scholarly journals Considerations on bubble fragmentation models

2010 ◽  
Vol 661 ◽  
pp. 159-177 ◽  
Author(s):  
C. MARTÍNEZ-BAZÁN ◽  
J. RODRÍGUEZ-RODRÍGUEZ ◽  
G. B. DEANE ◽  
J. L. MONTAÑES ◽  
J. C. LASHERAS
Keyword(s):  
Surface Tension ◽  
Particle Size ◽  
Probability Density Function ◽  
Weber Number ◽  
Dissipation Rate ◽  
Continuous Phase ◽  
Symmetry Relation ◽  
Dimensionless Form ◽  
Size Of Particles ◽  
Bubble Fragmentation

In this paper we describe the restrictions that the probability density function (p.d.f.) of the size of particles resulting from the rupture of a drop or bubble must satisfy. Using conservation of volume, we show that when a particle of diameter, D0, breaks into exactly two fragments of sizes D and D2 = (D30−D3)1/3 respectively, the resulting p.d.f., f(D; D0), must satisfy a symmetry relation given by D22f(D; D0) = D2f(D2; D0), which does not depend on the nature of the underlying fragmentation process. In general, for an arbitrary number of resulting particles, m(D0), we determine that the daughter p.d.f. should satisfy the conservation of volume condition given by m(D0) ∫0D0 (D/D0)3f(D; D0) dD = 1. A detailed analysis of some contemporary fragmentation models shows that they may not exhibit the required conservation of volume condition if they are not adequately formulated. Furthermore, we also analyse several models proposed in the literature for the breakup frequency of drops or bubbles based on different principles, g(ϵ, D0). Although, most of the models are formulated in terms of the particle size D0 and the dissipation rate of turbulent kinetic energy, ϵ, and apparently provide different results, we show here that they are nearly identical when expressed in dimensionless form in terms of the Weber number, g*(Wet) = g(ϵ, D0) D2/30 ϵ−1/3, with Wet ~ ρ ϵ2/3D05/3/σ, where ρ is the density of the continuous phase and σ the surface tension.

scholarly journals Surface Activity of Humic Acid and Its Sub-Fractions from Forest Soil

2021 ◽  
Vol 13 (15) ◽  
pp. 8122
Author(s):  
Shijie Tian ◽  
Weiqiang Tan ◽  
Xinyuan Wang ◽  
Tingting Li ◽  
Fanhao Song ◽  
...  
Keyword(s):  
Surface Tension ◽  
Particle Size ◽  
Humic Acid ◽  
Forest Soil ◽  
Surface Activity ◽  
Self Assembly ◽  
Average Particle Size ◽  
Gaussian Model ◽  
Exponential Model ◽  
Average Particle

Surface activity of humic acid (HA) and its six sub-fractions isolated from forest soil were characterized by surface tension measurements, dynamic light scattering, and laser doppler electrophoresis. The surface tension of HA and its sub-fractions reduced from 72.4 mN·m−1 to 36.8 mN·m−1 in exponential model with the increasing concentration from 0 to 2000 mg·L−1. The critical micelle concentration (CMC) and Z-average particle size ranged from 216–1024 mg·L−1 and 108.2–186.9 nm for HA and its sub-fractions, respectively. The CMC have related with alkyl C, O-alkyl C, aromatic C, and carbonyl C (p < 0.05), respectively, and could be predicted with the multiple linear regression equation of CMC, CMC = 18896 − 6.9 × C-296 × alkyl C-331 × aromatic C-17019 × H/C + 4054 × HB/HI (p < 0.05). The maximum particle size was 5000 nm after filtered by a membrane with pore size of 450 nm, indicating HA and its sub-fractions could progressed self-assembly at pH 6.86. The aggregate sizes of number-base particle size distributions were mainly in six clusters including 2 ± 1 nm, 5 ± 2 nm, 10 ± 3 nm, 21 ± 8 nm, 40 ± 10 nm, and >50 nm analyzed by Gaussian model that maybe due to the inconsistency of the components and structures of the HA sub-fractions, requiring further study. It is significance to explore the surface activity of HA and its sub-fractions, which is helpful to clarify the environmental behavior of HA.

