Interactions and Collisions of Bubbles in Thermocapillary Motion: A 3D Study

Two- and three-dimensional simulations (created using volume of fluid-fluent) concerning the rise and interactions of two/multiple thermocapillary bubbles arranged horizontally and perpendicular to a hot surface are investigated and presented in this paper. The results indicate that thermocapillary bubble agglomeration can occur in zero gravity. Furthermore, the temperature gradient and bubble diameter were found to have a major impact on the collision between bubbles. The results of Nas and Tryggvason (1993 Nas, S., and G. Tryggvason. 1993. Computational investigation of the thermal migration of bubbles and drops. 175 Fluid Mechanics Phenomena In Microgravity 71–83. [Google Scholar]) in their three-dimensional numerical study reported that no such collisions could occur in zero gravity and that bubbles repel each other due to the cold liquid carried between particles during migration. Their results contrast with both the present results and those recorded onboard the Chinese 22nd recoverable satellite experiment by Kang et al. (2008 Kang, Q., H. L. Cui, L. Hu, and L. Duan. 2008. On-board experimental study of bubble thermocapillary migration in a recoverable satellite. Microgravity Science And Technology 20:67–71.[Crossref], [Web of Science ®] , [Google Scholar]), who observed a total of 19 coalescences between the air bubbles injected in the direction of the temperature gradient of the stagnant heated liquid.     

Numerical Simulation of Thermocapillary Flow Induced by Non-Uniform Evaporation on the Meniscus in Capillary Tubes

Three-dimensional numerical simulation was developed to investigate thermocapillary flow induced by non-uniform evaporation on the meniscus in capillary tubes. Capillary tube radiuses ranging from 0.1 to 1 mm were considered and the working liquid was methanol. The effects of tube size, evaporation heat flux and buoyancy on thermocapillary flow were investigated. The results show that the non-uniform evaporation on the meniscus leads to two opposite temperature gradients along the radial direction, which generate two thermocapillary flow vortexes under the meniscus. For horizontal capillary tubes with r ₀?≥ 0.32 mm, the path-lines in the vertical center plane are asymmetrical, which is attributed to the combined buoyancy and thermocapillary effects. For the vertical capillary tube, with increasing average evaporation heat flux, the steady axisymmetrical flow will gradually transit to a steady asymmetrical flow and eventually becomes a three-dimensional oscillatory flow.     

Numerical Simulations of Thermocapillary Flow of a Binary Mixture with the Soret Effect in a Shallow Annular Pool

In order to understand the characteristics of thermocapillary flow of a toluene/n-hexane mixture with the Soret effect in a shallow annular pool, a series of three-dimensional numerical simulations were carried out. The shallow annular pool was heated from the outer cylinder and cooled at the inner cylinder. The initial toluene concentration in the toluene/n-hexane mixture varied from 0 to 0.4467. Results indicate that the flow undergoes two transitions from the axisymmetric steady flow to the hydrothermal waves, and then to chaos with the increase of the thermocapillary Reynolds number. The critical thermocapillary Reynolds number for the incipience of the oscillatory flow decreases with the increase of the initial solute concentration. When the thermocapillary flow transits to a three-dimensional oscillatory flow, a concentration fluctuation is observed on the free surface, which is similar to the hydrothermal waves. However, compared with that of the temperature, the dimensionless fluctuation amplitude of the concentration is relatively weak. Furthermore, the fundamental oscillation frequency increases linearly with the initial solute concentration, but the wave number of the hydrothermal waves is almost unchangeable.     

