Infinite Liquid Research Articles

Bacterial Locomotion in an Infinite Liquid Medium and in the Presence of a Nearby Surface

Bacterial Locomotion in an Infinite Liquid Medium and in the Presence of a Nearby Surface

Study on the Equivalent Circuit of Quartz Crystal Microbalance (QCM) with Material Properties

The quartz crystal micro balances (QCM) principle is simply introduces. LEM model can accurately describe TSM sensors with surface the load, instead of complicated TLM model. The configuration of sensor has pure quality load, liquid load in fluid Newton system, the sticky elastic thin film, and viscoelastic membrane plus half infinite liquid. Two kinds of material properties model prediction deviate with no more than 3% error. The rule of Judging TLM to be the LEM is Zl/Zq<0.1

Mutual Attractions of Partially Immersed Parallel Plates

We complete a study initiated in an earlier paper, on the horizontal attracting and repelling forces acting on two parallel semi-infinite plates, partly immersed in an infinite liquid bath and subject to capillary attractions in a uniform gravity field. We find a considerable range of behavior patterns, depending on the contact angles on the plate sides and on the plate separation, in ways that we did not anticipate.

Models of cylindrical bubble pulsation

Three models are considered for describing the dynamics of a pulsating cylindrical bubble. A linear solution is derived for a cylindrical bubble in an infinite compressible liquid. The solution accounts for losses due to viscosity, heat conduction, and acoustic radiation. It reveals that radiation is the dominant loss mechanism, and that it is 22 times greater than for a spherical bubble of the same radius. The predicted resonance frequency provides a basis of comparison for limiting forms of other models. The second model considered is a commonly used equation in Rayleigh-Plesset form that requires an incompressible liquid to be finite in extent in order for bubble pulsation to occur. The radial extent of the liquid becomes a fitting parameter, and it is found that considerably different values of the parameter are required for modeling inertial motion versus acoustical oscillations. The third model was developed by V. K. Kedrinskii [Hydrodynamics of Explosion (Springer, New York, 2005), pp. 23-26] in the form of the Gilmore equation for compressible liquids of infinite extent. While the correct resonance frequency and loss factor are not recovered from this model in the linear approximation, it provides reasonable agreement with observations of inertial motion.

Analytical approximations for the collapse of an empty spherical bubble

The Rayleigh equation 3/2R+RR+pρ(-1)=0 with initial conditions R(0)=R(0), R(0)=0 models the collapse of an empty spherical bubble of radius R(T) in an ideal, infinite liquid with far-field pressure p and density ρ. The solution for r≡R/R(0) as a function of time t≡T/T(c), where R(T(c))≡0, is independent of R(0), p, and ρ. While no closed-form expression for r(t) is known, we find that r(0)(t)=(1-t(2))(2/5) approximates r(t) with an error below 1%. A systematic development in orders of t(2) further yields the 0.001% approximation r(*)(t)=r(0)(t)[1-a(1)Li(2.21)(t(2))], where a(1)≈-0.01832099 is a constant and Li is the polylogarithm. The usefulness of these approximations is demonstrated by comparison to high-precision cavitation data obtained in microgravity.

Gravitational Effects on Multi-component Droplet Evaporation

This paper focuses on the analysis of multi-component droplet heating and evaporation under microgravity and normal gravity conditions. This analysis is based on the conventional conservation equations of species and energy for the gas phase, and the energy balance equation at the liquid–gas interface. The species diffusion is based on the Hirschfelder law, rather than on the less general Fick’s equation. Moreover, the heat flux due to species diffusion is taken into account in addition to the classical conduction heat flux between the gas and the liquid droplets. The liquid phase analysis is based on the infinite thermal conductivity liquid phase model, which has been justified by a reasonably good agreement between the predicted and experimental results. Indeed, the developed evaporation model has been validated against experimental data reported by Chauveau et al. (2008), where the droplets evaporation has been observed in microgravity and normal gravity conditions. The effects of gravity have been taken into account by introducing the Grashof number in the expressions of the Sherwood and Nusselt numbers. This model has been implemented in the multidimensional IFP-C3D industrial software. The modeling and experimental results have been shown to be reasonably close and the gravitational effects have been revealed to be significant especially for multi-component liquids including heavy components.

