Bubble embryo

As stated in Section 2.1, there is a waiting period between the time of release of one bubble and the time of nucleation of the next at a given nucleation site. This is the period when the thermal boundary layer is reestablished and when the surface temperature of the heater is reheated to that required for nucleation of the next bubble. To predict the waiting period, Hsu and Graham (1961) proposed a model using an active nucleus cavity of radius rc which has just produced a bubble that eventually departs from the surface and has trapped some residual vapor or gas that serves as a nucleus for a new bubble. When heating the liquid, the temperature of the gas in the nucleus also increases. Thus the bubble embryo is not activated until the surrounding liquid is hotter than the bubble interior, which is at... 

The first approach developed by Hsu (1962) is widely used to determine ONE in conventional size channels and in micro-channels (Sato and Matsumura 1964 Davis and Anderson 1966 Celata et al. 1997 Qu and Mudawar 2002 Ghiaasiaan and Chedester 2002 Li and Cheng 2004 Liu et al. 2005). These models consider the behavior of a single bubble by solving the one-dimensional heat conduction equation with constant wall temperature as a boundary condition. The temperature distribution inside the surrounding liquid is the same as in the undisturbed near-wall flow, and the temperature of the embryo tip corresponds to the saturation temperature in the bubble 7s,b- The vapor temperature in the bubble can be determined from the Young-Laplace equation and the Clausius-Clapeyron equation (assuming a spherical bubble) ... 

Let us consider a superheated liquid which has attained the limit of superheat and a vapor embryo forms in equilibrium with the liquid. The bubble radius is ro, the pressure in the bulk liquid is Pq, and the temperature is Tq. Assume the liquid is pure. 

The vapor embryo, or bubble, is in unstable equilibrium and will either collapse or grow. We are only interested in those that follow the latter path. The chemical criteria of equilibrium between the bubble and liquid state that the temperature and chemical potential of the material in the bubble are equal to those in the superheated liquid, i.e.. 

Escalation is, however, encouraged for cases where the initial coolant liquid is sufficiently fragmented so that initial embryo growth is rapid and without excessive interference due to other embryos (which would increase the local pressure and, thereby, reduce the growth rate). If the fragmentation is such that very small drop sizes are present, then during the inertial growth of vapor embryos, the bubble radius will reach the... 

The basic reason why superheated liquids can exist is that the nucleation step requires that a vapor embryo bubble of a minimum size must be achieved. Vapor embryos less than the critical size are unstable and tend... 

Availability change to form embryo Initial bubble diameter Frequency factor in nucleation Enthalpy of vaporization Rate of formation of critical-sized embryos per unit volume Jacob numter [Eq. (17)] Boltzmann s constant or thermal conductivity... 

Calcite embryos nucleate Crystals nucleate Bubbles nucleate... 

The problems of phase transition always deeply interested Ya.B. The first work carried out by him consisted in experimentally determining the nature of memory in nitroglycerin crystallization [8]. In the course of this work, questions of the sharpness of phase transition, the possibility of existence of monocrystals in a fluid at temperatures above the melting point, and the kinetics of phase transition were discussed. It is no accident, therefore, that 10 years later a fundamental theoretical study was published by Ya.B. (10) which played an enormous role in the development of physical and chemical kinetics. The paper is devoted to calculation of the rate of formation of embryos—vapor bubbles—in a fluid which is in a metastable (superheated or even stretched, p < 0) state. Ya.B. assumed the fluid to be far from the boundary of absolute instability, so that only embryos of sufficiently large (macroscopic) size were thermodynamically efficient, and calculated the probability of their formation. The paper generated extensive literature even though the problem to this day cannot be considered solved with accuracy satisfying the needs of experimentalists. Particular difficulties arise when one attempts to calculate the preexponential coefficient. 

In the problem of bubble production the size of the embryo is the independent variable in the diffusion equation. The value of the diffusion coefficient itself is determined by solving the hydrodynamic equations describing the growth of a bubble in a viscous fluid. 

This paper by Ya.B. helped lay the foundation for the study of the kinetics of phase transitions of the first kind. It considers the fluctuational formation and subsequent growth of vapor bubbles in a fluid at negative pressures. It is assumed that the fluid state is far from the boundary of metastability and that the volume of the bubbles formed is still small in comparison with the overall volume of the fluid. The first assumption ensures slowness of the process the time of transition to another phase is large compared to the relaxation times of the fluid per se. This allows the application of the Fokker-Planck equation in the space of embryo dimensions to describe the growth of the embryos. 

Nucleation of gas bubbles is notoriously difficult, and the following calculation may explain it. Assume that a gas embryo of 2 nm radius is formed in a liquid at atmospheric pressure. The interfacial tension will generally be about 0.07N-m 1. The Laplace pressure in the embryo will then be about 2x0.07/2-10 9 = 7-107 Pa, which equals 700 bar. The supersaturation ratio of the gas should then be about 700 for such a small bubble to survive, and that is very unlikely to be the case. In a beer bottle the pressure is a few bar, in an aerosol can with N20 about 7 bar. Moreover, the number of gas molecules inside the embryo would be about 560 (try to make the calculation), more than could possibly associate by chance. Homogeneous nucleation can therefore not occur. By similar reasoning, it can be derived that heterogeneous nucleation on a surface, as depicted in Figure 14.5b, frames 1 and 2, is not possible either, even if 6 is quite small. 

In the metastable condition, an embryo bubble may be formed inside the liquid. Whether this embryo collapses after formation or grows depends on the size of the embryo and the conditions of the liquid. 