Penetration Dynamics of Solid Particles into Liquids High-Speed Experimental Results and Modelling

2005 ◽  
Vol 473-474 ◽  
pp. 429-434 ◽  
Author(s):  
Olga Verezub ◽  
György Kaptay ◽  
Tomiharu Matsushita ◽  
Kusuhiro Mukai
Keyword(s):  
Contact Angle ◽  
Particle Size ◽  
Aqueous Solutions ◽  
Particle Velocity ◽  
Weber Number ◽  
High Speed ◽  
Solid Particles ◽  
Bulk Liquid ◽  
Distilled Water ◽  
Critical Weber Number

Penetration of model solid particles (polymer, teflon, nylon, alumina) into transparent model liquids (distilled water and aqueous solutions of KI) were recorded by a high speed (500 frames per second) camera, while the particles were dropped from different heights vertically on the still surface of the liquids. In all cases a cavity has been found to form behind the solid particle, penetrating into the liquid. For each particle/liquid combination the critical dropping height has been measured, above which the particle was able to penetrate into the bulk liquid. Based on this, the critical impact particle velocity, and also the critical Weber number of penetration have been established. The critical Weber number of penetration was modelled as a function of the contact angle, particle size and the ratio of the density of solid particles to the density of the liquid.

Numerical Simulation of Droplet Generation in Series Co-Flow Capillaries

2009 ◽  
Author(s):  
Yanxi Song ◽  
Jinliang Xu
Keyword(s):  
Reynolds Number ◽  
Disperse Phase ◽  
Weber Number ◽  
Three Dimensional ◽  
Continuous Phase ◽  
Disperse Flow ◽  
Double Emulsions ◽  
Wide Range ◽  
In Series ◽  
Dispersed Phases

We study the production and motion of monodisperse double emulsions in microfluidics comprising series co-flow capillaries. Both two and three dimensional simulations are performed. Flow was determined by dimensionless parameters, i.e., Reynolds number and Weber number of continuous and dispersed phases. The co-flow generated droplets are sensitive to the Reynolds number and Weber number of the continuous phase, but insensitive to those of the disperse phase. Because the inner and outer drops are generate by separate co-flow processes, sizes of both inner and outer drops can be controlled by adjusting Re and We for the continuous phase. Meanwhile, the disperse phase has little effect on drop size, thus a desirable generation frequency of inner drop can be reached by merely adjusting flow rate of the inner fluid, leading to desirable number of inner drops encapsulated by the outer drop. Thus highly monodisperse double emulsions are obtained. It was found that only in dripping mode can droplet be of high mono-dispersity. Flow begins to transit from dripping regime to jetting regime when the Re number is decreased or Weber number is increased. To ensure that all the droplets are produced over a wide range of running parameters, tiny tapered tip outlet for the disperse flow should be applied. Smaller the tapered tip, wider range for Re and we can apply.

Effect of the modified dispersing agent and milling time on the properties and particle size distribution of inkjet ink formulation for textile printing

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
H. Abd El-Wahab ◽  
A.M. Nasser ◽  
H.M. Abd ElBary ◽  
M. Abd Elrahman ◽  
M. Hassanein
Keyword(s):  
Surface Tension ◽  
Particle Size ◽  
Milling Time ◽  
Polyester Fabric ◽  
Light Fastness ◽  
Content Type ◽  
Textile Printing ◽  
Dispersing Agent ◽  
Dispersing Agents ◽  
Ink Formulation

