Relationship between Onset of Sliding Behavior and Size of Droplet on Inclined Solid Substrate.

Whether a droplet slides or not on inclined solid surface is mainly influenced by a balance between the adhesion force at contact area and the gravitational force exerted on the droplet. Especially as the adhesion force is a key parameter for the determination of the sliding behavior of droplets. The adhesion force is mainly estimated by experimental observation for the sliding motion of the droplet. However, at present it is unknown whether the adhesion force is a constant value regardless of the droplet size or not. In the present study, focused on the onset for sliding of water-ethanol binary mixture droplets on inclined solid surface, experimental investigation on the sliding droplets is performed by considering the droplet volumes ranging from 7 to 600 µL in order to understand the effect of the size of the droplet on the adhesive property. The results are discussed using the existing analytical models. From the results, it is found that the adhesion force increases in the case of large droplet volume, while the force reaches constant value in the case of small droplet volume. This difference is related to the degree of the droplet shape deformation, which leads to a change in the contact angle. Finally, a simple empirical model for the adhesion force including the size effect is proposed.

Predicting the splash of a droplet impinging on solid substrates.

The impingement behaviours of droplets towards solid substrates depend on the liquid properties, impingement velocity and solid surface conditions, such as wettability and roughness. However, the prediction regarding whether the droplet splashes after the impingement, is still an open question. Here we show that the splashing can be predicted by the pressure balance of the liquid film appearing beneath the impingement droplet coupled with the modified energy balance equation. Hydrodynamic and hydrostatic pressures are the driving forces for the droplet's radial spreading, while the capillary pressure at the rim edge and viscous stress oppose the driving forces. Thus, splashing occurs when the driving forces overcome the opposing forces. Moreover, the splashing condition is affected by various surface factors, such as wettability and surface roughness. Our work would pave the way to understand the basic physics for rim or liquid film fragmentation and enabling advances in important for engineering field such as printing, sprays for cooling and pesticide.

Analytical consideration of liquid droplet impingement on solid surfaces.

In industrial applications involving spray-cooling, combustion, and so on, prediction of the maximum spreading diameter of a droplet impinging on a solid surface permits a quantitative estimation of heat removal and energy consumption. However, although there are many experimental studies regarding droplet impingement behaviour, theoretical models have an applicability limit for predicting the maximum spreading diameter. In the present study, we have developed an analytical model for droplet impingement based on energy conservation that considers adhesion energy in both horizontal and vertical directions at the contact line. The theory is validated by our experiment and existing experimental data possessing a wide range of Weber numbers. We demonstrate that our model can predict ß m (i.e., the maximum spreading diameter normalised in terms of initial droplet diameter) for various Newtonian liquids ranging from micro- to millimetre-sized droplets on different solid surfaces and can determine the transition between capillary and viscous regimes. Furthermore, theoretical relations for scaling laws observed by many researchers are derived.

Theoretical model of droplet wettability on a low-surface-energy solid under the influence of gravity.

The wettability of droplets on a low surface energy solid is evaluated experimentally and theoretically. Water-ethanol binary mixture drops of several volumes are used. In the experiment, the droplet radius, height, and contact angle are measured. Analytical equations are derived that incorporate the effect of gravity for the relationships between the droplet radius and height, radius and contact angle, and radius and liquid surface energy. All the analytical equations display good agreement with the experimental data. It is found that the fundamental wetting behavior of the droplet on the low surface energy solid can be predicted by our model which gives geometrical information of the droplet such as the contact angle, droplet radius, and height from physical values of liquid and solid.

Detection of microbubble position by a digital hologram.

This paper reports on a new technique of measurements of microbubble position in three dimensions with high time-resolution. The technique is based on micro digital holographic particle tracking velocimetry. In this technique, an intensity profile is constructed from a holographic image of a microbubble where the profile results in showing two peaks. The distance between the two peaks appears to relate to the size of the microbubble's diameter. The three-dimensional position of the bubble can be detected by the center of the two peaks and the center point of the bubble image focused by a digital hologram. We also theoretically obtained the intensity profile of a microbubble by considering a refraction of light on a bubble surface to a ring-shaped aperture model. The theoretically obtained distance between the two peaks is found to be in good agreement with the values obtained experimentally.

