Numerical Analysis of 3‐D Flow Past a Stationary Sphere with Slip Condition at Low and Moderate Reynolds Numbers

Computations are performed to determine the steady 3‐D viscous fluid flow forces acting on the stationary spherical suspended particle at low and moderate Reynolds numbers in the range of 0.1≤Re≤200. A slip is supposed on the boundary so that the slip velocity becomes proportional to the shear stress. This model possesses a single parameter to account for the slip coefficient λ (Pa.s/m), which is made dimensionless and is called Trostel number (Tr=λ a/μ). Decreasing slip, increases drag in all Reynolds limits, but slip has smaller effects on drag coefficient at lower Reynolds number regimes. Increasing slip at known Reynolds number causes to delay of flow separation and inflect point creation in velocity profiles. At full slip conditions, shear drag coefficient will be zero and radial drag coefficient reaches to its maximum values. Flow around of sphere at full‐slip condition is not equal to potential flow around a sphere. Present numerical results corresponding to full slip (Tr→0) are in complete accord with certain results of flow around of inviscid bubbles, and the results corresponding to no‐slip (Tr→∞) have excellent agreement with the results predicted by the no‐slip boundary condition.     

Physical properties of nanobubbles on hydrophobic surfaces in water and aqueous solutions

In recent years there has been an accumulation of evidence for the existence of nanobubbles on hydrophobic surfaces in water, despite predictions that such small bubbles should rapidly dissolve because of the high internal pressure associated with the interfacial curvature and the resulting increase in gas solubility. Nanobubbles are of interest among surface scientists because of their potential importance in the long-range hydrophobic attraction, microfluidics, and adsorption at hydrophobic surfaces. Here we employ recently developed techniques designed to induce nanobubbles, coupled with high-resolution tapping-mode atomic force microscopy (TM-AFM) to measure some of the physical properties of nanobubbles in a reliable and repeatable manner. We have reproduced the earlier findings reported by Hu and co-workers. We have also studied the effect of a wide range of solutes on the stability and morphology of these deliberately formed nanobubbles, including monovalent and multivalent salts, cationic, anionic, and nonionic surfactants, as well as solution pH. The measured physical properties of these nanobubbles are in broad agreement with those of macroscopic bubbles, with one notable exception: the contact angle. The nanobubble contact angle (measured through the denser aqueous phase) was found to be much larger than the macroscopic contact angle on the same substrate. The larger contact angle results in a larger radius of curvature and a commensurate decrease in the Laplace pressure. These findings provide further evidence that nanobubbles can be formed in water under some conditions. Once formed, these nanobubbles remain on hydrophobic surfaces for hours, and this apparent stability still remains a well-recognized mystery. The implications for sample preparation in surface science and in surface chemistry are discussed.     

Polymer-surfactant complex formation and its effect on turbulent wall shear stress

Turbulent drag reduction in Couette flow was investigated in terms of a decrease in wall shear stress for aqueous solutions of a nonionic polymer, poly(ethylene oxide) (PEO), a cationic surfactant, hexadecyltrimethylammonium chloride (HTAC), and their mixtures. Consistent with literature data, drag reduction was observed for PEO solutions above a critical molecular weight, 0.91 x 10(5) < Mc < 3.04 x 10(5) g/mol. Maximum drag reduction occurred at an optimum concentration, c(PEO)*, which scales inversely with molecular weight, and the % maximum drag reduction increases with molecular weight. For aqueous HTAC solutions, wall shear stress decreased with increasing HTAC concentration and leveled off at an optimum concentration, c(HTAC)*, comparable to the critical micelle concentration. For HTAC/PEO mixtures, the critical PEO molecular weight for drag reduction decreases, interpreted as due to an increase in hydrodynamic volume because of binding of HTAC micelles to PEO. Consistent with this interpretation, at fixed PEO concentration, maximum drag reduction was observed at an optimum HTAC concentration, c(HTAC/PEO)*, comparable to the maximum binding concentration, MBC. Also, with HTAC concentration fixed at the MBC, the optimum PEO concentration for drag reduction, c(PEO/HTAC)*, decreases relative to that, c(PEO)*, in the absence of HTAC.     