Purpose This paper aims to study the effect of the new modified dispersing agent, milling time of the properties and particle size distribution (PSD) of inkjet ink formulation for polyester fabric printing. Design/methodology/approach The study’s methods include preparation of different formulations of textile inkjet inks based on different types of dispersing agents, then applying and evaluating the prepared formulations on the polyester fabric. The properties of the prepared ink formulations were analyzed by measuring viscosity, surface tension and particle size. The current work is including the study of the effect of using different doses of different dispersing agents and the milling time on their characteristics. Also, the study was extended to evaluate the printed polyester by using the prepared inks according to light fastness, washing fastness, alkali perspiration fastness and crock fastness. Findings The results showed that the used dispersing agents and the different milling time enhanced the viscosity and dynamic surface tension in the accepted range, but it was largely cleared in the PSD which tends to perform the inks on the printhead and prevent clogging of nozzles. Light fastness, washing fastness, alkali perspiration fastness and crock fastness gave good results in agreement with this type of inkjet inks for textile printing. Research limitations/implications In this work, good results were obtained with this type of dispersing agent for inkjet ink formulations, but for other dispersing agents, other tests could be performed. The inkjet ink could also be formulated with other additives to prevent clogging of nozzles on the printhead. Practical implications These ink formulations could be used for printing on polyester fabric by the inkjet printing. Originality/value Recently, there was a considerable interest in the study of the effect of PSD on the inkjet inks to prevent clogging of nozzles on the printhead and to improve the print quality on the textile fiber.

scholarly journals Cavity Detachment from a Wedge with Rounded Edges and the Surface Tension Effect

2021 ◽  
Vol 9 (11) ◽  
pp. 1253
Author(s):  
Yuriy N. Savchenko ◽  
Georgiy Y. Savchenko ◽  
Yuriy A. Semenov
Keyword(s):  
Surface Tension ◽  
Weber Number ◽  
Solution Process ◽  
Cavity Flow ◽  
Surface Tension Effect ◽  
Force Coefficient ◽  
Hodograph Method ◽  
Wide Range ◽  
Critical Weber Number ◽  
Cavity Boundary

Cavity flow around a wedge with rounded edges was studied, taking into account the surface tension effect and the Brillouin–Villat criterion of cavity detachment. The liquid compressibility and viscosity were ignored. An analytical solution was obtained in parametric form by applying the integral hodograph method. This method gives the possibility of deriving analytical expressions for complex velocity and for potential, both defined in a parameter plane. An expression for the curvature of the cavity boundary was obtained analytically. By using the dynamic boundary condition on the cavity boundary, an integral equation in the velocity modulus was derived. The particular case of zero surface tension is a special case of the solution. The surface tension effect was computed over a wide range of the Weber number for various degrees of cavitation development. Numerical results are presented for the flow configuration, the drag force coefficient, and the position of cavity detachment. It was found that for each radius of the edges, there exists a critical Weber number, below which the iterative solution process fails to converge, so a steady flow solution cannot be computed. This critical Weber number increases as the radius of the edge decreases. As the edge radius tends to zero, the critical Weber number tends to infinity, or a steady cavity flow cannot be computed at any finite Weber number in the case of sharp wedge edges. This shows some limitations of the model based on the Brillouin–Villat criterion of cavity detachment.

scholarly journals On the contribution of Aitken mode particles to cloud droplet populations at continental background areas – a parametric sensitivity study

2007 ◽  
Vol 7 (3) ◽  
pp. 6077-6112
Author(s):  
T. Anttila ◽  
V.-M. Kerminen
Keyword(s):  
Surface Tension ◽  
Particle Size ◽  
Chemical Composition ◽  
Pure Water ◽  
Particle Surface ◽  
Chemical Properties ◽  
Sensitivity Study ◽  
Geometric Standard Deviation ◽  
Cloud Droplets ◽  
Aitken Mode

Abstract. Aitken mode particles are potentially an important source of cloud droplets in continental background areas. In order to find out which physico-chemical properties of Aitken mode particles are most important regarding their cloud-nucleating ability, we applied a global sensitivity method to an adiabatic air parcel model simulating the number of cloud droplets formed on Aitken mode particles, CD2. The technique propagates uncertainties in the parameters describing the properties of Aitken mode to CD2. The results show that if the Aitken mode particles do not contain molecules that are able to reduce the particle surface tension more than 30% and/or decrease the mass accommodation coefficient of water, α, below 10−2, the chemical composition and modal properties may have roughly an equal importance at low updraft velocities characterized by maximum supersaturations <0.1%. For larger updraft velocities, however, the particle size distribution is clearly more important than the chemical composition. In general, CD2 exhibits largest sensitivity to the particle number concentration, followed by the particle size. Also the shape of the particle mode, characterized by the geometric standard deviation (GSD), can be as important as the mode mean size at low updraft velocities. Finally, the performed sensitivity analysis revealed also that the chemistry may dominate the total sensitivity of CD2 to the considered parameters if: 1) the value of α varies at least one order of magnitude more than what is expected for pure water surfaces (10−2–1), or 2) the particle surface tension varies more than roughly 30% under conditions close to reaching supersaturation.

