In Seok Kang

Numerical solution of axisymmetric, unsteady free‐boundary problems at finite Reynolds number. I. Finite‐difference scheme and its application to the deformation of a bubble in a uniaxial straining flow

A brief description of a numerical technique suitable for solving axisymmetric, unsteady free‐boundary problems in fluid mechanics is presented. The technique is based on a finite‐difference solution of the equations of motion on a moving orthogonal curvilinear coordinate system, which is constructed numerically and adjusted to fit the boundary shape at any time. The initial value problem is solved using a fully implicit first‐order backward time differencing scheme in order to insure numerical stability. As an example of application, the unsteady deformation of a bubble in a uniaxial extensional flow for Reynolds numbers is considered in the range of 0.1≤R≤100. The computation shows that the bubble extends indefinitely if the Weber number is larger than a critical value (W>Wc). Furthermore, it is shown that a bubble may not achieve a stable steady state even at subcritical values of Weber number if the initial shape is sufficiently different from the steady shape. Finally, potential‐flow solutions as an ...

Electrophoresis of a Charged Droplet in a Dielectric Liquid for Droplet Actuation

Electrophoretic motion of a charged droplet in a dielectric fluid under an electric field has been investigated experimentally for use as a microdroplet actuation method. The effects of the droplet size, electric field strength, and electrolyte concentration and ion species on the charging of an aqueous droplet have been examined. The amount of electrical charging has been measured by two different methods: indirect measurement using the image analysis of droplet motion and direct measurement using the electrometer. Quantitative comparison of the droplet charge measured experimentally and the theoretical value of a perfectly conductive sphere shows that an aqueous droplet is less charged than the corresponding perfectly conductive sphere. The limiting effect on electrical charging is more significant for an electrolyte droplet, and the effect is positively correlated to the electrolyte concentration rather than the ion species. This implies that the low electrical conductivity of water is not a major cause of the limiting effect. The scaling law of the charging amount for a deionized water droplet nearly follows that of the perfect conductor, whereas for an electrolyte droplet, the scaling law exponent is slightly higher. Some advantages and potentials of the current droplet actuation method are also discussed in comparison with the conventional ones.

Electrical charging of a conducting water droplet in a dielectric fluid on the electrode surface

It has been conceived that a charged droplet driven by Coulombic force can be used as a droplet-based microreactor. As a basic research for such applications, electrical charging of a conducting water droplet is studied experimentally. The effects of electric field, medium viscosity, and droplet size are investigated. It is found that the amount of electrical charging increases with the droplet size and the electric field. However, the medium viscosity does not have a significant effect in the range of the present study. A scaling law is derived from the experimental results. Unlike the case of a perfect conductor, the estimated amount of electrical charge (Q(est)) of a water droplet is proportional to the 1.59 power of the droplet radius (R) and the 1.33 power of the electric field strength (E). (For a spherical perfect conductor, Q is proportional to R(2) and E.) In order to understand these differences, numerical simulations are performed for the idealized droplets of perfect conductor. Comparison of the numerical and experimental results suggests that the differences are mainly due to incomplete charging of a water droplet resulted from the combined effect of electrochemical reaction at electrode and the relatively low conductivity of water.

Spontaneous electrical charging of droplets by conventional pipetting

We report that a droplet dispensed from a micropipette almost always has a considerable electrical charge of a magnitude dependent on the constituents of the droplet, on atmospheric humidity and on the coating material of pipette tip. We show that this natural electrification of a droplet originates from the charge separation between a droplet and pipette tip surface by contact with water due to the ionization of surface chemical groups. Charge on a droplet can make it difficult to detach the droplet from the pipette tip, can decrease its surface tension, can affect the chemical characteristics of solutions due to interactions with charged molecules, and can influence the combination and localization of charged bio-molecules; in all cases, the charge may affect results of experiments in which any of these factors is important. Thus, these findings reveal experimental parameters that should be controlled in experiments that use micropipettes.

Quantitative visualization of flow inside an evaporating droplet using the ray tracing method

Liquid droplets possess many practically important applications and academically interesting issues. Accurate flow data are necessary to correlate the hydrodynamic characteristics with the physicochemical processes occurring inside a droplet. However, the refraction of light at the droplet surface makes it difficult to measure the flow field inside the droplet accurately. To resolve this problem, two correction methods based on the ray tracing technique are employed. One is the image mapping method and the other is the velocity mapping method. For this, a mapping function between the image plane and the object plane is derived. The two correction methods are applied to the flow inside evaporating droplets of different ethanol concentrations for measuring their velocity fields, using a PIV method. The results obtained with the two methods are nearly identical. The major differences between the original results and the corrected results are found in the locations of the vortex centres and the magnitude of velocity vectors. Between the two correction methods, the velocity mapping method is recommended, because it is more convenient and recovers a greater number of velocity vectors, compared with the image restoration method.

