Bubble volume control method and bubble volume controlling apparatus

Abstract

Provided is a bubble volume control method and apparatus, and more particularly, to a bubble volume control method and apparatus for controlling the volume of a bubble by increasing or decreasing the volume of the bubble by emitting an ultrasonic wave having a resonance frequency corresponding to the size of the bubble located at the bottom of a container containing a liquid, such as water with bubbles composed of air, vapor, etc., toward the bubble by using an ultrasonic generator above the container, and maximizing a function of adjusting the volume of a bubble through a resonance effect by adjusting a liquid surface height of a liquid with the bubble according to a wavelength of an emitted ultrasonic wave.

Claims

1. A bubble volume control method comprising, when there is a bubble of a radius R at the bottom of a container containing a liquid of a density p and a specific heat ratio γ, controlling volume of the bubble to be reduced by emitting an ultrasonic wave having a resonance frequency f.sub.N toward the bubble through an ultrasonic generator provided above a surface of the liquid to pressurize the bubble, wherein the resonance frequency f.sub.N is defined by: $f_N=\frac{1}{2\pi }\sqrt{\frac{1}{\rho R^2}\left[3\gamma p_o+2\left(3\gamma -1\right)\frac{\sigma }{R}\right]},$ wherein p represents the density of the liquid contained in the container, R represents the radius of the bubble, Po represents an atmospheric pressure, and σ represents surface tension of the liquid.

2. The bubble volume control method of claim 1, wherein the ultrasonic generator pressurizes the bubble by transmitting a pressure wave Ps of a sinusoidal shape to the bubble through the liquid as a medium, wherein the pressure wave Ps is defined by:
Ps=P+a*sin(2π*f*t), wherein a represents an amplitude of the ultrasonic wave, f represents a frequency of the ultrasonic wave, and t represents time.

3. The bubble volume control method of claim 2, wherein the bubble is located at the bottom of the container, and a height H from the bubble to the surface of the liquid is ¼ of a wavelength λ of the ultrasonic wave.

4. The bubble volume control method of claim 1, wherein the ultrasonic generator transmits a pressure wave Ps of a sinusoidal shape to the bubble.

5. The bubble volume control method of claim 4, wherein the bubble is located at the bottom of the container, and a height H from the bubble to the surface of the liquid is ½ of a wavelength λ of the ultrasonic wave.

6. The bubble volume control method of claim 1, wherein, when an operation of the ultrasonic generator is stopped, pressure applied to the bubble is removed and thus the volume of the bubble is restored to its original volume.

7. The bubble volume control method of claim 6, wherein the volume of the bubble is controlled to be within a predetermined range by repeating an operation period in which the ultrasonic generator is operated and a non-operation period in which the operation of the ultrasonic generator is stopped.

8. The bubble volume control method of claim 1, wherein the radius of the bubble of which the volume is controlled by the ultrasonic wave generated by the ultrasonic generator is in a range of 1 μm to 100 μm.

9. The bubble volume control method of claim 2, wherein a pressure of an amplitude of the pressure wave Ps is in a range of 1.013 kPa to 10.13 kPa.

10. The bubble volume control method of claim 1, wherein the resonance frequency f.sub.N is in a range of 33 kHz to 4745 kHz.

11. The bubble volume control method of claim 3, wherein the height H of the surface of the liquid is in a range of 81 μm to 11647 μm.

12. The bubble volume control method of claim 1, wherein the radius of the bubble is inversely proportional to the resonance frequency f.sub.N of the ultrasonic wave generated by the ultrasonic generator, and is proportional to the height H of the surface of the liquid.

13. The bubble volume control method of claim 4, wherein a pressure of an amplitude of the pressure wave Ps is in a range of 1.013 kPa to 10.13 kPa.

14. The bubble volume control method of claim 5, wherein the height H of the surface of the liquid is in a range of 81 μm to 11647 μm.

15. A bubble volume control apparatus comprising: an ultrasonic generator; and a liquid container, wherein a liquid of a density p and a specific heat ratio γ is contained in the liquid container, the ultrasonic generator emits an ultrasonic wave toward a surface of the liquid in the liquid container, and when a radius of a bubble at the bottom of the liquid container is R, the ultrasonic generator generates an ultrasonic wave having a resonance frequency f.sub.N to pressurize the bubble to reduce the volume of the bubble, wherein the resonance frequency is defined by: $f_N=\frac{1}{2\pi }\sqrt{\frac{1}{\rho R^2}\left[3\gamma p_o+2\left(3\gamma -1\right)\frac{\sigma }{R}\right]},$ wherein p represents the density of the liquid contained in the container, R represents the radius of the bubble, Po represents an atmospheric pressure, and σ represents surface tension of the liquid.