Distorted gas bubbles at large Reynolds number

1974 ◽  
Vol 62 (1) ◽  
pp. 163-183 ◽  
Author(s):  
M. El Sawi
Keyword(s):  
Surface Tension ◽  
Weber Number ◽  
Liquid Metals ◽  
Gas Bubbles ◽  
Joint Effect ◽  
Large Reynolds Number ◽  
Recent Experimental Data ◽  
Approximate Theory ◽  
Axis Ratio ◽  
Comparison Of The Results

The distortion of a gas bubble rising steadily in an inviscid incompressible liquid of infinite extent under the action of surface tension forces is investigated theoretically using an appropriate extension of the tensor virial theorem. A convenient parameter for distinguishing the bubble shape is the Weber numberW. The virial method leads to an expression relatingWand the axis ratio χ, of the transverse and longitudinal axes of the bubble. To first order inW, this relation agrees with the linear theory established by Moore (1959). Also, comparison of the results with his (1965) approximate theory reveals similar features and excellent agreement up to χ = 2. In particular, it confirms his prediction of the existence of a maximum Weber number. Although the present work does not consider the stability of these bubbles, it is interesting to note that the maximum value of 3.271 attained byWdiffers only by about 2.8% from the critical Weber number obtained by Hartunian & Sears (1957) for the onset of instability.An approximate method for the study of slightly distorted spheroidal gas bubbles is also formulated and the resulting boundary-value problem solved numerically. The theory is then extended to include gravity. The joint effect of surface tension as well as gravitational forces has not been included in earlier theories. The shapes of the bubbles are traced and compared with the unperturbed spheroids. Comparisons for the velocity of bubble rise are made between the present predictions and some experimental results. In particular the results are compared with recent experimental data for the motion of gas bubbles in liquid metals.

Study on Process of Particle Impact on Curved Surface of Vane by Finite Element Method

2010 ◽  
Vol 139-141 ◽  
pp. 1303-1307
Author(s):  
Xiao Jing Yang ◽  
Yi Lin Chi ◽  
Guan Zhang He
Keyword(s):  
Particle Size ◽  
Energy Exchange ◽  
Surface Deformation ◽  
Plastic Property ◽  
Impact Angle ◽  
Surface Shape ◽  
Curved Surface ◽  
Particle Impact ◽  
Size Of Particles ◽  
Distribution Of Stress

The process of particle impacting and contacting curved surface of vane was studied, and the characteristics of particle size, particle initial velocity and its impacting direction affect the stress of subsurface were analyzed by using ANSYS/LS-DANY software. It is shown that the interaction between particles and surface of vane is affected by nonlinear factors such as the elastic-plastic property of material, the state of impacting and contacting and surface shape. The increment in particle size increases the stress of the surface impacted and the sphere of action is also enlarged. The influence of the size of particles is remarkable. Particle impact velocity is related to energy exchange and has influences on stress value and the area of surface deformation. Due to impact angle is related to shape of curved vane, so the distribution of stress is changed and the value of the stress in surface layer is also influenced when particles impact curved surface of vane from different directions. The research will be helpful to disclose the mechanics of the wear on the condition of particle impact.