Reliable measurements of interfacial slip by colloid probe atomic force microscopy. III. Shear-rate-dependent slip

We present experimental evidence and theoretical models that demonstrate that the slip length, which is the departure from the hydrodynamic no-slip boundary condition, cannot be constant as commonly assumed, but must decrease with increasing shear rate to avoid an unphysical divergence in the velocity of the fluid adjacent to the surface at small separations. The molecular origin of the shear rate dependence of the slip length is discussed. A new theoretical model for slip (the saturation model) is obtained, and it is shown to describe accurately colloid probe atomic force microscopy force measurements for all separations down to a few nanometers in two partially wetting situations (di-n-octyl phthalate on silanized silicon and bare silicon). Previous observations of slip length increasing with shear rate are explained as due to an imprecise calculation of the drag force on the cantilever. A new way of plotting experimental data is also presented, which provides a useful way to illustrate the slip length dependence on the shear rate.     

Viscous froth model for a bubble staircase structure under rapid applied shear: An analysis of fast flowing foam

The viscous froth model is applied to the rapid shear of ‘2-dimensional’, dry foams for bubbles confined in a monolayer and arranged in an ordered staircase configuration that forms part of a hexagonal honeycomb structure. High system energies are attained as particular films in the staircase become highly elongated under shear. Topological transformations during which bubbles exchange neighbours can relax the staircase energy, but their onset is postponed at high shear rates. Moreover as the imposed shear rate increases, the rate at which topological transformations subsequently occur cannot keep pace with the imposed shear, and secular film stretching onsets. A critical capillary number (a dimensionless measure of shear rate) separates a regime where film lengths are periodic functions of imposed strain from a regime of secular growth.     

Gas bubbles in simulation and experiment

An experimental setup for the examination of single bubbles, rising in a liquid, is presented. Its main part is a rotating chamber, in which the bubble is spatially stabilized by a balance of buoyancy, drag, and lift forces. This allows for long observation periods in time. Experimental results are presented for air bubbles in silicone oil. The experimental results are validated by a comparison with numerical simulations. A modified, mass-conserving level-set method is used for the representation of the free interface, while an immersed-boundary formulation is engaged for the conservation equations. The agreement between experiment and simulation, and to available correlations from literature, is found to be perfect. It is shown that the influence of the liquid shear due to the rotation is negligible. Also, for the presented liquid system, no influence by Marangoni stresses could be found, which makes the system of air and silicone oil a good choice for validation purposes.     

在低频振动场中注射成型HDPE试样的力学性能及其形态控制

利用自行研制的低频振动注射实验装置探讨HDPE振动注射试样力学性能和微观形态之间的关系 .实验中对常规注射和振动注射成型的试样力学性能和微观形态进行了对比实验 .SEM实验结果显示 ,振动注射制件芯层的形态由常规注射的球晶转变为垂直于振动波传递方向排列的片晶结构 ,在剪切层中同时存在串晶或柱状堆砌的片晶结构 .频率的改变 (0 相似文献   

Injectable microbubbles as contrast agents for diagnostic ultrasound imaging: the key role of perfluorochemicals

Ultrasonography has, until recently, lacked effective contrast-enhancing agents. Micrometer-sized gas bubbles that resonate at a diagnostic frequency are ideal reflectors for ultrasound. However, simple air bubbles, when injected into the blood stream, disappear within seconds through the combined effects of Laplace pressure, blood pressure, and exposure to ultrasound energy. Use of fluorocarbon vapor, by extending the persistence of microbubbles in vivo from seconds to minutes, propelled contrast ultrasonography into clinical practice. Imaging techniques that selectively suppress tissue, but not microbubble signal, further increase image contrast. Approved products consist of C3F8 or SF6 microbubbles, and N2 microbubbles osmotically stabilized with C6F14. These agents allow the detection and characterization of cardiovascular abnormalities and solid organ lesions, such as tumors. By providing higher quality images, they improve the accuracy and confidence of disease diagnosis, and can play a decisive role in clinical decision making. New objectives include agents that target specific cells for the molecular imaging of disease, and drug and gene delivery, including ultrasound-triggered delivery.     