Thermocapillary Convection in a Binary Mixture with Moderate Prandtl Number in a Shallow Annular Pool

This paper presented a series of numerical simulations on thermocapillary convection for mixed toluene/hexane solution with mass fraction of \(c_{0}=?26.27\)% in a shallow annular pool. The Prandtl number of the binary solution is 5.54. Results indicate that when the annular pool subjects to a radial temperature gradient, the solute shifts toward the inner wall under the Soret effect, which leads to a concentration gradient with the opposite direction to the temperature gradient. With the increase of surface heat dissipation, thermocapillary convection is enhanced and the flow is more prone to destabilization. Therefore, the critical thermocapillary Reynolds number of the flow destabilization and the corresponding critical oscillation frequency all decrease, but the critical wave number increases. After flow destabilization, the concentration fluctuation similar to the temperature fluctuation on the free surface appears. No matter the free surface is adiabatic or not, the flow always undergoes a transition from two-dimensional steady axisymmetric flow to the hydrothermal waves, and then to chaos with the increase of thermocapillary Reynolds number.     

Lateral motion and interaction of gas bubbles growing over spherical and plate heaters

This work investigates the motion of CO₂ bubbles emerging in n-heptane when a heat pulse given to a submerged heater creates local supersaturation. The ensuing slow diffusion-induced bubble expansion makes bubble motion easy to observe. The low gravity environment of a parabolic flight allows bubbles to reach large sizes without departing from the heater while retaining their spherical shape. A fast lateral displacement of single bubbles has often been noticed on two type of heaters. In cases where many bubbles grow adjacent to each other, they soon start to interact. Phenomena such as bubbles clustering, coalescence and lift-off from the heater of a large bubble induced by neighboring small ones, have been repeatedly observed. An interesting thermocapillary attraction has also been noticed between bubbles adhering to the heater and others free-floating in the nearby liquid.     

Thermal Gravitational‐Capillary Convection in a Cavity with a Longitudinal Temperature Gradient

Convective heat exchange in a flow of liquid in a rectangular cavity with the lengthtoheight ratio of a liquid layer L/H = 10 is investigated. The conditions of thermal insulation or linear distribution of temperature were kept on the lower horizontal surface. Three types of boundary conditions for velocity were set on the upper boundary: rigid, free without friction, and free with imposition of a thermocapillary effect. The vertical walls of the cavity are isothermal and heated to different temperatures. The investigated regimes were of thermogravitational, thermocapillary, and thermal gravitationalcapillary convection. A comparative analysis of the evolution of flow structure with increase in the Rayleigh (Ra) and Marangoni (Ma) numbers is carried out.     

Experimental investigations on heat transfer characteristics of pulsating single-phase liquid flow and two-phase Taylor bubble flow through a minichannel

Experimental investigations are reported for pulsating Taylor bubble (PTB) flow through a 2.12 mm horizontal circular minichannel. Air and water are used as working fluids. A T-junction is used to generate Taylor bubble flow in a minichannel. The superficial gas velocity (U _SG ) is kept as 0.0472 m/s. The superficial liquid velocity (U _SL ) is kept as 0.0472 and 0.0708 m/s. The pulsating liquid flow is generated by developing a pulse generator circuit. The investigations are carried out for various pulsating flow frequencies of 0 Hz (continuous flow), 0.1, 0.25, 0.5, 1 and 2 Hz, which correspond to Womersley number (W _o ) 0, 0.84, 1.39, 1.88, 2.65 and 3.75, respectively. Heat transfer enhancement is found to be negligible (less than 1%) for pulsating laminar liquid flow through the minichannel. On the contrary, heat transfer is observed to decrease by 35% for PTB flow compared with continuous Taylor bubble (CTB) flow for imposed frequency of pulsation up to 1 Hz.     

Cavitation Bubbles Generated by Vibrating Quartz Tuning Fork in Liquid $$^$$He Close to the $$\lambda $$λ-Transition

We report direct optical observation of cavitation bubbles in liquid helium, both in classical viscous He I and in superfluid He II, close to the \(\lambda \)-transition. Heterogenous cavitation due to the fast-flowing liquid over the rough surface of prongs of a quartz tuning fork oscillating at its fundamental resonant frequency of \(4\,\mathrm {kHz}\) occurs in the form of a cluster of small bubbles rapidly changing its size and position. In accord with previous investigators, we find the cavitation threshold lower in He I than in He II. In He I, the detached bubbles last longer than one camera frame (10 ms), while in He II the cavitation bubbles do not tear off from the surface of the fork up to the highest attainable drive.     