The second equation is Young-Laplace equation for a bubble and P e is the vapor pressure of an embryo in equilibrium with the liquid. Using the above equation along with Gibbs-Duhem equation it can be shown that the radius of an embryo at equilibrium conditions are ... 

The next question is whether this bubble is stable or not. The following equation shows the variation of the Gibbs free energy with bubble radius for an embryo formed in a superheated liquid due to a density fluctuation ... 

In the above equation AGe is the Gibbs free energy of formation of an embryo of size Te Since AG approaches zero as the bubble radius, r, approaches zero or infinity, the Gibbs free energy decreases (the free energy is consumed because... 

Air bubbles emit from the tungsten wire, indicating the current has been generated. It is essential that the embryo is correctly spaced between the plate and wire such that large bubbles anitting from the plate and wire do not touch and bum the embryo and also that the targeted embryo site is close to the wire to allow focused point of electroporation. 

Using the egg transfer pipet assembly, aspirate a little PBS, then pick up all the embryos in a minimal volume of PBS and transfer to the cryoprotectant. Do not expel bubbles into the dish. Allow to settle to the bottom for a minute or two. Distribute the embryos in groups of ten around the periphery of the dish. 

When the agar has cooled down, add the albumen to the agar solution and swirl gently to mix add 2.4ml of the lOOx antibiotic-antimycotic stock while continuing to mix. Using a sterile 10 ml pipet and pipet aid, distribute 2.5 ml agar-albumen into each petri dish, avoiding the formation of bubbles. Do not dispense more than 2.5 ml, since a thicker substrate will make observation of the embryos more difficult. 

After ensuring that there are no air bubbles in the syringe with Indian ink or the needle, insert the needle under the vitelline membrane, tangentially, at a position as far away from the embryo proper as possible (Fig. IG and IH). Point toward and slightly below the embryo, and inject about 20-50 ilL. It is important to minimize movement of the needle after penetrating the vitelline membrane, or the hole will be very large and yoUc-ink leak out. Introduce and withdraw the needle with one clean, decisive movement, and do not stir the needle inside the yolk. 

Remove the piece of segmental plate with a Gilson micropipet set to l-2pL. Replace the bubble over the embryo with fresh CMF twice to remove the trypsin solution. Make a new bubble of CMF while obtaining the graft from the donor. 

Pick up the graft with the Gilson. With the other hand, place the host under the microscope and, observing under low magnification, carefully place the graft into the CMF bubble over the embryo. 

Fig. 3. Finishing touches. A Remove excess trypsin-CMF from the bubble above the emhryo. B Remove 5 mL albumen through the side hole. C Wipe the shell. D Add the antibiotic. E Seal the egg with PVC tape. F Smooth out the tape. G and H. If desired, invert the egg to expose the embryo to clean shell and membrane before incubating...

Push the needle of the ink-filled syringe into the yolk outside the area pel-lucida, and move its tip, as horizontally as possible, into the subblastodermal space. Be careful not to scrape the underside of the embryo and, for older stages, not to rupture any blood vessels. Expel about 0.1 mL of ink, taking care not to introduce air bubbles see Note 3). 

When pulses are charged, bubbles form on both of the electrodes. Remember that the cathode produces more bubbles than the anode. Only the anode side of the tissue is transfected (Fig. 1, Fig. 2F). Under these conditions, damage to the embryo is usually minimal (Fig. 2G). 

Methyl cellulose A 3% (w/v) solution of methyl cellulose can be used to mount and photograph Uve anesthetized embryos. Powder is dissolved in water via gentle heating to a viscous solution. The solution is refrigerated to remove air bubbles and then brought to room temperature before use. Fish can simply be removed from the methyl cellulose by sequential rinses in water. 

The embryos that trigger vapor formation in a superheated liquid are microscopic bubbles small regions where the density is smaller than in the bulk. To calculate the rate of homogeneous nucleation in a superheated liquid according to the classical theory, one must therefore consider the energetics of bubble formation. The contents of vapor embryos can be treated as an ideal gas except near the critical point. Let P be the pressure inside the critical nucleus. Then, P being the bulk pressure in the superheated... 

In order to calculate the relationship between r and P away from equilibrium one must take into account the dynamics of bubble growth and decay. Such a hydrodynamic approach was developed by Zeldovich [9] and Kagan [73]. There are, however, two obvious limiting cases [69]. For small departures from equilibrium, the pressure inside the embryo can be plausibly assumed to remain constant at its equilibrium value. In this case, (44) becomes... 

Open the ovarian bursa, avoiding trauma to large blood vessels. Identify the opening of the ostium and insert the surgical transfer pipette. To ensure successful embryo transfer, the pipette should be advanced beyond the point of bursal attachment. Embryos are then expelled until the air bubble marker enters the oviductal lumen. Repeat this procedure on the opposite side if sufficient numbers of embryos are available. 

Note Do not shake the PBTA methanol mixture, because bubbles that form interfere with the ability of the embryos to sink to the bottom of the tube. 

Note It is important that the correct amount of mounting solution (containing embryos) is placed on the slide. For example, a 22 x 22-mm coverslip requires 40 i,l of mounting media. Less than this volume results in bubbles and more than this volume results in a floating coverslip that cannot be sealed with naU polish. 

Lower the needle into the halocarbon oil at one end of the line of embryos. Gently push the tip of the needle into the side of the 20 x 20-mm coverglass to break off a small portion of the tip. The goal is to create a l-2- im opening. Apply pressure to the needle to force a drop of the GAL4VP16 solution out of the needle and to remove any trapped air bubbles. 

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