16. The bubble volume control apparatus of claim 15, wherein the ultrasonic wave generated by the ultrasonic generator comprises a plane wave of a sinusoidal shape, and a liquid surface height of the liquid contained in the liquid container is ¼ of a wavelength λ of the ultrasonic wave having the resonance frequency f.sub.N and generated by the ultrasonic generator from the bottom of the liquid container.

Description

DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a diagram illustrating the structure of a bubble volume control apparatus employed in a bubble volume control method, according to the present invention.

(2) FIG. 2 illustrates a variation in a pressure of a liquid contained in a liquid container versus a position when an ultrasonic wave was generated on a surface of the liquid.

(3) FIG. 3 illustrates a variation in a pressure versus an angle of contact between a bubble and the bottom of a liquid container.

(4) FIG. 4 illustrates a variation in a ratio of increase in a pressure applied to a bubble to an atmospheric pressure according to a liquid surface height of a liquid container over time.

MODE OF THE INVENTION

(5) Hereinafter, exemplary embodiments of the present invention will be described in detail. The present invention is, however, not limited thereto and may be embodied in many different forms. Rather, the embodiments set forth herein are provided so that this disclosure will be thorough and complete, and fully convey the scope of the invention to those of ordinary skilled in the art. Throughout the specification, the same reference numbers represent the same elements.

(6) FIG. 1 is a diagram illustrating the structure of a bubble volume control apparatus 1 employed in a bubble volume control method, according to the present invention.

(7) The present invention provides a bubble volume control method of controlling the volume of a bubble b having a radius R to be reduced by applying pressure to the bubble b by emitting an ultrasonic wave having a resonance frequency f.sub.N defined below toward the bubble b under an atmospheric pressure of Po by an ultrasonic generator 100 provided above a surface of the liquid, when the bubble b is located at the bottom of a container 200 containing a liquid of a density of P, a specific heat ratio of γ, and a surface tension of a; and a bubble volume control apparatus employing the same.

(8) The bubble volume control apparatus 1 according to the present invention generates a bubble b composed of a gas such as fine air at a surface of an inner wall (particularly, a bottom) of the container 200 containing a liquid such as water. The resonance frequency f.sub.N of the bubble b is determined according to a radius R of the generated bubble b by using the following equation:

(9) $\begin{array}{cc}{f}_N=\frac{1}{2\pi }\sqrt{\frac{1}{\rho R^2}\left[3\gamma p_o+2\left(3\gamma -1\right)\frac{\sigma }{R}\right]}& \left(\mathrm{Equation}1\right)\end{array}$

(10) Here, p represents the density of the liquid contained in the container 200, R represents the radius of the generated bubble, P represents an atmospheric pressure, and a represents surface tension of the liquid. That is, the resonance frequency of the bubble represents the size of the bubble or characteristics of the bubble according to a property of the liquid or the like. Thus, it will be understood that as the size of the bubble or the like increases, the resonance frequency of the bubble decreases, as shown in Equation 1 below.

(11) As illustrated in FIG. 1, in the bubble volume control apparatus 1 according to the present invention, the ultrasonic generator 100 provided just above a surface of the liquid contained in the container 200 may emit a pressure wave p.sub.s of a sinusoidal shape, which is expressed below, to be transmitted to the bubble located at the bottom of the container 200 via the liquid as a medium.
Ps=P+a*sin(2π*f*t)  (Equation 2)

(12) Here, a represents the amplitude of the ultrasonic wave, f represents the frequency of the ultrasonic wave, and t represents time.

(13) In this case, the wavelength λ of the ultrasonic wave is defined as λ=c/f, wherein c represents the velocity of sound in the liquid L contained as a medium in the container 200.

(14) An amplitude of a plane pressure wave Ps emitted by the ultrasonic generator 100 is largest at a wavelength λ/4 according to the shape of a sine wave periodic function. On the other hand, a wavelength of a spherical wave having a largest amplitude may be λ/2.