Evaluation of Erosion Corrosion in Liquid–Solid and Liquid–Gas via Experimental Analysis Inside 90° Copper Elbow

Erosion–corrosion experiments of copper elbow were performed by acidified dichromate. Mass transfer coefficient inside 90° copper elbow has been investigated. The results showed that the mass transfer coefficient increases as solution velocity increases in both cases of one- and two-phase flow. The mass transfer coefficient can be related to the solution velocity in case one-phase flow by the following equations:

$$k \, \alpha \, v^{ 0. 4 4}\quad{\text{for\,Sc\,from\,678 to 845}}$$

$$k \, \alpha \, v^{ 0. 3}\quad{\text{for\,Sc\,from\,1040\,to\,1445}}$$

In case of liquid–solid flow

$$k \, \alpha \, v^{ 0. 3 3}$$

In case of liquid–gas flow

$$k \, \alpha \, vg^{ 0. 2 4}$$

The importance of these equations is to understand and predict erosion corrosion inside 90^o copper elbow.

     

Semianalytical solution of unsteady quasi-one-dimensional cavitating nozzle flows

Unsteady quasi-one-dimensional bubbly cavitating nozzle flows are considered by employing a homogeneous bubbly liquid flow model, where the nonlinear dynamics of cavitating bubbles is described by a modified Rayleigh–Plesset equation. The model equations are uncoupled by scale separation leading to two evolution equations, one for the flow speed and the other for the bubble radius. The initial-boundary value problem of the evolution equations is then formulated and a semianalytical solution is constructed. The solution for the mixture pressure, the mixture density, and the void fraction are then explicitly related to the solution of the evolution equations. In particular, a relation independent of flow dimensionality is established between the mixture pressure, the void fraction, and the flow dilation for unsteady bubbly cavitating flows in the model considered. The steady-state compressible and incompressible limits of the solution are also discussed. The solution algorithm is first validated against the numerical solution of Preston et al. [Phys Fluids 14:300–311, 2002] for an essentially quasi-one-dimensional nozzle. Results obtained for a two-dimensional nozzle seem to be in good agreement with the mean pressure measurements at the nozzle wall for attached cavitation sheets despite the observed two-dimensional cavitation structures.     

Interaction of Helium Rydberg State Atoms with Superfluid Helium

The pair potentials between ground state helium and Rydberg He $^*(2s,2p,3s)$ atoms are calculated by the full configuration interaction electronic structure method for both the electronic singlet and the triplet manifolds. The obtained pair potentials are validated against existing experimental molecular and atomic data. Most states show remarkable energy barriers at long distances ( $R > 5$ Å), which can effectively stabilize He $^*$ against the formation of He $_2^*$ at low nuclear kinetic energies. Bosonic density functional theory calculations, based on the calculated pair potential data, indicate that the triplet ground state He $^*$ reside in spherical bubbles in superfluid helium with a barycenter radius of 6.1 Å at the liquid saturated vapor pressure. The pressure dependency of the relative He $^*$ $2s$ $^3S$ $\rightarrow $ $2p$ $^3P$ absorption line blue shift in the liquid was obtained through both the statistical line broadening theory as well as the dynamic adiabatic following method. The pronounced difference between the results from the static and dynamic models is attributed to the dynamic Jahn–Teller effect that takes places in the electronically excited state within the dephasing time of 150 fs. Transient non-thermalized liquid surroundings near He $^*$ may contribute to an artificial reduction in the absorption line blue shift by up to 30 cm $^{-1}$ .     