Does capillarity influence chemical reaction in drops and bubbles? A thermodynamic approach

After a brief introduction on the variables which describe the physico-chemical properties of a fluid surface, this paper compares, in a very simple way, the equilibrium constant of homogeneous and heterogeneous reactions taking place in spherical micro-objects (uncharged and charged droplets and bubbles) and in media bordered by a flat interface. This quantity is by definition the exponential of the dimensionless standard chemical affinity whose values (< or = 0, > or = 0) may indicate the direction and the importance of the reaction (strictly true when the mixing term of the affinity is zero). The classical thermodynamic approach combined with the Laplace equation shows that: (i) high surface tension and high curvature influence the equilibrium constant, this effect being, however, much more important for bubbles than for droplets; (ii) charges on droplets reduce this effect; (iii) the constant of reaction taking place in the vapour in contact with a charged droplet depends significantly on the electric field pressure; (iv) reactions in droplets dispersed in the liquid phase are discussed and, in particular, capillarity seems to play a negligible role on reactions in micro-emulsions; (v) the surface amount of a gas bubble component transferred in the continuous liquid can be related to capillary quantities; (vi) expanding (or shrinking) bubble induced by a chemical reaction is analysed by using an extended Laplace law which includes the volumetric flow rate; (vii) the Laplace law is discussed in the frame of the choice of the dividing surface. Numerous actual examples from the atmosphere, sonochemistry and metallurgy illustrate the theory proposed. One of the interest, among other points, is that small objects (specially bubbles) give the potentiality to obtain, for steady or (near) equilibrium states, large amount of components which would not be possible when dealing with large reservoirs.     

Interactions between two bubbles on a hot or cold wall

A temperature gradient normal to a planar wall produces two-dimensional motion and aggregation or separation of bubbles on the hot or cold wall, respectively. The origin of the motion is fluid convection driven by the thermal Marangoni stress on the surface of the bubbles. Previous theories for the dynamics of two or more bubbles have been based on an analysis of flow about a single bubble and the resulting convection that entrains its neighbors. Here we extend the theory by solving the quasi-steady equations for the temperature and velocity fields for two bubbles. The result is a quantitative model for the relative velocity between two bubbles as a function of both the distance between them and the gap between each bubble and the surface. Interactions between the bubbles strongly increase the approach velocity, which is counter-intuitive because the hydrodynamic resistance increases as the bubbles approach each other. An asymptotic analysis indicates the thermocapillary force bringing them together or pushing them apart is singular in the separation when the bubbles are close to each other. The two-bubble theory agrees reasonably well with the experimentally measured velocities of pairs of bubbles on hot or cold surfaces, though it slightly overestimates the velocities.     

Effects of laterally heterogeneous slip on the resonance properties of quartz crystals immersed in liquids

A formalism is presented which predicts the influence of laterally heterogeneous slip (for instance, induced by nanoscopic air bubbles) on the shift of the resonance frequency and bandwidth of quartz crystal resonators immersed in liquids. The lateral heterogeneities are decomposed into their Fourier components. The distribution of slip lengths provides a boundary condition, giving rise to a small, secondary flow field. The mean stress exerted by this secondary field induces a shift in resonance frequency and bandwidth. If the slip length is much smaller than the penetration depth of the shear waves and smaller than the lateral correlation length, one finds that the effects of the heterogeneities scale as n(3/2), with n being the overtone order. The frequency, f, and half-band-half-width, Gamma, decrease by the same amount. These calculations match experimental results obtained with a gold-coated resonator in contact with various hydrophilic liquids.     

Direct measurement of the laplace pressure in a very thin liquid film

Meniscus force plays an important part in magnetic storage devices, scanning probe microscopy, and micromachines, because the meniscus force increases steeply as the clearance between solid surfaces decreases down to submicrometers. Recently increased experimental and analytical studies on the subject have been published from the point of view of mechanical engineering. Meniscus force is generated by the Laplace pressure within the thin liquid film. Investigating the Laplace pressure is a direct way to clarify the generation mechanism of meniscus force. However, no appropriate measuring method of the Laplace pressure is available for a very thin liquid film confined by solid surfaces. This paper proposes a simple method of direct measurement of the Laplace pressure for the cases. The principle of the measurement method is described. Measurement is conducted using the measuring device. Experimental results on the Laplace pressure show good agreement with the theoretical predictions.     