Free surface flow between two horizontal concentric cylinders

Results are reported on a combined experimental and numerical investigation of a free surface flow at small Reynolds numbers. The flow is driven by the rotation of the inner of two horizontal concentric cylinders, with an inner to outer radius ratio of 0.43. The outer cylinder is stationary. The annular gap is partially filled, from 0.5 to 0.95 full, with a viscous liquid leaving a free surface. When the fraction of the annular volume filled by liquid is 0.5, a thin liquid film covers the rotating inner cylinder and reenters the liquid pool. For relatively low rotation speeds, the evolution of the film thickness is consistent with the theory for a plate being withdrawn from an infinite liquid pool. The overall liquid flow pattern at this condition consists of two counter-rotating cells: one is around the inner cylinder and the other with weaker circulation rate is in the bottom part of the annulus and nearly symmetric about the vertical axis. With increasing rotation rate, the free surface becomes more deformed, and the dynamics of the stagnation line and the cusp line dividing the cells are tracked as quantitative measures of the interface shape. In addition, the recirculating flow cells lose symmetry and the cusp deforms the free surface severely. A comparison of numerically computed flow which describes the interface by a phase-field method confirms the dynamics of the two cells and the interface deformation. For filling fraction 0.75, the liquid level is slightly above the inner cylinder and a significant decrease in size of the bottom cell with increasing rotation rate is found. For filling fractions approaching unity, the liquid flow consists of one single cell and the surface deformation remains small.

Frequency characteristics of the noise of R600a refrigerant flowing in a pipe with intermittent flow pattern

The acoustic characteristics of a long-shaped cylindrical bubble for slug or churn flow in a pipe are different from those of a freely rising spherical bubble in infinite liquid. In this research, the theoretical estimation of the natural frequency of the long-shaped cylindrical bubble was derived using the energy conservation law for a single bubble in a pipe. The acoustic characteristics of bubbles in a pipe were also investigated with the R600a refrigerant, which is widely used in refrigerators when the flow pattern in a pipe is slug or churn flow. In order to make slug and churn flow artificially, refrigerant-supplying equipment was designed and developed. Using this test equipment, the frequency characteristics of the long-shaped cylindrical bubble in 2-phase flow were investigated experimentally.

Mechanical effects of laser-induced cavitation bubble on different geometrical confinements for laser propulsion in water

Laser propulsions of six kinds of propelled objects in water and air are studied in this paper. The kinetic energy and momentum coupling coefficients gained by the objects after implementation of single laser pulses are investigated experimentally. It is shown that the propulsion effects are better in water than in air. Both in water and in air, the propulsion effects are better if there is a cavity on the laser irradiated surface of the object, and a hemispherical cavity works better than a 90°-conical cavity. A concept of equivalent reference pressure is proposed in this paper. It means that the asymmetry in the liquid induced by a rigid boundary near a spherical or nonspherical oscillating bubble can be approximated as the perturbation induced by a compressive stress wave passing through a bubble in the infinite static liquid. Thus, the collapse time and the pressure surrounding the nonspherical collapsing bubble can be estimated based on the maximum velocity of the liquid jet tip. Experiments also show that cavitation with oscillations and collapse can be induced at the object–water interface on the outside surface of the object head by the penetrating intensive stress wave and the elastic deformation of the object head. The bulging velocity of the object surface is calculated based on the propagation theory of stress waves at medium interfaces.

Wetting and Dewetting Transition: An Efficient Toolbox for Characterizing Low-Energy Surfaces

The capillary bridge formed between a solid spherical surface and an infinite liquid bath is an efficient technique for characterizing the adhesion property of a solid surface. When the solid surface is pulled out of the liquid at a sufficiently high velocity, a thin liquid film is deposited on the solid and drains more slowly than the central capillary bridge. The retraction kinetics of this "pancake" and the critical velocity above which it appears are studied as a function of the viscosity of the liquid or the wettability of the solids. The dynamics of the liquid film follows the classical law of dynamic dewetting. This makes the capillary bridge test, used in the dynamical regime, a very efficient tool for discriminating between antiadhesive coatings.