Mixing enhancement by using electrokinetic instability under time-periodic electric field

Experimental studies have been performed to apply electrokinetic instability as a means of fluid mixing. A time-periodic electric field is introduced to excite the instability in a cross channel. It is generated by the sum of a static field and an alternating field. The characteristics of instability have been considered with the frequency of applied electric field as a key parameter. Through the frequency sweeping from 0.1 Hz to 50 Hz, it has been found that the instability is most enhanced when the period of the applied electric field is close to half of the period of instability in the form of a sinusoidal wave generated under a the static electric field. This fact may be explained based on the concept of hydrodynamic resonance. The degree of mixing is evaluated quantitatively by analyzing the distribution of fluorescent dye and it is confirmed that there exists an optimal frequency for enhancement of fluid mixing. The existence of the optimal frequency is expected to provide a valuable guideline for the design of an efficient micro-mixer.

Study of the behavior of a bubble attached to a wall in a uniform electric field

Abstract In order to investigate the effects of a uniform electric field on a bubble attached to a wall, numerical analyses and experiments have been carried out. The orthogonal curvilinear coordinate system generated numerically has been employed for the numerical studies based on a finite-difference solution of the governing equations. The steady bubble shape is obtained under the fixed contact radius condition as part of the solution of the free boundary problem. Along with the shape determination, the Laplace equation for electric potential is solved simultaneously. In experimental studies, an air bubble attached to one plate of a parallel-plate electrode system has been visualized under an applied electric field. The numerical and experimental results show generally good agreements. An air bubble on the lower electrode is found to be extended in the direction parallel to the applied electric field. The elongation increases with an increase of the electric field strength. Consequently, the contact angle also increases with an increase of the electric field strength if the contact radius is fixed. On the other hand, if the contact angle is fixed, the contact radius decreases as the electric field strength increases. It has been observed experimentally that the bubble departure volume remains nearly constant under the uniform electric field. This fact suggests that the downward electric force exerted on the bubble surface is nearly the same as the decrease in the surface tension force due to contact radius decrease under the uniform electric field.

Bubble dynamics in time-periodic straining flows

The dynamics and breakup of a bubble in an axisymmetric, time-periodic straining flow has been investigated via analysis of an approximate dynamic model and also by time-dependent numerical solutions of the full fluid mechanics problem. The analyses reveal that in the neighbourhood of a stable steady solution, an O(ϵ1/3) time-dependent change of bubble shape can be obtained from an O(e) resonant forcing. Furthermore, the probability of bubble breakup at subcritical Weber numbers can be maximized by choosing an optimal forcing frequency for a fixed forcing amplitude.

Circulating flows inside a drop under time-periodic nonuniform electric fields

The circulating flows formed inside a spherical drop under time-periodic nonuniform electric fields are considered. For simplicity, it is assumed that there are axisymmetric electric fields and that the flow fields are in the Stokes flow regime. An analytical solution of the streamfunction distribution inside and outside the drop is obtained. The flow field is found to be dependent on the frequency of the time-periodic electric field and the ratios of the material properties such as the viscosity, the electrical conductivity, and the electrical permittivity. As part of the solution, an analytical expression of the dielectrophoretic migration velocity of a drop under a time-periodic electric field is also obtained. The result shows an interesting physics—that dielectrophoretic migration is possible in a time-periodic electric field even in the situation where dielectrophoresis would be impossible in a static electric field. By using the analytical solution of the streamfunction, fluid mixing inside a drop is analyzed based on the Poincare maps. The mass transfer enhancement factor due to fluid mixing has also been computed by solving the unsteady mass transfer equation numerically. The existence of an optimal frequency has been confirmed as in other mass transfer enhancement processes by time-periodic forcing.

Neural algorithm for solving differential equations

Finite difference equations are considered to solve differential equations numerically by utilizing minimization algorithms. Neural minimization algorithms for solving the finite difference equations are presented. Results of numerical simulation are described to demonstrate the method. Methods of implementing the algorithms are discussed. General features of the neural algorithms are discussed.