A double layer model of the gas bubble/water interface

Zeta potential is a physico-chemical parameter of particular importance to describe sorption of contaminants at the surface of gas bubbles. Nevertheless, the interpretation of electrophoretic mobilities of gas bubbles is complex. This is due to the specific behavior of the gas at interface and to the excess of electrical charge at interface, which is responsible for surface conductivity. We developed a surface complexation model based on the presence of negative surface sites because the balance of accepting and donating hydrogen bonds is broken at interface. By considering protons adsorbed on these sites followed by a diffuse layer, the electrical potential at the head-end of the diffuse layer is computed and considered to be equal to the zeta potential. The predicted zeta potential values are in very good agreement with the experimental data of H₂ bubbles for a broad range of pH and NaCl concentrations. This implies that the shear plane is located at the head-end of the diffuse layer, contradicting the assumption of the presence of a stagnant diffuse layer at the gas/water interface. Our model also successfully predicts the surface tension of air bubbles in a KCl solution.     

Surface shear rheological studies of marine phytoplankton cultures-Nitzschia closterium, Thalassiosira rotula, Thalassiosira punctigera and Phaeocystis sp

The study of interfacial properties in the marine environment is important for the understanding of air-sea gas exchange processes, especially with respect to the behaviour of entrained air bubbles. Seawater contains surfactant material, much of which is thought to origin from the exudation of dissolved organic material (DOM) by phytoplankton. This study aims at investigating the influence of different phytoplankton species on the surface shear viscosity of an air-water interface. Measurements of surface shear viscosity were carried out with the ISR1 interfacial shear rheometer. Surface shear viscosities of stock cultures of Phaeocystis sp., Thalassiosira rotula, Thalassiosira punctigera and Nitzschia closterium as well as of F/2 nutrient medium and seawater were measured. The surface shear viscosity of N. closterium was investigated during different stages of its growth as well as for an unfiltered stock culture sample and its filtrate. Results reveal that the influence of phytoplankton on the surface shear viscosity is species specific. An increase in surface shear viscosity occurred for the N. closterium stock culture only. The remaining cultures showed similar behaviour to F/2 nutrient medium. The increase of surface shear viscosity during the growth of N. closterium occurred mainly during the exponential growth phase. The increases in surface shear viscosity depend on the presence of phytoplankton cells in the sample. The formation of compact mechanical structures at the air-water interface originating from the aggregation of DOM released by N. closterium as a cause for the observed increases in surface shear viscosity is discussed.     

Mesoscale constitutive modeling of magnetic dispersions

A constitutive model for dispersions of acicular magnetic particles has been developed by modeling the particles as rigid dumbbells dispersed in a solvent. The effects of Brownian motion, anisotropic hydrodynamic drag, a steric force in the form of the Maier-Saupe potential, and, most importantly, a mean-field magnetic potential are included in the model. The development is similar to previous models for liquid-crystalline polymers. The model predicts multiple orientational states for the dispersion, and this phase behavior is described in terms of an orientational order parameter S and an average alignment parameter J; the latter is introduced because the magnetic particles have distinguishable direction due to polarity. A transition from isotropic to nematic phases at equilibrium is predicted. Multiple nematic phases-both prolate and oblate-are predicted in the presence of steady shear flow and external magnetic field parallel to the flow. The effect of increasing magnetic interparticle interactions and particle concentration is also presented. Comparisons with experimental data for the steady shear viscosity show very good agreement.     