A model for the dynamics of ultrasound contrast agents in vivo.

The Rayleigh-Plesset (RP) equation for a clean gas bubble in an incompressible and infinite liquid has previously been applied to approximately simulate the behavior of ultrasound contrast agents (UCA) in vivo, and extended RP equations have been proposed to account for the effects of the UCA shell or surrounding soft tissue. These models produce results that are consistent with experimental measurements for low acoustic pressure scenarios. For applications of UCAs in therapeutic medicine, the transmitted acoustic pulse can have a peak negative pressure (PNP) up to a few megapascals, resulting in discrepancies between measurements and predictions using these extended RP equations. Here, a model was developed to describe the dynamics of UCAs in vivo while taking account of the effects of liquid compressibility, the shell and the surrounding tissue. Liquid compressibility is approximated to first order and the shell is treated either as a Voigt viscoelastic solid or a Newtonian viscous liquid. Finite deformation of the shell and tissue is derived. Dynamics of UCAs with a shell of lipid, polymer, albumin and liquid are investigated for typical therapeutic ultrasound pulses. The effects of liquid compressibility and shell and tissue parameters are analyzed.

A study on thermophysiological comfort properties of fabrics in relation to constituent fibre fineness and cross-sectional shapes

The present study reports the effect of linear densities and profiles of polyester fibres on the physiological properties of their fabrics. Four different polyester fibre finenesses along with microdenier and four cross-sectional shapes (circular, scalloped oval, tetrakelion and trilobal) were selected to produce two sets of 2/1 twill fabrics; one composed of 100% polyester and the other 67:33 P/V blends. In studying the thermophysiological component of the clothing comfort, heat, air and moisture transmission characteristics of the fabrics were assessed. The principal thermal properties, such as thermal absorptivity, thermal resistance and thermal conductivity, were experimentally evaluated, using the Alambeta instrument. The study of the obtained results established the fabrics of non-circular cross-sections as against circular ones, and increase in the linear density results in higher thermal resistance, lower thermal conductivity and lower thermal absorptivity. Wicking behaviour of fabrics was studied under two conditions–wicking from an infinite liquid reservoir (transverse wicking) and wicking from a finite liquid reservoir (single drop wicking into the fabrics). Increase in fibre linear density enhances transplaner wicking but slows down the spreading speed of water drops. Air permeability and moisture vapour permeability are found to be positively correlated with fibre decitex. The role of fibre cross-sectional shapes in influencing mass-flow characteristics is quite considerable. Use of non-circular polyester in place of a circular one augments the wickability of liquid water along with the permeability of air and moisture vapour through the fabrics, revealing their high porosity, which assists air and moisture to propagate. Mixing viscose into polyester brings down the air permeability and moisture vapour transmission rate (MVTR) of fabrics. Results show that moisture absorption of viscose is an important factor in influencing the moisture transport characteristics including both wickability and MVTR of 100% viscose and P/V-blended fabrics.

DENSITY OF STATES AND LASING THRESHOLD IN DYE-DOPED CHOLESTERIC LIQUID CRYSTALS

As the complex transmission coefficient for a Fabry–Perot dielectric plate is well-known, the density of states (DOS) approach by J. Bendickson et al. [Phys. Rev. E53, 4107 (1996)] was applied to the plate and a formula was found for the spectrum of its threshold gain for lasing from the dye-doped plate. Next, the dispersion relation and the spectrum of the threshold gain was discussed for the infinite helical cholesteric liquid crystal (CLC). Then the DOS approach was applied to the non-absorbing CLC layers having finite, different thickness. The threshold gain spectra were calculated and dependences were found of the minimum threshold gain on the layer thickness and the optical anisotropy of the material. Finally, the results of the DOS analytical technique were compared with numerical calculations based on the precise solutions of the Maxwell equations and, in such a way, the DOS technique has been proven. The contribution of the dye absorption was discussed separately. The experimental data presented in the paper are in good agreement with the threshold gain calculations.

