Nano- and microfluidics have been a key issue for recent miniaturized flow systems. In a small confined space like microchannels, the electrostatic potential at the wall, i.e., the zeta-potential, significantly affects the flow structure and also induces electroosmotic flows under external electric fields. This paper presents fluorescence-based optical measuring techniques for the zeta-potential and fluid velocity to investigate electroosmotic flows with nonuniform zeta-potential. The evanescent wave and volume illumination are used as excitation lights for the near-wall and bulk regions, respectively. The zeta-potential is obtained imaging the near-wall fluorescent ions excited by the evanescent wave. On the other hand, the near-wall and bulk flow velocities are measured tracing the motion of submicron fluorescent particles. The spatial and temporal resolutions of velocity measurements are improved focusing on the reproducibility of laminar flows. These techniques will contribute to further development of flow systems using electrokinetics.

View full abstract

The reverse osmosis (RO) method is a method obtaining the fresh water by using semi permeable RO membrane that does not percolate the low molecular weight material such as a salt. However, the RO method has to give continuous operation at high pressure in seawater desalination plants. In the present study, in order to improve the efficiency of RO desalination under low pressure conditions, the water treatment system is proposed by using microbubbles in salt water disposal and the effect of the microbubbles on the osmosis rate was investigated by measurements of the electric conductivity. It is confirmed that the fresh water is effectively produced for the system with microbubbles in contrast to that with no microbubbles, and the efficiency of desalination is significantly improved by microbubbles with a high electrical potential. The electric conductivity decreases with increasing the zeta potential of the microbubbles.

View full abstract

It is known that the interface current exists besides the bulk current in the channel of the electroosmotic flow (EOF). Interface current in electric double layer (EDL) is a main driving force of the EOF. However, due to its small size and the various geometrical constraint to access EDL, it is difficult to measure the interface current experimentally. In this study, a specially designed doughnut channel is utilized to measure the interface current. Two parallel doughnut-shaped glass plates were used for the doughnut channel. It is possible to adjust the height of doughnut channel continuously. The interface currents were measured experimentally on the basis of Helmholtz model. Interface current based on Helmholtz model is compared with that of Gouy-Chapmann model.

View full abstract

The velocity measurement was performed in the micro chemical reactor with AC electroosmotic pump using particle tracking velocimetry (PTV). Based on the reproducibility of laminar flows and the periodicity of AC electroosmotic pump, time series velocity measurement were iterated to increase spatial velocity information and to overlap the vector map at the same time of cycle the AC electroosmotic pump. This technique improves the spatial and temporal resolution at low number density of tracer particles. A visualization measurement by laser induced fluorescence was also performed using fluorescent dye. This study evaluated both the variation of flow structure and the mixing enhancement in the reactor.

View full abstract

To clear the time-dependent feature of the cavitation pattern within small separation distances between the viratory horn tip and the glass wall, we study the periodic behavior of the cavitation bubbles and bubble clouds on the surface of horn tip, the sign of shock waves and the corresponding erosion dents for various concentrations C of the ethanol aqueous solutions and the separation distance S, using by acoustic cavitation device with 20kHz in frequency. It is found that the area of the cavitation region and the bubble clouds with time depend on C and S.

View full abstract

The T-shape micromixer configuration dependences on the nanoparticles characterization were discussed by the CFD simulation and NiO nanoparticle synthesis experiments. The homogeneous and small nanoparticles were produced using a micromixer which could heat to the reaction conditions, 400℃ and 30 MPa.

View full abstract

The permeability of poly-dimethyl-siloxane (PDMS) to CO_2 focused on distance between gas and liquid channels was experimentally investigated utilizing simultaneous measurement of liquid velocity and pH distribution via micro-PTV/LIF method. CO_2 concentration was calculated from pH considering the chemical equilibration in water. CO_2 penetrated into PDMS and dissolved into the liquid flow quickly when the gas flow rate was raised or the gas passed through a thinner PDMS wall. It was found that large convection flux of CO_2 in water was induced near the wall by the non-slip condition and the high concentration gradient.