Rheology of weakly wetted granular materials: a comparison of experimental and numerical data

Shear cell simulations and experiments of weakly wetted particles (a few volume percent liquid binders) are compared, with the goal to understand their flow rheology. Application examples are cores for metal casting by core shooting made of sand and liquid binding materials. The experiments are carried out with a Couette-like rotating viscometer. The weakly wetted granular materials are made of quartz sand and small amounts of Newtonian liquids. For comparison, experiments on dry sand are also performed with a modified configuration of the viscometer. The numerical model involves spherical, monodisperse particles with contact forces and a simple liquid bridge model for individual capillary bridges between two particles. Different liquid content and properties lead to different flow rheology when measuring the shear stress-strain relations. In the experiments of the weakly wetted granular material, the apparent shear viscosity $\eta _g$ η g scales inversely proportional to the inertial number $I$ I , for all shear rates. On the contrary, in the dry case, an intermediate scaling regime inversely quadratic in $I$ I is observed for moderate shear rates. In the simulations, both scaling regimes are found for dry and wet granular material as well.     

Electron Bubbles in Superfluid $$^$$He-A: Exploring the Quasiparticle–Ion Interaction

When an electron is forced into liquid \(^3\)He, it forms an “electron bubble”, a heavy ion with radius, \(R\simeq 1.5\) nm, and mass, \(M\simeq 100\,m_3\), where \(m_3\) is the mass of a \(^3\)He atom. These negative ions have proven to be powerful local probes of the physical properties of the host quantum fluid, especially the excitation spectra of the superfluid phases. We recently developed a theory for Bogoliubov quasiparticles scattering off electron bubbles embedded in a chiral superfluid that provides a detailed understanding of the spectrum of Weyl Fermions bound to the negative ion, as well as a theory for the forces on moving electron bubbles in superfluid \(^3\)He-A (Shevtsov and Sauls in Phys Rev B 94:064511, 2016). This theory is shown to provide quantitative agreement with measurements reported by the RIKEN group (Ikegami et al. in Science 341(6141):59, 2013) for the drag force and anomalous Hall effect of moving electron bubbles in superfluid \(^3\)He-A. In this report, we discuss the sensitivity of the forces on the moving ion to the effective interaction between normal-state quasiparticles and the ion. We consider models for the quasiparticle–ion (QP–ion) interaction, including the hard-sphere potential, constrained random-phase-shifts, and interactions with short-range repulsion and intermediate-range attraction. Our results show that the transverse force responsible for the anomalous Hall effect is particularly sensitive to the structure of the QP–ion potential and that strong short-range repulsion, captured by the hard-sphere potential, provides an accurate model for computing the forces acting on the moving electron bubble in superfluid \(^{3}\)He-A.     

Thermocapillary Convection and Buoyant-Thermocapillary Convection in the Annular Pools of Silicon Melt and Silicone Oil

The thermocapillary convection and buoyant-thermocapillary convection in the annular pool of silicon melt (Pr=0.011) and silicone oil (Pr=6.7) with depth d=10 mm differentially heated at the outer wall and cooled at the inner wall are investigated by 2-D numerical simulation. The numerical results exhibit that the thermocapillary flow is enhanced by buoyancy force for silicon melt while it is weakened for silicone oil. Linear stability analysis indicates that the buoyancy force destabilizes the thermocapillary convection, which is different from that for silicone oil. The detailed reason of different influence of buoyancy force on the thermocapillary flow with different Pr numbers is explained according to present numerical results.     

Thermodynamic Properties at Saturation Derived from Experimental Two-Phase Isochoric Heat Capacity of 1-Hexyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide

