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.

The growth of vapor bubbles in superheated liquids. report no. 26-6

The style and evolution of volcanic eruptions are dictated by the fluid mechanics governing magma ascent. Decompression during ascent causes dissolved volatile species, such as water and carbon dioxide, to exsolve from the melt to form bubbles, thus providing a driving force for the eruption. Ascent is influenced not only by the nucleation and growth of gas bubbles, but also magma rheology and brittle deformation (fragmentation). In fact, all processes and magma properties within the conduit interact and are coupled. Ultimately, it is the ability of gas trapped within growing bubbles to expand or to be lost by permeable gas flow, which determines whether ascending magmas can erupt nonexplosively. We review and integrate models of the primary conduit processes to show when each process or property dominates and how these interact within a conduit. In particular, we illustrate how and why ascent rate may control eruptive behavior: slowly ascending magmas erupt effusively and rapidly ascending magmas erupt explosively.

The Fluid Mechanics inside a volcano

Implication of Bio-convection and Cattaneo-Christov heat flux on Williamson Sutterby nanofluid transportation caused by a stretching surface with convective boundary

The non-monotonic beam energy dependence of the higher cumulants of net-proton fluctuations is a widely studied signature of the conjectured presence of a critical point in the QCD phase diagram. In this work we study the effect of resonance decays on critical fluctuations. We show that resonance effects reduce the signatures of critical fluctuations, but that for reasonable parameter choices critical effects in the net-proton cumulants survive. The relative role of resonance decays has a weak dependence on the order of the cumulants studied with a slightly stronger suppression of critical effects for higher-order cumulants.

/pdf/impact-of-resonance-decays-on-critical-point-signals-in-net-2aulv7ftv3.pdf

Impact of resonance decays on critical point signals in net-proton fluctuations

https://iopscience.iop.org/article/10.1088/1402-4896/ab2efb/pdf

Numerical simulation of the peristaltic motion of a viscous fluid through a complex wavy non-uniform channel with magnetohydrodynamic effects

This article analyzes the growth of the vapor bubble in a novel model of power-law nanofluids (Al2O3/H2O) under a new effect of variable surface tension. The governing equations of the rising vapor bubble flow model are formulated and converted to a single equation describing the bubble dynamics behavior. By employing the model of Plesset and Zwick method, we investigate a new model of equations within power-law nanofluids to examine the effect of different physical parameters such as initial superheating liquid, critical bubble radius, and thermal diffusivity on the vapor bubble formation. Furthermore, the effects of surface tension behavior with the initial bubble radius, time, and initial rate of bubble radius are examined. It is found that the growth of the vapor bubble radius increases with the increase of initial superheating liquid, critical bubble radius, and thermal diffusivity. In addition, the connection between shear stress and shear rate is analyzed in detail. Using appropriate values for the physical parameters, the behavior of solutions of the vapor bubble is discussed. Based on the conducted simulation analysis, the behavior of the solutions is found to be more accurate than those in the previous studies. Besides, the obtained results demonstrate that the vapor bubble in power-law nanofluids grows slower than in pure water.

https://iopscience.iop.org/article/10.1088/1402-4896/abdb5a/pdf

Theoretical investigation of a single vapor bubble during Al2O3/H2O nanofluids in power-law fluid affected by a variable surface tension

Thermophysical bubble dynamics in N-dimensional Al2O3/H2O nanofluid between two-phase turbulent flow

The growth of a gas bubble between two-phase flow represents the current physical problem. The mathematical model is performed by mass, momentum and diffusion equations. The Problem is solved analytically by using the modified Plesset and Zwick method. The growth process is affected by shear stress, coefficient of consistency, surface tension and void fraction in order to derive the growth of a gas bubble between two-phase in non-Newtonian fluids. The growth of a gas bubble in non-Newtonian fluids flow performs lower values than that in case of Newtonian one. The initial time of bubble growth for the different values of superheating and flow index n in the thermal stage is obtained. Moreover, the effect of critical bubble radius R cr is studied on the growth process. The results satisfy the growth model in Newtonian fluids given by Foster and Zuber (1954) [34] and Scriven theory (Scriven, 1959) [35] for limited values of physical parameters.

Analytical solution of gas bubble dynamics between two-phase flow

We present the theoretical study and mathematical modelling of vapour bubble growth in a non-Newtonian fluid, viscous, superheated liquid for the turbulent flow. The mathematical model is formulate...

Vapour bubble growth within a viscous mixture non-Newtonian fluid between two-phase turbulent flow

This paper investigates the fluidized granular materials (FGM) with the van der Waals normal form (VDWF) under the effects of friction and viscosity. The system of macroscopic balance is presented, including the mass, momentum, and energy equations of local densities. For two different types of collisions, elastic and inelastic collisions, analytical solutions of the nonlinear PDEs governing the granular model are investigated using the hydrodynamic equations for granular matter motion. The integrability of the proposed model is analyzed by applying the Painleve analysis. Moreover, the Backlund transformation (BT) is established using the Painleve truncation expansion. New traveling wave solutions of the VDWF within FGM are obtained by using the BT, tanh function, Jacobi elliptic function methods to study the phase separation phenomenon. As two pairs of rarefaction and shock waves emerge and travel away giving the appearance of bubbles, the resulting solutions of the proposed model show a behavior similar to those found in the molecular dynamic simulations. The dispersion relation and their properties to the model equation are investigated. Besides, stability analysis of the VDWF in its ODE form is demonstrated using the phase portrait classifications. Finally, using two- and three-dimensional graphics for seeking model solutions under the influence of friction and viscosity, qualitative agreements with previous related works are shown.

A. K. Abu-Nab

Papers

Theoretical investigation of a single vapor bubble during Al2O3/H2O nanofluids in power-law fluid affected by a variable surface tension

Thermophysical bubble dynamics in N-dimensional Al2O3/H2O nanofluid between two-phase turbulent flow

Analytical solution of gas bubble dynamics between two-phase flow

Vapour bubble growth within a viscous mixture non-Newtonian fluid between two-phase turbulent flow

Bubbles interactions in fluidized granular medium for the van der Waals hydrodynamic regime