| 학회 | 한국화학공학회 |
| 학술대회 | 2001년 봄 (04/27 ~ 04/28, 연세대학교) |
| 권호 | 7권 1호, p.1977 |
| 발표분야 | 이동현상 |
| 제목 | 선형 전기장 하의 3차원 기포 진동의 비선형 해석 |
| 초록 | The Rayleigh-Plesset (RP) equation and the Prosperetti-Seminara (PS) equations have been developed continuously (Plesset and Prosperetti 1977, Feng and Leal 1997, Prosperetti 1977). Applying electromagnetic force is an important part of bubble/drop dynamics in recent. A bubble in an electric field may be deformed from spherical shape due to the nonuniform normal stress imbalance over the spherical bubble surface. These electrohydrodynamic phenomena have attracted much attention of researchers since the seminal work of Taylor. The electric force due to the permittivity difference between inside and outside a bubble makes a bubble oscillation dynamic and complicated. Lee and Kang (1999) investigated the linear electric field effects in natural frequencies of a bubble in a dielectric liquid. Oh et al. derived the extended RP equation and PS equations including electric field effects. They considered two kinds of linear electric fields : uniform field and axisymmetric straining field. When the viscosity effect is considerable, both the volume and shape mode oscillations can be chaotic at the same time. In the present work, Oh et al.\'s results are extended to bubble oscillations in general linear electric fields. Oscillation equations are derived by using the domain perturbation method with Taylor and Melcher\'s leaky dielectric model and weak viscosity assumption. The shape of a bubble can be expressed in terms of volume averaged radius and surface spherical harmonics. As noted by Lee and Kang (1999), to the first order, the shape of a bubble in arbitrary linear electric field can be represented by a linear combination of finite number of spherical harmonics. It is important in bubble dynamics to understand the exchange of gases across the interface between free state within the bubble and the dissolved state outside the bubble. It is well known that in the volume oscillation of a bubble the usual tendency to dissolve in undersaturated liquids may be reversed through a phenomenon known as rectified diffusion. Most researches in rectified diffusion are restricted to volume oscillations and the effect of bubble shape deformation in rectified diffusion has been less investigated though a lot of progress in understanding mass transport in bubble oscillations have been made. If the shape of oscillating bubble is deformed, the problems become much complex. One of the difficulties lies in solving the diffusion equation on the domain deformed from spherical shape, in which spherical coordinate cannot be applied. Instead of solving the transport equation directly, we concentrate on the dynamical behavior of the surface area of oscillating bubble. The surface area of deformed bubble can be calculated analytically without loss of degree of accuracy by using the orthogonality of surface harmonics. The detail of calculation is explained in the present work. Two kinds of measures relating to dynamical behaviors of surface area of oscillating bubble are also defined. In this study, the surface area dynamics is investigated by observing the defined measures for three kinds of electric fields : axisymmetric straining electric field, 2-dimensional hyperbolic field, and combination of uniform and hyperbolic fields. And the effects of deformation of oscillating bubble in time-periodic electric fields are considered. |
| 저자 | 오정민1, 강인석2 |
| 소속 | 1포항공과대, 2기계산업공학부 |
| 키워드 | bubble dynamics; electric field; oscillation; nonlinear dynamics |
| 원문파일 | 초록 보기 |