(15) Accordingly, if a liquid surface height H to which the ultrasonic wave generated by the ultrasonic generator 100 is transmitted, i.e., a distance from the ultrasonic generator 100 to the bottom of the container 200 to which the ultrasonic wave having the wavelength λ travels, satisfies H=λ/4, the bubble at the bottom of the container 200 meets the ultrasonic wave which is the pressure wave Ps emitted by the ultrasonic generator 100 when an amplitude of the ultrasonic wave is largest, thereby causing multiple resonance.

(16) Thus, a change of the pressure of the bubble may be amplified due to multiple resonance or the like and the amount of pressure applied to the bubble may be maximum, when the ultrasonic generator 100 emits the ultrasonic wave, which is the pressure wave Ps having a frequency which is the same as the resonance frequency f.sub.N of the bubble according to Equation (1) above, onto a liquid surface with a height H(=λ/4) corresponding to a wavelength λ of a largest amplitude.

(17) It is noted that the volume of a bubble, such as air, located at a wall surface, i.e., the bottom, of a liquid container may be controlled to be, for example, grown, reduced, or removed, based on the above principle.

(18) Examples of a resonance frequency according to a size of a fine bubble and a height H of a liquid surface at which resonance is amplified according to the present invention are as shown in Table 1 below.

(19) It was experimentally found that a range in which a bubble volume control method according to the present invention is applicable is effective under the following conditions.

(20) First, the effects of the present invention were proved when the size of a bubble such as fine air was in a range of 1 μm to 100 μm, an amplitude of pressure of a pressure wave Ps emitted by an ultrasonic generator was in a range of 1.013 kPa to 10.13 kPa, a frequency of an ultrasonic wave generated by the ultrasonic generator to match a resonance frequency according to the size of the bubble was in a range of 33 kHz to 4745 kHz, and a liquid surface height H satisfying a multiple resonance condition was in a range of 81 kHz to 11647 μm. The volume of the bubble was controlled to some extent even when the radius of the bubble, the resonance frequency, or the liquid surface height H was beyond the above ranges, but it is desirable to adjust parameters to satisfy the above ranges in order to obtain a remarkable effect.

(21) As shown in Table 1 below, the resonance frequency f.sub.N is inversely proportional to the radius R of the bubble and is proportional to the liquid surface height H. When conditions of the radius R of the bubble, the resonance frequency f.sub.N, and the liquid surface height H with respect to the bubble are determined in combinations as shown in Table 1 below, a function of controlling the volume of the bubble using a pressure wave Ps due to multiple resonance may be maximized.

(22) TABLE-US-00001 TABLE 1 R(μm) F.sub.N(kHz) H (μm) 1 4.745 × 10.sup.3 8.113 × 10.sup.1 2 2.041 × 10.sup.3 1.886 × 10.sup.2 5 7.252 × 10.sup.2 5.308 × 10.sup.2 7.5 4.689 × 10.sup.2 8.209 × 10.sup.2 10 3.461 × 10.sup.2 1.112 × 10.sup.3 20 1.687 × 10.sup.2 2.281 × 10.sup.3 50 6.646 × 10.sup.1 5.792 × 10.sup.3 75 4.415 × 10.sup.1 8.719 × 10.sup.3 100 3.305 × 10.sup.1 1.164 × 10.sup.4

(23) A result of a test according to an embodiment of the present invention will be described in detail with reference to FIGS. 2 to 4 below.

(24) Conditions of the test will be described in detail below. A pressure a of an amplitude of an ultrasonic wave which is a pressure wave Ps was 2.026 kpa, an ultrasonic generator emitting a sinusoidal plane wave having a frequency f=725 kHz (in the case of water vapor, the frequency varies according to a specific heat ratio γ) equal to a natural frequency f.sub.N of an underwater air bubble was provided on a liquid surface, and a container with a height H=531 μm corresponding to λ/4 of the plane wave (having a wavelength λ of 2,124 μm) at which an amplitude was largest was filled with water and an air bubble with a radius of 5 μm was generated at the bottom of the container.

(25) FIG. 2 illustrates a variation in a pressure of a liquid contained in a liquid container versus a position of a bubble when an ultrasonic wave was generated on a surface of the liquid.

(26) A pressure wave Ps emitted by an ultrasonic generator has a repetitive sinusoidal shape as indicated by a blue solid line graph.