Electrokinetic potentials at the gas-aqueous interface by spinning cylinder electrophoresis

The natural buoyancy of gas bubbles has hampered conventional electrokinetic methods of evaluating charge at the gas-liquid interface. In this study, bubbles are held by centripetal force at the centre of a horizontal, rotating cylinder filled completely with liquid. Migration of the bubble along the axis of the cylinder can be achieved by applying a gravity force or an electrophoretic force. An expression for the drag coefficient has been developed and used to calculate surface charge densities and electrokinetic potentials. In the presence of potassium chloride, anionic and non-ionic surfactants, the electrokinetic potentials were negative (～2–5 mV) at the air-aqueous interface. A cationic surfactant rendered the zeta potential positive. A knowledge of the air-aqueous interfacial rheology is desirable if the drag coefficient, and consequently the zeta potential, at all types of gas-liquid interfaces is to be evaluated.     

Tailoring the microstructure of particle-stabilized wet foams

Inorganic colloidal particles which are in situ hydrophobized upon adsorption of short-chain amphiphilic molecules can be used as foam stabilizers. In this study, we tailor the microstructure of particle-stabilized wet foams, namely, the foam air content, average bubble size, and bubble size distribution, by changing the composition of the initial colloidal suspension. Wet foams featuring average bubble sizes between 10 and 200 microm and air contents between 45% and 90% were obtained by adjusting the amphiphile and particle concentration, pH, ionic strength, and particle size in the initial suspension. The influence of these parameters on the bubble size was satisfactorily described in terms of a balance between the shear stress applied during mixing and the counteracting Laplace pressure of the air bubbles. This model, originally developed for oil droplets in emulsions, can therefore be used to deliberately tailor the microstructure of particle-stabilized wet foams.     

Restructuring and break-up of two-dimensional aggregates in shear flow

We consider single two-dimensional aggregates, containing glass particles, placed at a water/air interface. We have investigated the critical shear rate for break-up of aggregates with different sizes in a simple shear flow. All aggregates break-up nearly at the same shear rate (1.8 +/- 0.2 s(-)(1)) independent of their size. The evolution of the aggregate structure before break-up was also investigated. With increasing shear rate, the aggregates adopt a more circular shape, and the particles order in a more dense, hexagonal structure. A simple theoretical model was developed to explain the experimentally observed break-up. In the model, the aggregate is considered as a solid circular disk that will break near its diameter. The capillary and drag force on the two parts of the aggregate were calculated, and from this force balance, the critical shear rate was found. The model shows a weak size dependence of the critical shear rate for the considered aggregates. This is consistent with the experimental observations.     

Strain-induced yielding in bubble clusters

We study how shearing clusters of two or four bubbles induces bubble separation or topological rearrangement. The critical deformation at which this yielding occurs is measured as a function of shear rate, liquid composition, and liquid content in the cluster. We establish a geometrical yield criterion in the quasistatic case on the basis of these experimental data as well as simulations. In the dynamic regime, the deformation where the cluster yields increases with the strain rate, and we derive a scaling law describing this phenomenon based on the dynamical inertial rupture of the liquid meniscus linking the two bubbles. Our experiments show that the same scaling law applies to two- and four-bubble clusters.     

The range of ambient radius for an active bubble in sonoluminescence and sonochemical reactions

Numerical simulations of nonequilibrium chemical reactions inside an air bubble in liquid water irradiated by ultrasound have been performed for various ambient bubble radii. The intensity of sonoluminescence (SL) has also been calculated taking into account electron-atom bremsstrahlung, radiative attachment of electrons to neutral molecules, radiative recombination of electrons and ions, chemiluminescence of OH, molecular emission from nitrogen, etc. The lower bound of ambient radius for an active bubble in SL and sonochemical reactions nearly coincides with the Blake threshold for transient cavitation. The upper bound is in the same order of magnitude as that of the linear resonance radius. In actual experiments, however, the distribution of ambient radius for active bubbles may be narrow at around the threshold ambient radius for the shape instability. The threshold peak temperature inside an air bubble for nitrogen burning is higher than that for oxidant formation. The threshold peak temperatures depend on ultrasonic frequency and acoustic amplitude because chemical reactions inside a bubble are in nonequilibrium. The dominant emission mechanism in SL is electron-atom bremsstrahlung except at a lower bubble temperature than 2000 K, for which molecular emissions may be dominant.