concave spherical substrate. There also exist stable as well as metastable droplets, whose phase diagrams can be complex. When the line tension is negative and its magnitude increases, the contact line approaches the equator infinitesimally from either above or below. However, it cannot cross the equator of a spherical cavity continuously. The droplet with a contact line that coincides with the equator is a singular droplet. The contact line is pinned and cannot move, irrespective of the magnitude of the line tension.

cond-mat.soft↗

arXiv2016

Line tension and morphology of a sessile droplet on a spherical substrate

The effects of line tension on the morphology of a sessile droplet placed on top of a convex spherical substrate are studied. The morphology of the droplet is determined from the global minimum of the Helmholtz free energy. The contact angle between the droplet and the spherical substrate is expressed by the generalized Young's formula. When the line tension is positive and large, the contact angle jumps discontinuously to $180^{\circ}$, the circular contact line shrinks towards the top of the substrate, and the droplet detaches from the substrate, forming a spherical droplet if the substrate is hydrophobic (i.e., the Young's contact angle is large). This finding is consistent with that predicted by Widom [J. Phys. Chem. {\bf 99}, 2803 (1995)]; the line tension induces a drying transition on a flat substrate. On the other hand, the contact angle jumps to $0^{\circ}$, the circular contact line shrinks towards the bottom of the substrate, and the droplet spreads over the substrate to form a wrapped spherical droplet if the substrate is hydrophilic (i.e., the Young's contact angle is small). Therefore, not only the drying transition of a cap-shaped to a detached spherical droplet but also the wetting transition of a cap-shaped to a wrapped spherical droplet could occur on a spherical substrate as the surface area of the substrate is finite. When the line tension is negative and its magnitude increases, the contact line asymptotically approaches the equator from either above or below. The droplet with a contact line that coincides with the equator is an isolated, singular solution of the first variational problem. In this instance, the contact line is pinned and cannot move as far as the line tension is smaller than the critical magnitude, where the wetting transition occurs.

cond-mat.soft↗

arXiv2015

Line-tension-induced scenario of heterogeneous nucleation on a spherical substrate and in a spherical cavity

Line-tension-induced {scenario of heterogeneous nucleation} is studied for a lens-shaped nucleus with a finite contact angle nucleated on a spherical substrate and on the bottom of the wall of a spherical cavity. The effect of line tension on the free energy of a critical nucleus can be separated from the usual volume term. By comparing the free energy of a lens-shaped critical nucleus of a finite contact angle with that of a spherical nucleus, we find that a spherical nucleus may have a lower free energy than a lens-shaped nucleus when the line tension is positive and large, which is similar to the drying transition predicted by Widom [B. Widom, J. Phys. Chem. {\bf 99} 2803 (1995)]. Then, the homogeneous nucleation rather than the heterogeneous nucleation will be favorable. Similarly, the free energy of a lens-shaped nucleus becomes negative when the line tension is negative and large. Then, the barrier-less nucleation with no thermal activation called athermal nucleation will be realized.

cond-mat.soft↗

arXiv2015

Line-tension effects on heterogeneous nucleation on a spherical substrate and in a spherical cavity

The line-tension effects on heterogeneous nucleation are considered when a spherical lens-shaped nucleus is nucleated on top of a spherical substrate and on the bottom of the wall of a spherical cavity. The effect of line tension on the nucleation barrier can be separated from the usual volume term. As the radius of the substrate increases, the nucleation barrier decreases and approaches that of a flat substrate. However, as the radius of the cavity increases, the nucleation barrier increases and approaches that of a flat substrate. A small spherical substrate is a less active nucleation site than a flat substrate, and a small spherical cavity is a more active nucleation site than a flat substrate. In contrast, the line-tension effect on the nucleation barrier is maximum when the radii of the nucleus and the substrate or cavity become comparable. Therefore, by tuning the size of the spherical substrate or spherical cavity, the effect of the line tension can be optimized. These results will be useful in broad range of applications from material processing to understanding of global climate, where the heterogeneous nucleation plays a vital role.

cond-mat.soft↗

arXiv2014

Nucleation and growth by diffusion under Ostwald-Freundlich boundary condition

The critical radius of a nucleus grown by diffusion in a solution is studied thermodynamically as well as kinetically. The thermodynamic growth equation called Zeldovich equation of classical nucleation theory (CNT) and the kinetic diffusional growth equation combined with the Ostwald-Freundlich boundary condition lead to the same critical radius. However, it should be pointed out that the diffusional equation may lead to a kinetic critical radius that is different from the thermodynamic critical radius, thus indicating the possibility of kinetically controlling the critical radius of a nucleus.

cond-mat.soft↗