View full abstract

The intermediate state between microdroplets and microfluidics in two immiscible fluids is described. It was found that Y-shaped two-phase flow is formed with a stable liquid/liquid interface at a cross junction in a hydrophilic microchannel. A velocity vector map, obtained by microparticle image velocimetry, reveals the Y-shaped flow consists of aqueous phase flow along the edge of the channel and an acrylate monomer phase flow penetrating the center of the channel. The transition from the Y-shaped flow of other flow patterns can be characterized by a state diagram that depends on the capillary number and the Weber number of each injecting phase.

View full abstract

In a microfluidic device, utilization of electrokinetics is effective for particle control. Under high frequency alternating-current (AC) electric field, the control of particles can be achieved in the condition with low voltage. In this study, we focus on electrothermal flow subjected to AC electric field. A lateral observation system with a minute prism has been developed in order to measure the velocity field normal to the substrate. In this system, clear particle image can be obtained by using the PDMS (polydimethylsiloxane) channel with the side wall thickness of 125μm. It is observed that the particle velocity in the vicinity of electrode edge with 20 V_<P-P> at 300 kHz is 75 μm/s. This result indicates that the electrothermal effect is valid for controlling the fluid with high electric conductivity.

View full abstract

MHD micropump with AC current and permanent magnet is studied. In order to achieve continuous flow, AC current is modulated. A lumped parameter system for the objective pump is numerically analyzed. When AC current is applied for one cycle and is ceased, the fluid in the pump flows in one direction due to the fluid momentum in the case of turbulent flow resistance. However in the case of laminar flow resistance, the driven fluid returns to the starting point. If the fluid viscosity can be temporally controlled by addition of extra AC current, the fluid in the pump can flow in one direction even in the case of laminar flow resistance.

View full abstract

The synchronized oscillation plays an important role in physiological functions in biological systems. Synchronized motion of motile cilia realizes unidirectional transport of fluid in vertebrate body. The collective behavior is believed to arise by hydrodynamic interactions via the extracellular fluid, but how this synchrony appears and develops during the embryogenesis are unknown. We analyze synchrony dynamics of nodal cilia, which determine the left-right axis, by quantifying the fluid flow and cilia rotation. We construct a model based on coupled phase oscillators explaining the offset of the synchronization of cilia after the left-right axis determination. This suggests that the synchronization of nodal cilia is governed by global and local hydrodynamic coupling.

View full abstract

In order to investigate vascular diseases such as cause of atherosclerosis and myocardial infarction, relationships of endothelial cells (ECs) covered with surface blood vessels and blood flow stimulation have been experimentally studied. In the study, ECs were cultured in a straight microchannel with 400 μm width and 88 μm depth made from polydimethylsiloxane (PDMS) and fluid shear stress were measured using by micro particle image velocimetry (μ-PIV) technique. Wall shear stresses on EC surface and shapes of EC were estimated using velocity distributions near surface the ECs were measured varying observed plane in depth direction.

View full abstract

To investigate the propulsion mechanism in a narrow and deformable passage, we applied a coupling method of immersed boundary method (IBM) of body force type and finite element method (FEM). In our model, the object profile mimics a fish and the undulatory motion is not predetermined. Sinusoidal forces are given at a few nodes on the spine of the fish and it propels itself forward by the hydrodynamic force on its surface. The speed and the flow around the body are compared for different types of ambient fluid boundary conditions: an open space, a narrow channel with rigid walls and a narrow channel with deformable walls.

View full abstract

The propulsion speed and efficiency of actively swimming flexible fish like hydrofoil are investigated numerically. The finite difference method based on Airbitraly-Lagrangian and Eulerian method with moving deformed mesh is employed and translational and rotational equation of motion of the body are solved to determine the position of the gravitational center of the body. As the results of this investigation, it was cleared that the rotational motion greatly influenced the propulsion. Propulsive speed decreased 25 percent and efficiency increased 50 percent than the past method that fixed the lateral and rotational motion.

View full abstract

Capillaroscopy is a "lens" that is able to observe capillary loops of blood vessels in the human finger skin nail fold, of which blood flow can be easily visualized, and has been long used for clinical diagnosis. We have been developing digital high speed video capillaroscopy by integrating to high-speed high-sensitivity video camera with deep-focus zoom lens. We discuss quantitative evaluation of blood velocity in both arteriol and venule of human nailfold microcirculation, using two different methods, namely, plasma gap tracking method and fixed point observation method with correlation.

