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Dynamics of a Capillary Invasion in a Closed-End Capillary
Lim, Hosub,Tripathi, Anubhav,Lee, Jinkee American Chemical Society 2014 Langmuir Vol.30 No.31
<P>The position of fluid invasion in an open capillary increases as the square root of time and ceases when the capillary and hydrostatic forces are balanced, when viscous and inertia terms are negligible. Although this fluid invasion into open-end capillaries has been well described, detailed studies of fluid invasion in closed-end capillaries have not been explored thoroughly. Thus, we demonstrated, both theoretically and experimentally, a fluid invasion in closed-end capillaries, where the movement of the meniscus and the invasion velocity are accompanied by adiabatic gas compression inside the capillary. Theoretically, we found the fluid oscillations during invasion at short time scales by solving the one-dimensional momentum balance. This oscillatory motion is evaluated to determine which physical forces dominate the different conditions, and is further described by a damped driven harmonic oscillator model. However, this oscillating motion is not observed in the experiments. This inconsistency is due to the following: first, a continuous decrease in the radius of the curvature caused by decreasing the invasion velocity and increasing pressure inside the closed-end capillary, and second, the shear stress increase in the short time scale by the plug like velocity profile within the entrance length. The viscous term of modified momentum equation can be written as <I>K</I>(8μ<I>l</I>/<I>r</I><SUB>c</SUB><SUP>2</SUP>)(d<I>l</I>/d<I>t</I>) by using the multiplying factor <I>K</I>, which represents the increase of shear stress. The <I>K</I> is 7.3, 5.1, and 4.8 while capillary aspect ratio χ<SUB>c</SUB> is 740, 1008, and 1244, respectively.</P><P><B>Graphic Abstract</B> <IMG SRC='http://pubs.acs.org/appl/literatum/publisher/achs/journals/content/langd5/2014/langd5.2014.30.issue-31/la501927c/production/images/medium/la-2014-01927c_0010.gif'></P>
임호섭(Hosub Lim),임성진(Seong Jin Lim),이진기(Jinkee Lee) 한국가시화정보학회 2014 한국가시화정보학회지 Vol.12 No.2
Although many studies have been done on an open-end capillary, the invasion into a closed end capillary is still novel in its investigation. In this research we have explored the fluid invasion in closed-end capillaries where the shape of the meniscus and the height of invasion were accompanied by gas compression inside the capillary. Theoretically, the one dimensional momentum balance equation shows the fluid oscillation. In the experiments, we have found the different phenomena, either the fluid oscillation with low frequency or no oscillation. This discrepancy is mostly caused by two factors. First, a continuous decrease of the advancing contact angle due to decreasing invasion velocity as increasing pressure inside the closed-end capillary reduces the invasion velocities. Second, the high shear stress within the entrance length region was generated by the plug like velocity profile.
임호섭(Hosub Lim),임성진(Seongjin Lim),이진기(Jinkee Lee) 대한기계학회 2013 대한기계학회 춘추학술대회 Vol.2013 No.12
The position of fluid invasion in an open capillary increases as the square root of time when the capillary and viscous forces are balanced when gravity and inertia terms are neglected. Although this fluid invasion into open-end capillaries has been well described, detailed studies of fluid invasion and motion in closed-end capillaries have not been explored throughly. We demonstrate, theoretically and experimentally, a fluid motion in closed-end capillaries where the movement of the meniscus is accompanied by adiabatic gas compression inside the capillary. Theoretically, we find fluid oscillations during invasion at short time scales by solving the one dimensional momentum balance. This oscillatory motion is evaluated to determine which physical forces dominate for different conditions.