NUMERICAL INVESTIGATION OF THE INTERACTION MECHANISM OF TWO BUBBLES

In the frame of inviscid and incompressible fluids without taking into consideration of surface tension effects, the axisymmetric evolution of two buoyancy-driven bubbles in an infinite and initially stationary liquid are investigated numerically by VOF method. The numerical experiments are performed for two bubbles with same size, with the following one being half of the leading one, and with the leading one being half of the following one, and for different bubble distances. The ratio of gas density to liquid density is 0.001. It is found by numerical experiment that when the distance between the two bubbles is greater than or equal to one and half of the bigger bubble radius, the interaction is very weak and the two bubbles evolute like isolated ones rising in an infinite liquid. When the two bubbles come closer, the leading bubble itself evolutes like an isolated one rising in an infinite liquid. However, due to the smaller distance between the two bubbles, large pressure gradient forms in the liquid region near the top of the following bubble, which causes the upward stretch of its top part no matter what sizes of the two bubbles are. When the distance between the two bubbles is less than or equal to three-tenth of the bigger bubble radius, before the liquid jet behind the leading bubble fully developed, the top part of the following bubble has already been sucked into the leading one, giving a pear-like shape. Soon after the following bubble merges with the leading one. It is also found that for the smaller bubble, its transition to toroidal is always faster than that of the bigger one because of its smaller size. The mechanism of the above phenomena has been analyzed numerically.

On Young’s Paradox, and the attractions of immersed parallel plates

A seemingly paradoxical prediction for behavior of objects with nonconstant contact angles when dipped into fluids is clarified in a new way. The method is then applied to the problem of determining the attraction (or repulsion) of parallel vertical plates dipped into an infinite liquid bath. A criterion is given for determining whether the plates attract or repel each other, and estimates for the forces are obtained, which are asymptotically exact for small plate separations. It is shown that the attracting force is asymptotically proportional inversely to the square of the distance between the plates; however the repelling force remains under a fixed bound in magnitude. In all cases the net forces are independent of the contact angles of the exterior fluid with the plates, although that is not the case for the individual forces ascribable to pressure differences and to surface tensions. It is shown that regardless of the data, each of the plates experiences the same net force as does the other. Finally a new and more precise and inclusive clarification is given for a phenomenon described in 1806 by Laplace, who noted conditions under which repelling forces can change abruptly into (much larger) attracting forces.

Temperature-controlled ionic liquid–liquid-phase microextraction for the pre-concentration of lead from environmental samples prior to flame atomic absorption spectrometry

Hydrophobic ionic liquid could be dispersed into infinite droplets under driving of high temperature, and then they can aggregate as big droplets at low temperature. Based on this phenomenon a new liquid-phase microextraction for the pre-concentration of lead was developed. In this experiment, lead was transferred into its complex using dithizone as chelating agent, and then entered into the infinite ionic liquid drops at high temperature. After cooled with ice-water bath and centrifuged, lead complex was enriched in the ionic liquid droplets. Important parameters affected the extraction efficiency had been investigated including the pH of working solution, amount of chelating agent, volume of ionic liquid, extraction time, centrifugation time, and temperature, etc. The results showed that the usually coexisting ions containing in water samples had no obvious negative effect on the recovery of lead. The experimental results indicated that the proposed method had a good linearity ( R = 0.9951) from 10 ng mL −1 to 200 ng mL −1. The precision was 4.4% (RSD, n = 6) and the detection limit was 9.5 ng mL −1. This novel method was validated by determination of lead in four real environmental samples for the applicability and the results showed that the proposed method was excellent for the future use and the recoveries were in the range of 94.8–104.1%.

A model for the dynamics of ultrasound contrast agents in soft tissue.