View full abstract

Numerical simulation for blood flows in cerebral vessels with aneurysm and laboratory experiments using a particle image velocimetry (PIV) are carried out to identify risk factors of aneursym rupture. The results of numerical simulation in three simplified models of a terminal aneurysm of the basilar artery show that the wall shear stress is higher at the bleb's neck than that around the aneurysm's neck and low-wall-shear stress area extends as an aneurysm's aspect ratio increases from 1.2 to 2.0. The PIV measurements of the flow in realistic aneurysm models are also conducted.

View full abstract

In order to investigate the cause of arteriosclerosis or thrombosis, research of the flow characteristic of blood attracts attention. In this research, a flow and modification in the micro blood vessel of a fingertip are analyzed using the blood-flow analysis technique by the particle method. Furthermore, the relation between blood fluid and blood vessel modification is studied.

View full abstract

The purpose of our study is to analyze swimming motion of a mosquito larva. When it meets some dangerous situations, it escapes actively from air-water surface to bottom with rapid swimming motion and some time later it is back to water surface for its breathing. A swimming thrust is obtained by a paddling motion of its tail fin with a separation of a vortex in the power stroke. We measured velocity vector fields around the body and wake by micro PIV measurements. It was found that a snapping motion of its tail fin yielded thrust.

View full abstract

In this study, we evaluated the lift force generated by the crane-fly's flapping wing with the passive pitching using the three dimensional finite element method for the fluid-structure interaction. The torsional flexibility of the wing was modeled as the spring attached to the wing plane. In the computational simulation, the model wing kept the high angle of attack during the flapping translation and rotated quickly upon the stroke reversal without any aid for the pitching motion. The generated lift force was comparable to the insect's weight. Our result strongly suggests that the pitching motion can be passive in the cranefly's flapping flight.

View full abstract

In this study, we evaluated the passive pitching motion and lift force during the insect flapping flight using the dynamically scaled model. Since the wing and the surrounding fluid interact with each other, the dynamic similarity between the model and the insect flights was measured using not only Reynolds and Strouhal numbers but also the mass and Cauchy numbers. Our model includes the plate spring to simulate the low torsional stiffness of the insect wing. Our model wing simulated the pitching motion similar to the actual insect and generated the enough force to lift the insect.

View full abstract

Micro-Air-Vehicle (MAV) using insect and bird flight mechanisms have been researching all over the world in recent years since the micro-electro-mechanical systems (MEMS) have been developed. Many researchers have developed MAV with various actuators and devices however their MAV have not been put to practical use yet. One of the reasons is that flying mechanism of birds and insect has not been clarified sufficiently. In this study, the authors developed the micro flapping robot used insect and bird flight mechanisms. The micro flapping robot has two wings which have the proper elasticity and do not have tail plane. The micro flapping robot has smaller flapping and lead-lag angles than that of a butterfly. Moreover, the proper elasticity of wing realizes wing elastic deformation and the feathering angle variation like a butterfly. The wing elastic deformation of micro flapping robot realizes stable flight for 15 minutes which was the battery's duration.

View full abstract

Ordinary pitching machines using two wheels with parallel rotating shafts throw only balls with spinning axis perpendicular to the thrown directions. A pitching machine using two rotating wheels arranged with offset shaft angles is developed to throw various curving balls such as gyro ball, slider ball, cut ball and so on. The machine pitches various balls as if they were thrown by real pitchers in spite of its simple mechanism. Assuming that velocities at two contact points on a ball with wheel surfaces are instantly accelerated to the wheel surface velocities, characteristics of the pitching machine are analyzed by using schematic and vector analysis.

View full abstract

Characteristics of pitching machines using more than three rotating wheels are analyzed by vector analysis. The vector expressions give straightforward the necessary wheel velocities and offset angles of the wheel shafts, being coplanar each other, for an arbitrary ball velocity and its spin velocity. To obtain the ball velocity and offset angle of the wheel shafts the vector analysis is simpler than a schematic method. A three wheels pitching machine without offset angles of the shafts only throw balls with spin axis perpendicular to the thrown direction. The offset angles of the shafts and the wheel velocities of arbitrary selected two wheels define the offset angles and the wheel velocity of other wheels.

View full abstract

The present report aims to clarify the flow structures involving the stream-wise vertices which was generated on the dimple surface of golf ball. The experiments was carried out to obtain the velocity vectors around the flying golf ball. The boundary layer behavior was observed in detail and the separation was measured experimentally. Furthermore, the flow structure in the wake was investigated by examining the vorticities at the transvers cross section behind the golf ball. The results was compared with numerically obtained solution.