(27) The pressure wave Ps transmitted via a medium (a liquid such as water) arrived at a bubble located at the bottom of a container, and the amount of pressure of the liquid increased with time due to an effect the height of the container and characteristics of the water when compressed, as indicated by a red solid line graph.

(28) That is, it was found that, when the radius of the bubble, the frequency of the ultrasonic wave, and the heights of the bubble and a liquid surface were appropriately combined, the volume of the bubble was controlled by pressurizing the bubble by emitting the ultrasonic wave onto the liquid as a medium to transmit the pressure wave Ps of a sinusoidal shape of which the size increases with time as indicated by the red solid line graph of FIG. 2 to the bubble located at the bottom of the container containing the liquid. That is, the volume of the bubble may be gradually reduced during an operation period in which the operation of the ultrasonic generator 100 is maintained, and be gradually recovered to its original size in a non-operation period in which the generation of the ultrasonic wave was stopped. Thus, the original size of the bubble may be reduced to be within a certain range and the reduced volume of the bubble may be maintained to be within a desired range by appropriately combining the operation period and the non-operation period of the ultrasonic generator 100.

(29) In other words, because the size of the pressure wave Ps increases with time, the present invention is distinguished from the techniques introduced in the past. The existing studies have been conducted to try to seek various uses of bubbles, based on an assumption that the sizes of the bubbles are adjustable, but a method of controlling the volume of bubbles, and particularly, the relationship among the size of the bubbles, a frequency of an ultrasonic wave, a wavelength, and a liquid surface height, etc. has not been investigated. However, the volume of a bubble can be actively controlled under the above conditions.

(30) FIG. 3 illustrates a variation in a pressure versus an angle of contact between a bubble and the bottom of a liquid container.

(31) A pressure of the bottom of a container at which a bubble was located was sharply changed due to resonance produced by an ultrasonic wave and the bubble and multiple resonance produced when the resonance was amplified due to an effect of the height of the container, achieved by taking into account a wavelength corresponding to a largest amplitude.

(32) As time went by, a liquid contained in the container was more sharply pressurized from 1 Mpa to 2 Mpa than when there was no bubble (as indicated by the red solid line in FIG. 2), thereby causing a behavior (growth, contraction, or removal) of the bubble due to the change of the pressure.

(33) Furthermore, an effect of compressing a liquid contained in the container through the growth, contraction, or removal of the bubble was increased and thus was more pressurized over time, as the angle of contact between the bottom of the container and the bubble became smaller.

(34) Accordingly, it is expected that the bubble may be formed to be relatively flat in order to control a responsiveness of control of the volume of a bubble or a bubble volume change ratio volume, or control performance when a change of the volume of the bubble is needed will be maximized by pre-pressurizing the bubble using an ultrasonic wave.

(35) FIG. 4 illustrates a variation in a ratio of increase in a pressure applied to a bubble to an atmospheric pressure according to a liquid surface height of a liquid container over time.

(36) The size of a pressure wave Ps was not greatly changed over time when a condition of maximizing the resonance effect, i.e., H=λ/4, according to an embodiment was not satisfied, i.e., in an experiment indicated by a blue solid line, in which a frequency of an ultrasonic wave was set to match a radius of a bubble according to Equation (1) above and a liquid surface height was set to about 75% of a wavelength of the ultrasonic wave (i.e., H=0.75λ) and an experiment indicated by a green solid line, in which a liquid surface height was set to about 50% of a wavelength of the ultrasonic wave (i.e., H=0.50λ), even when a frequency of the ultrasonic wave satisfied a multiple resonance condition according to the size of a bubble.

(37) That is, the volume of the bubble did not change to a large extent over time.

(38) In contrast, in an experiment indicated by a red solid line, in which a liquid surface height was set to about 25% of a wavelength of an ultrasonic wave, i.e., a quarter of the wavelength λ of the ultrasonic wave (i.e., H=0.25λ), a size of a pressure wave Ps was sharply increased with time due to a resonance phenomenon, thereby maximizing a function of controlling the volume of a bubble.

(39) While the present invention has been described above with respect to exemplary embodiments thereof, it would be understood by those of ordinary skilled in the art that various changes and modifications may be made without departing from the technical conception and scope of the present invention defined in the following claims. Thus, it is clear that all modifications are included in the technical scope of the present invention as long as they include the components as claimed in the claims of the present invention.