A Nonsteady Heat Diffusion Problem with Spherical Symmetry

A solution in successive approximations is presented for the heat diffusion across a spherical boundary with radial motion. The approximation procedure converges rapidly provided the temperature variations are appreciable only in a thin layer adjacent to the spherical boundary. An explicit solution for the temperature field is given in the zero order when the temperature at infinity and the temperature gradient at the spherical boundary are specified. The first-order correction for the temperature field may also be found. It may be noted that the requirements for rapid convergence of the approximate solution are satisfied for the particular problem of the growth or collapse of a spherical vapor bubble in a liquid when the translational motion of the bubble is neglected

On the Dynamics of Small Vapor Bubbles in Liquids

When a vapor bubble in a liquid changes size, evaporation or condensation of the vapor takes place at the surface of the bubble. Because of the latent heat requirement of evaporation, a change in bubble size must therefore be accompanied by a heat transfer across the bubble wall, such as to cool the surrounding liquid when the bubble grows (or heat it when the bubble becomes smaller). Since the vapor pressure at the bubble wall is determined by the temperature there, the result of a cooling of the liquid is a decrease of the vapor pressure, and this causes a decrease in the rate of bubble growth. A similar effect occurs during the collapse of a bubble which tends to slow down the collapse. In order to obtain a satisfactory theory of the behavior of a vapor bubble in a liquid, these heat transfer effects must be taken into account. In this paper, the equations of motion for a spherical vapor bubble will be derived and applied to the case of a bubble expanding in superheated liquid and a bubble collapsing in liquid below its boiling point. Because of the inclusion of the heat transfer effects, the equations are nonlinear, integro-differential equations. In the case of the collapsing bubble, large temperature variations occur; therefore, tabulated vapor pressure data were used, and the equations of motion were integrated numerically. Analytic solutions are obtainable for the case of the expanding bubble if the period of growth is subdivided into several regimes and the simplifications possible in each regime are utilized. The growth is considered here only during the time that the bubble is small. An asymptotic solution of the equations of motion, valid when the bubble becomes large (i.e. observable), has been presented previously, together with experimental verification. We shall be specifically concerned in the following discussion with the dynamics of vapor bubbles in water. This restriction was made for convenience only, since the theory is applicable without modification to many other liquids

The Growth of Vapor Bubbles in Superheated Liquids

The growth of a vapor bubble in a superheated liquid is controlled by three factors: the inertia of the liquid, the surface tension, and the vapor pressure. As the bubble grows, evaporation takes place at the bubble boundary, and the temperature and vapor pressure in the bubble are thereby decreased. The heat inflow requirement of evaporation, however, depends on the rate of bubble growth, so that the dynamic problem is linked with a heat diffusion problem. Since the heat diffusion problem has been solved, a quantitative formulation of the dynamic problem can be given. A solution for the radius of the vapor bubble as a function of time is obtained which is valid for sufficiently large radius. This asymptotic solution covers the range of physical interest since the radius at which it becomes valid is near the lower limit of experimental observation. It shows the strong effect of heat diffusion on the rate of bubble growth. Comparison of the predicted radius-time behavior is made with experimental observations in superheated water, and very good agreement is found

Functional stability of HIV-1 envelope trimer affects accessibility to broadly neutralizing antibodies at its apex

ABSTRACT The trimeric envelope glycoprotein spike (Env) of HIV-1 is the target of vaccine development to elicit broadly neutralizing antibodies (bnAbs). Env trimer instability and heterogeneity in principle make subunit interfaces inconsistent targets for the immune response. Here, we investigate how functional stability of Env relates to neutralization sensitivity to V2 bnAbs and V3 crown antibodies that engage subunit interfaces upon binding to unliganded Env. Env heterogeneity was inferred when antibodies neutralized a mutant Env with a plateau of less than 100% neutralization. A statistically significant correlation was found between the stability of mutant Envs and the MPN of V2 bnAb, PG9, as well as an inverse correlation between stability of Env and neutralization by V3 crown antibody, 447-52D. A number of Env-stabilizing mutations and V2 bnAb-enhancing mutations were identified in Env, but they did not always overlap, indicating distinct requirements of functional stabilization versus antibody recognition. Blocking complex glycosylation of Env affected V2 bnAb recognition, as previously described, but also notably increased functional stability of Env. This study shows how instability and heterogeneity affect antibody sensitivity of HIV-1 Env, which is relevant to vaccine design involving its dynamic apex. IMPORTANCE The Env trimer is the only viral protein on the surface of HIV-1 and is the target of neutralizing antibodies that reduce viral infectivity. Quaternary epitopes at the apex of the spike are recognized by some of the most potent and broadly neutralizing antibodies to date. Being that their glycan-protein hybrid epitopes are at subunit interfaces, the resulting heterogeneity can lead to partial neutralization. Here, we screened for mutations in Env that allowed for complete neutralization by the bnAbs. We found that when mutations outside V2 increased V2 bnAb recognition, they often also increased Env stability-of-function and decreased binding by narrowly neutralizing antibodies to the V3 crown. Three mutations together increased neutralization by V2 bnAb and eliminated binding by V3 crown antibodies. These results may aid the design of immunogens that elicit antibodies to the trimer apex. </jats:p