Effect of Monomer on Performance of UV-LED Inkjet Ink

2013 ◽  
Vol 469 ◽  
pp. 68-73
Author(s):  
Qing Yi ◽  
Xian Fu Wei ◽  
Bei Qing Huang ◽  
Qi Wang
Keyword(s):  
Surface Tension ◽  
Particle Size ◽  
Research And Development ◽  
Energy Saving ◽  
Significant Influence ◽  
Uv Led ◽  
Film Forming ◽  
Overall Performance ◽  
The Impact ◽  
Reaction Speed

UV-LED inkjet ink is a promising environmental ink which has advantages as higher reaction speed, higher efficiency and energy saving, better environmental protection, its research and development can contribute to realizing green printing and its important for food packing security. Monomer is the important component of the UV-LED ink, in order to investigate the impact of monomer on dispersivity of UV-LED inkjet ink, seven kinds of monomers were chosen to prepare cyan color paste respectively and test their particle size and distribution. Then the ratio of co-monomers was achieved by formulation experiment to obtain the best dispersivity. In order to improve the performance of the UV-LED inkjet ink, different monomers were used to make ink samples separately, viscosity, surface tension, curing rate of the ink and flexibility and adhesion were tested. In the end, the ratio of co-monomers was achieved by formulation experiment to obtain the best overall performance. The results show that the monomer has a significant influence on the dispersion and curing rate of the UV-LED inkjet ink, but also has a great impact on film-forming properties of the ink after UV-LED curing.

On the interaction of Taylor length scale size droplets and isotropic turbulence

2016 ◽  
Vol 806 ◽  
pp. 356-412 ◽  
Author(s):  
Michael S. Dodd ◽  
Antonino Ferrante
Keyword(s):  
Surface Tension ◽  
Surface Area ◽  
Dissipation Rate ◽  
Isotropic Turbulence ◽  
Droplet Surface ◽  
Rate Of Change ◽  
Length Scale ◽  
Fluid Viscosity ◽  
Carrier Fluid ◽  
Two Fluid

Droplets in turbulent flows behave differently from solid particles, e.g. droplets deform, break up, coalesce and have internal fluid circulation. Our objective is to gain a fundamental understanding of the physical mechanisms of droplet–turbulence interaction. We performed direct numerical simulations (DNS) of 3130 finite-size, non-evaporating droplets of diameter approximately equal to the Taylor length scale and with 5 % droplet volume fraction in decaying isotropic turbulence at initial Taylor-scale Reynolds number $\mathit{Re}_{\unicode[STIX]{x1D706}}=83$. In the droplet-laden cases, we varied one of the following three parameters: the droplet Weber number based on the r.m.s. velocity of turbulence ($0.1\leqslant \mathit{We}_{rms}\leqslant 5$), the droplet- to carrier-fluid density ratio ($1\leqslant \unicode[STIX]{x1D70C}_{d}/\unicode[STIX]{x1D70C}_{c}\leqslant 100$) or the droplet- to carrier-fluid viscosity ratio ($1\leqslant \unicode[STIX]{x1D707}_{d}/\unicode[STIX]{x1D707}_{c}\leqslant 100$). In this work, we derive the turbulence kinetic energy (TKE) equations for the two-fluid, carrier-fluid and droplet-fluid flow. These equations allow us to explain the pathways for TKE exchange between the carrier turbulent flow and the flow inside the droplet. We also explain the role of the interfacial surface energy in the two-fluid TKE equation through the power of the surface tension. Furthermore, we derive the relationship between the power of surface tension and the rate of change of total droplet surface area. This link allows us to explain how droplet deformation, breakup and coalescence play roles in the temporal evolution of TKE. Our DNS results show that increasing $\mathit{We}_{rms}$, $\unicode[STIX]{x1D70C}_{d}/\unicode[STIX]{x1D70C}_{c}$ and $\unicode[STIX]{x1D707}_{d}/\unicode[STIX]{x1D707}_{c}$ increases the decay rate of the two-fluid TKE. The droplets enhance the dissipation rate of TKE by enhancing the local velocity gradients near the droplet interface. The power of the surface tension is a source or sink of the two-fluid TKE depending on the sign of the rate of change of the total droplet surface area. Thus, we show that, through the power of the surface tension, droplet coalescence is a source of TKE and breakup is a sink of TKE. For short times, the power of the surface tension is less than $\pm 5\,\%$ of the dissipation rate. For later times, the power of the surface tension is always a source of TKE, and its magnitude can be up to 50 % of the dissipation rate.

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