New measurements are reported for the isochoric heat capacity of the ionic liquid substance 1-hexyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide ([C6mim][NTf2]). These measurements extend the ranges of our earlier study (Polikhronidi et al. in Phys Chem Liq 52:657, 2014) by 5 % of the compressed liquid density and by 75 K. An adiabatic calorimeter was used to measure one-phase \((C_{\mathrm{V1}})\) liquid and two-phase \((C_{\mathrm{V2}})\) liquid + vapor isochoric heat capacities, densities \((\rho _s)\), and phase-transition temperatures \((T_s)\) of the ionic liquid (IL) substance. The combined expanded uncertainty of the density \(\rho \) and isochoric heat capacity \(C_\mathrm{V}\) measurements at the 95 % confidence level with a coverage factor of \(k = 2\) is estimated to be 0.15 % and 3 %, respectively. Measurements are concentrated in the immediate vicinity of the liquid + vapor phase-transition curve, in order to closely observe phase transitions. The present measurements and those of our earlier study are analyzed together and are presented in terms of thermodynamic properties \((T_s\), \(\rho _s\), \(C_{\mathrm{V1}}\) and \(C_{\mathrm{V2}})\) evaluated at saturation and in terms of key-derived thermodynamic properties \(C_\mathrm{P}\), \(C_\mathrm{S}\), \(W_\mathrm{S}^{{\prime }}\), \(K_{\mathrm{TS}}^{{\prime }}\), \(\left( {\partial P/\partial T} \right) _{\mathrm{V}}^{\prime }\), and \(\left( {\partial V/\partial T} \right) _\mathbf{P}^{\prime })\) on the liquid + vapor phase-transition curve. A thermodynamic relation by Yang and Yang is used to confirm the internal consistency of measured two-phase heat capacities \(C_{\mathrm{V2}} \), which are observed to fall perfectly on a line as a function of specific volume at a constant temperature. The observed linear behavior is exploited to evaluate contributions to the quantity \(C_{\mathrm{V2}} = f(V, T)\) from chemical potential \(C_{{\mathrm{V}\upmu }} =-T\frac{\mathrm{d}^{{2}}\mu }{\mathrm{d}T^{2}}\) and from vapor pressure \(C_{\mathrm{VP}} =VT\frac{\mathrm{d}^{2}P_{\mathrm{S}} }{\mathrm{d}T^{2}}\). The physical nature and specific details of the temperature and specific volume dependence of the two-phase isochoric heat capacity and some features of the other derived thermodynamic properties of IL at liquid saturation curve are considered in detail.     

Influence of Buoyancy Force on Thermocapillary Convection Instability in the Differentially Heated Annular Pools of Silicon Melt

The influence of buoyancy force on the thermocapillary convection instability in the annular pools (R _i = 20 mm, R _o = 40 mm, and depth d ranging from 1 to 10 mm) of silicon melt (Pr = 0.011), differentially heated at the outer wall and cooled at the inner wall, is investigated numerically. The critical Marangoni numbers (Ma _c) for the incipience of oscillatory flow are determined by linear stability analysis (LSA) under both microgravity and normal gravity conditions. The results indicate that the buoyancy force destabilizes the thermocapillary convection under different liquid layer depths from 3 to 10 mm. With increasing the layer depth, the critical Ma number, critical azimuthal wave number and critical phase velocity decrease. Some of 3-D simulation results are compared with those of LSA. 3-D results are found consistent with the LSA results except for a case of D = 0.05 where 3-D simulation gives a stationary 3-D flow under a large Ma.     

Three dimensional numerical and asymptotic solutions for the peristaltic transport of a heat-conducting fluid

Summary Using the Oberbeck-Boussinesq (O-B) equations as a mathematical model, asymptotic solutions in closed form and numerical solutions are obtained for the peristaltic transport of a heat-conducting fluid in a three-dimensional flexible tube. The results show that the relation between mass flux and pressure drop remains almost linear and the efficiency of the transport depends mainly on the ratio of the wave amplitudeh and the average radius of the tubed. However, the 3-D flow is much different from the 2-D flow in the following ways: (i) The 3-D flow is much more sensitive to the change of the volume expansion coefficient _r ; (ii) Trapping and backflow are much more common in 3-D case; (iii) The longwave asymptotic approximation in 3-D case is not as good as in 2-D case, especially when _r is not small; (iv) The 3-D flow is more sensitive to Reynolds number change.