View full abstract

An interesting phenomenon that the measured induced fluid velocity by a rotating circular cylinder is much smaller than that of conventional fluid dynamic theory will be reported and discussed. While authors have been suggesting that there are centurial misunderstandings in vortex theories of fluid dynamics in these several years, in this paper, it will be cleared that there are finite vortex flow layer adjust to the outer wall of rotating circular cylinder, the phenomenon has been overlooked so far. Authors will present some new hypothesis about the boundary phenomena to explain and to contribute the progress of vortex flow theory.

View full abstract

Japanese Sport makers earnestly started to develop various sporting goods for the top Winter Olympic Athletes. It was 1972, in the 70m Ski Jumping Event of the Sapporo Olympic Games, all 3 medals were won by Japanese jumpers. Since this splendid achievement, our sportswear development has been proceeded with the slogan, 'Faster, Farther and Safer'. Here we will show you our history of sports wear development.

View full abstract

Our aim is to clarify the mechanism about the generation of unsteady force in human swimming motion. Experiments were made on a robot arm and forces were measured by a balance. Pressure distributions were also calculated based on the velocity data obtained by PIV and the relation to the force variation was discussed. The maximum force was attained soon after the start of the stroke movement in the direct force measurement. The instant of the maximum force coincides with that when the pressure difference between the maximum and minimum becomes largest.

View full abstract

We have measured aerodynamic forces acting on a ski-jumping robot. The commercially available robot was applied for the wind tunnel test to measure aerodynamic forces in the transient phases just after the takeoff and before the landing. The robot moves in the direction of nose-down rotation in the take-off phase, while it does in the direction of nose-up rotation in the landing phase. It was found that the lift increased at the beginning of nose-up rotation in the landing phase, and then it decreased until the body coincided with the vertical direction.

View full abstract

Temporally irregular switching of rotating free surface is investigated by means of ultrasonic velocity profiling, UVP. Two methods, Doppler method and echo method, are complementarily used to detect position of the free surface together with spatio-temporal velocity distribution. Horizontal cross section of the free surface shape is estimated from the obtained interface variation.

View full abstract

In this study, our purpose is to obtain instantaneous and mean velocity profiles in a Taylor-Couette vortex flow(TVF) by using a ultrasonic measurement system. The experiment was carried out with a small aspect ratio where the Ekman boundary layer was not neglected. The device has a radial ratio of 0.667 or 0.375, aspect ratio of 3 and the gap length between the inner and outer cylinders of 25mm. The mean velocity profiles and their absolute values were in good agreement with those obtained with the ultrasonic velocity profiler (UVP). This measurement system was applied to the solid-liquid phase flow experimentally, and well measured even in the opaque dilute solution.

View full abstract

Effect of an intermediate standing baffle on the flow structure in a rectangular open channel has been studied by using Ultrasonic Doppler Velocimetry (UVP). Distributions of time-averaged on-axis velocity profiles at different streamwise positions indicate the flow structure of the uprising flow at the upstream of baffle and specifically vortex shedding at the downstream of the baffle. Importantly, comparison of space-dependent power spectra of upstream and downstream sections of the baffle indicates the existence of some peak structures near the baffle's edge for downstream sections which are corresponding to the periodic nature of flow concentrated mainly near the baffle's edge in the spatio-temporal velocity distribution. Such peak structures could not be observed for the upstream sections. For downstream sections mainly the existence of peak values in the space distribution of two frequency modes near the baffle's edge could be confirmed which can be attributed to the vortex shedding.

View full abstract

At hydraulic power stations, it is very important to measure inlet flowrate for the plant management. Pitot tubes were commonly used to measure flow rates in steel penstocks for the performance tests of hydraulic turbines. Due to the difficulties of installations of Pitot tubes, transit time ultrasonic flow meters are being popular instead. However, accuracies of transit time ultrasonic flow meters are sensitive for velocity profiles which depend on Reynolds numbers and pipe surface roughness. Recently, ultrasonic pulse Doppler flow meters are considered to be suitable tool for the measurements of flowrates in steel penstock because it can measure instantaneous velocity profiles directly without draining the water in steel penstock. In this paper, we investigate number densities of the micro bubbles as tracer particles for the flowrate measurements using Ultrasonic Pulse Doppler Method.