For a bubble suspended in an incompressible and infinite liquid, the dynamics of a clean gas bubble can be described by the Rayleigh–Plesset (RP) equation. The RP equation has been applied to approximately simulate the behavior of ultrasound contrast agents (UCAs) in blood, and extended RP equations have been proposed to account for the effects of the UCA shell and surrounding soft tissue. These models produce consistent results with experimental measurements for low acoustic pressure scenarios. For applications of UCAs in therapeutic medicine, the transmitted acoustic pulse can have a peak negative pressure up to a few megapascals, resulting in violent oscillations of UCAs and discrepancies between measurements and predictions using these extended RP equations. Based on the Keller equation, we developed a new model to describe the dynamics of UCAs in the body while taking account of liquid compressibility and shell and soft tissue effects. Liquid compressibility is approximated to the first order, and the shell is treated either as a layer of visco‐elastic solid or a viscous liquid. Finite deformation of the shell is included. Typical UCAs with a lipid or albumin shell are investigated, and the effects of soft tissue and blood are examined.

Ac conductance and nonsymmetrized noise at finite frequency in quantum wires and carbon nanotubes

We calculate the AC conductance and the finite-frequency non-symmetrized noise in interacting quantum wires and single-wall carbon nanotubes in the presence of an impurity. We observe a strong asymmetry in the frequency spectrum of the non-symmetrized excess noise, even in the presence of the metallic leads. We find that this asymmetry is proportional to the differential AC conductance of the system. The asymmetry disappears for a linear system (in the absence of interactions). In the quantum regime, for temperatures much smaller than the frequency and the applied voltage, we find that the emission noise is exactly equal to the impurity partition noise. Moreover the noise exhibits oscillations with respect to frequency, whose period is inversely proportional to the value of the interaction parameter g, and whose envelope is given by the noise in an infinite Luttinger liquid with the same value of g.

Direct simulation of the buoyant rise of bubbles in infinite liquid using level set method

AbstractIn this study, 3‐D level set method is applied to investigate the rise of gas bubbles in infinite liquid domain due to the buoyancy force. A number of typical regimes for single bubble rising are studied, including the ellipsoidal, ellipsoidal cap, spherical cap, and skirted bubbles. The bubble shape and rise velocity predicted by the simulation are compared with the graphical correlations of Grace, Trans. Inst. Chem. Eng., 51, 116–120, (1973) and Bhaga and Weber, J. Fluid Mech., 105, 61–85, (1981). Good agreement is found between the simulation results and the correlations. These simulations cover a wide range of the parameters, including Eo, Mo, and Re, and demonstrate the capability and accuracy of level set method for simulation of bubbles under various conditions with considerable deformation. Finally, simulation results for the coalescence of two bubbles are also presented.

On the fulfillment of the energy conservation law in mathematical models of evolution of single spherical bubble

The problem of the evolution of a single spherical bubble in an infinite liquid is considered, as the result of a variation of the pressure in the liquid at an infinite distance from the bubble. It has been assumed the bubble is filled with vapor from the surrounding liquid or insoluble gas. The question of the fulfillment of the integral energy conservation law is investigated using different ways of describing the hydrodynamic and heat and mass exchange processes in both the bubble and surrounding liquid and at the bubble interface. Kinetic and internal energy of vapor (gas) in the bubble, kinetic and internal energy of the liquid, and energy of surface tension are taken into account in the energy balance. The liquid is assumed to be incompressible, viscous and heat-conducting, the vapor (gas) to be nonviscous, heat-conducting and obeying the Clapeyron equation. Thermal–physical properties, exclusive of specific heats, are allowed to be temperature-dependent. For the above suppositions and assumptions, a mathematical model ensuring exact fulfillment of the integral energy conservation law has been developed. It has been shown that the conservation integral can be fulfilled by the given model. As simplified variants of the principal model, models of the uniform bubble and pressure uniform bubble, have been proposed which ensure the exact fulfillment of the integral energy balance disregarding the relatively small vapor kinetic energy. A relation defining the imbalance in the integral energy conservation law for some often-used extra simplifications has been derived.