Direct collapse of exceptionally heavy black holes in the merger-driven scenario

We revisit the conditions present in supermassive discs (SMDs) formed by the merger of gas-rich, metal-enriched galaxies at red-shift z ∼ 10. We find that SMDs naturally form hydrostatic cores which go through a rapidly accreting supermassive star phase, before directly collapsing into massive black holes via the general relativistic instability. The growth and collapse of the cores occurs within ∼5 × 105 yr from the formation of the SMD, producing bright electromagnetic, neutrino and gravitational wave transients with a typical duration of a few minutes and, respectively, a typical flux and a typical strain amplitude at Earth of ∼10−8 erg s−1 cm−2 and ∼4 × 10−21. We provide a simple fitting formula for the the resulting black hole masses, which range from a few 106 M⊙ to 108 M⊙ depending on the initial SMD configuration. Crucially, our analysis does not require any specific assumption on the thermal properties of the gas, nor on the angular momentum loss mechanisms within the SMD. Led by these findings, we argue that the merger-driven scenario provides a robust pathway for the rapid formation of supermassive black holes at z &gt; 6. It provides an explanation for the origin of the brightest and oldest quasars without the need of a sustained growth phase from a much smaller seed. Its smoking gun signatures can be tested directly via multi-messenger observations

Oscillatory enhancement of the squeezing flow of yield stress fluids: A novel experimental result

The extrusion of a yield stress fluid from the space between two parallel plates is investigated experimentally. Oscillating the magnitude of the squeezing force about a mean value (F = f[1+αcos(ωt)]) was observed to significantly enhance the flow rate of yield stress fluids, while having no effect on the flow rate of Newtonian fluids. This is a novel result. The enhancement depends on the magnitude of the force, the oscillatory frequency and amplitude, the fluid being squeezed, and the thickness of the fluid layer. Non-dimensional results for the various flow quantities have been presented by using the flow predicted for the constant-force squeezing of a Herschel-Bulkley yield stress fluid as the reference. In the limit of constant-force squeezing, the present experimental results compare very well with those of our earlier theoretical model for this situation (Zwick, Ayyaswamy & Cohen 1996). The results presented in this paper have significance, among many applications, for injection moulding, in the adhesive bonding of microelectronic chips, and in surgical procedures employed in health care

Optimization of suppression for two-element treatment liners for turbomachinery exhaust ducts

Sound wave propagation in a soft-walled rectangular duct with steady uniform flow was investigated at exhaust conditions, incorporating the solution equations for sound wave propagation in a rectangular duct with multiple longitudinal wall treatment segments. Modal analysis was employed to find the solution equations and to study the effectiveness of a uniform and of a two-sectional liner in attenuating sound power in a treated rectangular duct without flow (M = 0) and with uniform flow of Mach 0.3. Two-segment liners were shown to increase the attenuation of sound as compared to a uniform liner. The predicted sound attenuation was compared with measured laboratory results for an optimized two-segment suppressor. Good correlation was obtained between the measured and predicted suppressions when practical variations in the modal content and impedance were taken into account. Two parametric studies were also completed

The Growth and Collapse of Vapor Bubbles

A theory is developed which describes the behavior of a vapor bubble in a liquid. Its physical basis is the assumption that the heat transfer effects which accompany the evaporation occurring at the bubble wall when the bubble grows, 0r the condensation that occurs there when the bubble collapses, are dynamically important. The basic equations of hydrodynamics are shown to reduce, for the problem under consideration, to a dynamic equation which describes the behavior of the bubble wall, and a heat convection equation for the liquid which is coupled to the dynamic equation by a boundary condition at the bubble surface. A solution for the heat problem is obtained under the assumption that significant temperature variation in the liquid occurs only in a thin thermal boundary layer surrounding the bubble wall. An estimate of the correction to the temperature solution is also derived. Once the temperature at the bubble wall is given, the vapor pressure within the bubble is known and the dynamic problem becomes determinate. The theory is applied to the cases of the growth of a vapor bubble in a superheated liquid, and the collapse of a vapor bubble in a liquid below its boiling temperature at the external pressure. The simplifying physical assumptions made in the course of the investigation are justified for the specific example of vapor bubble behavior in water. A comparison of the theory with experiment is given for the observable range of bubble growth in superheated water, and the agreement is found to be very good