Macroscopic wettability based on an interfacial jump condition.

Young's equation, describing an interfacial equilibrium condition of a liquid droplet on a smooth solid surface, raises issues concerning the existence of a sine term which has not yet been resolved theoretically and continues to be discussed to the present day. From a thermodynamics viewpoint, the equilibrium condition arises by minimizing the total free energy of the system while intensive parameters are kept constant. In the derivation, variations in the virtual work in both horizontal and vertical directions of the droplet on the smooth solid are considered. From a hydrodynamics viewpoint, there is a momentum jump condition at the gas-liquid interface that is derived based on a mechanical balance. Using standard mathematical procedures such as Stokes' theorem and differential geometry, a test volume is considered across the interface between two continuous phases from which the jump condition is derived. In the present paper, Young's equation is revisited from the point of view of the momentum jump condition at the two-phase interface and a modified Young's equation is derived. The analytical solution derived from the modified Young's equation is then used to compare theory with experimental data. The line tension and contact angle for a lens droplet are also discussed on the basis of this model.

Discussion on a mechanical equilibrium condition of a sessile drop on a smooth solid surface.

Young's equation describes an interfacial equilibrium condition of a liquid droplet on a smooth solid surface. This relation is derived by Thomas Young in 1805. It has been discussed until today after his work. In general, Young's equation is discussed from the viewpoint of thermodynamics and derived by minimizing the total free energy of the system with intensive parameters in the total free energy kept constant, i.e., the variation in the total free energy is zero. In the derivation, the virtual work variations in the horizontal and vertical directions of the droplet on the smooth solid are considered independently. However, the virtual work variation at the droplet surface depends on the variation of the horizontal and vertical directions, which are related to an incline of the droplet surface. This point has been overlooked in past studies. In this study, by considering this directional dependency, we derive the modified Young's equation based on the thermodynamics. Finally, we evaluate the modified Young's equation by comparing the analytical solution of the relationship between a contact angle and the contact line radii of the droplet with some experimental data. Moreover, we investigated the line tension itself.

Special purpose computer system for flow visualization using holography technology.

We have designed a special purpose computer system for visualizing fluid flow using digital holographic particle tracking velocimetry (DHPTV). This computer contains an Field Programmble Gate Array (FPGA) chip in which a pipeline for calculating the intensity of an object from a hologram by fast Fourier transform is installed. This system can produce 100 reconstructed images from a 1024 x 1024-grid hologram in 3.3 sec. It is expected that this system will contribute to fluid flow analysis.

Parallel computing of a digital hologram and particle searching for microdigital-holographic particle-tracking velocimetry.

We have developed a parallel algorithm for microdigital-holographic particle-tracking velocimetry. The algorithm is used in (1) numerical reconstruction of a particle image computer using a digital hologram, and (2) searching for particles. The numerical reconstruction from the digital hologram makes use of the Fresnel diffraction equation and the FFT (fast Fourier transform), whereas the particle search algorithm looks for local maximum graduation in a reconstruction field represented by a 3D matrix. To achieve high performance computing for both calculations (reconstruction and particle search), two memory partitions are allocated to the 3D matrix. In this matrix, the reconstruction part consists of horizontally placed 2D memory partitions on the x-y plane for the FFT, whereas, the particle search part consists of vertically placed 2D memory partitions set along the z axes. Consequently, the scalability can be obtained for the proportion of processor elements, where the benchmarks are carried out for parallel computation by a SGI Altix machine.

Special purpose computer for digital holographic particle tracking velocimetry.

We have designed a special purpose computer system for digital holographic particle tracking velocimetry (DHPTV). We present the pipeline for calculating the intensity of an object from a hologram by fast Fourier transform in an FPGA chip. This system uses four FPGA chips and can make 100 reconstructed images from a 256x256-grid hologram in 266 msec. It is expected that this system will improve the efficiency of analysis in DHPTV.