View full abstract

Authors proposed ultrasonic cleaning machine using the ultrasonic waveguide mode in order to reduce damage of the LSI pattern or to clean the wafer after CMP cleaning process. The sound pressure emitted at the end of the waveguide is applied to cleaning the wafer in the same way of the conventional cleaning equipment. Additionally, the sound pressure emitted through the side surface of the waveguide is also applied to the wafer cleaning process. Authors also proposed the sound pressure measurement method for the large magnitude and high frequency ultrasonic in the case that conventional hydrophone cannot be applied.

View full abstract

Measuring quantity of water intake is important to manage a hydroelectric power plant. However, there are some plants without a sufficient straight steel penstock nor open channel, where traditional measuring methods are difficult to apply to. On the other hand, since ultrasonic Doppper method (UDM) can measure flow velocity profiles, this method has an advantage of application to a non-developed flow condition. In this paper, cross-wise velocity profiles are measured using pitot tube in an open-channel test section with and without a blockage. And velocity profiles, which are measured by using the electromagnetic current meter and UDM, are compared. Then the results of these cross-sectional average flow velocities calculated using Gauss-Legendre quadrature show good agreements.

View full abstract

Hydraulic power is one of the most important base powers in Japan. Usually, the intake water flow is controlled by some methods such as surface flow rate measurement and water height measurement for cross-sectional flow rate. However, these methods are influenced by the changes of natural environment and the maintenance of the stable output becomes increasingly difficult. Therefore, high accuracy flow rate measurement, which evaluates a flow rate by cross-sectional integration of the velocity profiles, is an effective method to measure the flow rate. In this study, we focused on an ultrasonic array sensor which has been successfully applied to nondestructive inspection and medical diagnostics. An array sensor can measure the multi-line velocity profiles by using an ultrasonic Doppler method (UDM) for flow rate estimation. In addition, the bottom shape was evaluated from the velocity profile data when the bottom shape was changed.

View full abstract

The flow between two concentric cylinders with the inner one rotating and with an imposed pressure-driven axial flow is studied experimentally. The objective of this work is to study the detailed flow field including the vortical structure. In the first, the performance of the experimental equipments was studied by comparing the mean velocity profiles with the theoretical ones. The helical vortex at high Reynolds number locates almost around the inner cylinder but not near the outer cylinder. This vortex pattern is different from that of low Reynolds number reported by Lueptow et al.

View full abstract

The influence of transverse vorticity on the dissimilarity between turbulent heat flux and Reynolds stress was investigated by using the result of direct numerical simulation. The dissimilarity can be strengthened by the transverse vorticity ω_z because the correlation between wall-normal velocity and pressure gradient in the flow direction becomes noticeable in the region with strong ω_z. The swirl motion with the axis in the spanwise direction can be extracted in the turbulent flow field by use of the condition proposed in this study. A strong dissimilarity can be recognized in such region, especially in the upstream of the vortex center. The transverse vortex should be responsible for the dissimilarity in the turbulent flow, since the contribution to the overall dissimilarity is concentrated and is roughly 150% in the region with the swirl motion.

View full abstract

A thermosensitive liquid crystal suspention method gives the temperature field on fluid in a drum rotated by a heating center shaft inserted in. The obtained temperature field indicates the heat transfer process pattern in the fluid, which is classified associating with the governing equations. When the Taylor number is larger, the forced rotation flow generated by the inertia force is dominant and the heat radially diffuses by the heat conduction (Pattern(c)). When the Grashof number is lager and/or the Peclet number is smaller, i.e. the Grashof number per the Peclet number is larger, the buoyant force acting on the heated fluid is larger and the heat convention is dominant on the heat transfer, so that heated fluid pools in the upper region inside the drum (Pattern(a)). In the case that the forced rotation effect is almost equivalent to the heat convection effect, the heated fluid rapidly prevails in the whole region inside the drum (Pattern(b)).

View full abstract

Conducting a direct numerical simulation, we analyzed the flow in a symmetrically bifurcated Y-shaped channel having a high aspect ratio rectangular cross-sectional area. The channel could be considered as a combination of an introduction channel, an expansion part and two bifurcation channels. In the region near the expansion original point, the pressure gradient and the velocity in the main flow direction increase. The distance between the expansion original plane and the bifurcation original plane along the side wall is shorter than that along the center line, so that the pressure in the expansion direction side area is greater than that in the bifurcation point side area on the bifurcation original plane. The expansion and the bifurcation of the channel make the velocity profile and the pressure distribution on the bifurcation original plane, and the pressure gradient restores the velocity profile to be fully developed.

View full abstract

The turbulent flow over a wavy wall was quantitatively measured with a time-series PIV. The test section is consisted of a flat wall and a wavy wall. The wave length and the amplitude of the wavy wall are 32 mm and 4.5 mm, respectively. The Reynolds number, defined with the half channel height, was varied from 550 to 3300. Distribution of time-averaged velocity vector, turbulent intensities and Reynolds shear stress are obtained. A two-point correlation of velocity components is estimated in order to show coherent structure. The flow separates from the wavy wall at the upstream of the trough and reattaches at the downstream of the trough. A recirculation region appears in the trough of the wavy wall. A bursting motion out of the trough is observed. Features of wavy wall turbulence are clarified.

View full abstract

Cavitation cloud shows an unsteady periodic behavior and causes high impact. The periodicity of cavitation cloud shedding can be related to a reentrant motion and formation of pressure waves. A pattern of reentrant motion is dependent on re-circulating flow as well as pressure wave due to collapse of shedding clouds. In this study, we present some shedding patterns of cavitation cloud and the role of pressure wave accompanied with cloud collapse using an image analysis method.

View full abstract

The characteristics of the swirl-type micro bubble generation device were investigated by changing the inflow diameter, the exit angle, and inner pressure. The performance of the micro bubble generation device was evaluated by the bubble diameter which was measured by the image measurement method. When the micro bubbles were generated, it was confirmed that there were two kinds of generation forms. In one form, the nozzle exit flow discharges in radial direction, and the other form, the flow discharges in axial direction. In radial flow out type, the axial flow velocity was widely distributed at the exit of nozzle, and causing strong recirculation zone in the central portion. And it was proved that the micro bubble became minuter in this discharge form, and the relation between the bubble diameter and pressure changed irregularly.

View full abstract

Quantitatively characterizing long-period fluctuations, which reflect the large-scale structure of a bubbly flow in a bubble column reactor, is essential to improving the reactor efficiency. First, in order to extract long-period fluctuations of bubbly flow, we proposed a newly developed method to extract the long-period fluctuations based on point-wise void fraction measurements. Analyzing the time-series point-wise void fractions measured via Four-Tip Optical-fiber Probe (F-TOP), we demonstrate that the long-period fluctuations can be extracted via wave form analysis. Second, we measured point-wise liquid-phase motion via Laser Doppler Anemometry (LDA) at the same time with the point-wise void fraction measurements. As a result, we observed that the characteristic bubble-swarm forms surrounding liquid-phase motion.

View full abstract

A laser 2-focus velocimeter (L2F) with a micro-scale probe was used for measurements of velocity, size, and vortex scale in diesel sprays. The focal diameter of the laser probe was about 3 μm, and the distance between two foci was 17 μm. The data sampling rate of the L2F system has been increased to 15 MHz. Investigated were diesel fuel sprays injected intermittently into the atmosphere from the injector with a nozzle orifice 0.113 mm in diameter. The injection pressure was set at 40 MPa by using a common rail system. Measurement position was located at 25 mm from the nozzle exit. It was found that the vortex scale estimated by the L2F was close to the one observed by image measurement.

View full abstract

Numerical study is performed on the flow of incompressible fluid driven in a square cavity. Behavior of the unsteady flows beyond the first Hopf bifurcation is investigated. The first Hopf bifurcation is localized at Re_<cr> = 7987 with the fundamental frequency f = 0.4512, in good agreement with the previous studies. The secondary Hopf bifurcation occurs at 9600< Re_<cr2> &le; 9800. Quasi-periodic solution at Re = 10000 exhibits frequencies f_1 = 0.4381 and f_2 = 0.7128. Solution loses one frequency at 10800 < Re_<cr3> < 11200 and bistable periodic solutions with different fundamental frequencies appear for higher Reynolds numbers. It is shown that the latter bifurcation is of subcritical nature.

View full abstract