scholarly journals Liquid Force and Rupture Distance between Two Particles

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Cheng Pu ◽  
Fengyin Liu ◽  
Shaohan Wang
Keyword(s):  
Surface Tension ◽  
Particle Diameter ◽  
Decisive Role ◽  
Diameter Ratio ◽  
Liquid Volume ◽  
Distance Curve ◽  
Industrial Manufacturing ◽  
Local Range ◽  
Force Displacement ◽  
Rupture Distance

The study of liquid force has a special meaning to industrial manufacturing. By taking the liquid bridges between equal and unequal particles as objects, the liquid force-displacement curves were measured and recorded by using a novel Nano UTM T150 tensile system. The influences of diameter, diameter ratio, liquid volume, and the surface tension on the liquid force-distance curve, the maximum liquid force, and rupture distance were compared and sorted. The results show that the maximum liquid force and rupture distance both increase with the increase in liquid volume, particle diameter, diameter ratio, and surface tension. The diameter plays a decisive role in determining the value of the maximum liquid force compared with surface tension and liquid volume, which only influence the force value in a local range. The rupture distance shows a positive correlation with liquid volume and surface tension and a negative correlation with the diameter or diameter ratio. The maximum liquid force between unequal particles is about half of the sum of the force between the equal spheres of larger and smaller size in that system.

scholarly journals Influence of Macroscopic Wall Structures on the Fluid Flow and Heat Transfer in Fixed Bed Reactors with Small Tube to Particle Diameter Ratio

Processes ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 689
Author(s):  
Thomas Eppinger ◽  
Nico Jurtz ◽  
Matthias Kraume
Keyword(s):  
Heat Transfer ◽  
Fixed Bed ◽  
Particle Diameter ◽  
Diameter Ratio ◽  
Spherical Particles ◽  
Reactor Wall ◽  
Entry Length ◽  
Fixed Bed Reactors ◽  
Wall Structures ◽  
Small Tube

Fixed bed reactors are widely used in the chemical, nuclear and process industry. Due to the solid particle arrangement and its resulting non-homogeneous radial void fraction distribution, the heat transfer of this reactor type is inhibited, especially for fixed bed reactors with a small tube to particle diameter ratio. This work shows that, based on three-dimensional particle-resolved discrete element method (DEM) computational fluid dynamics (CFD) simulations, it is possible to reduce the maldistribution of mono-dispersed spherical particles near the reactor wall by the use of macroscopic wall structures. As a result, the lateral convection is significantly increased leading to a better radial heat transfer. This is investigated for different macroscopic wall structures, different air flow rates (Reynolds number Re = 16 ...16,000) and a variation of tube to particle diameter ratios (2.8, 4.8, 6.8, 8.8). An increase of the radial velocity of up to 40%, a reduction of the thermal entry length of 66% and an overall heat transfer increase of up to 120% are found.

The Effect of Turbulence on Momentum and Heat Transport in Packed Beds with Low Tube to Particle Diameter Ratio

2018 ◽  
Vol 16 (11) ◽  
Author(s):  
F. I. Molina-Herrera ◽  
C. O. Castillo-Araiza ◽  
H. Jiménez-Islas ◽  
F. López-Isunza
Keyword(s):  
Thermal Conductivity ◽  
Heat Transport ◽  
Mass Flux ◽  
Flow Model ◽  
Particle Diameter ◽  
Packed Bed ◽  
Diameter Ratio ◽  
Packed Beds ◽  
Measured Temperature ◽  
Orthogonal Collocation

Abstract This is a theoretical study about the influence of turbulence on momentum and heat transport in a packed-bed with low tube to particle diameter ratio. The hydrodynamics is given here by the time-averaged Navier-Stokes equations including Darcy and Forchheimer terms, plus a κ-ε two-equation model to describe a 2D pseudo-homogeneous medium. For comparison, an equivalent conventional flow model has also been tested. Both models are coupled to a heat transport equation and they are solved using spatial discretization with orthogonal collocation, while the time derivative is discretized by an implicit Euler scheme. We compared the prediction of radial and axial temperature observations from a packed-bed at particle Reynolds numbers (Rep) of 630, 767, and 1000. The conventional flow model uses effective heat transport parameters: wall heat transfer coefficient (hw) and thermal conductivity (keff), whereas the turbulent flow model includes a turbulent thermal conductivity (kt), estimating hw via least-squares with Levenberg-Marquardt method. Although predictions of axial and radial measured temperature profiles with both models show small differences, the calculated radial profiles of the axial velocity component are very different. We demonstrate that the model that includes turbulence compares well with mass flux measurements at the packed-bed inlet, yielding an error of 0.77 % in mass flux balance at Rep = 630. We suggest that this approach can be used efficiently for the hydrodynamics characterization and design and scale-up of packed beds with low tube to particle diameter ratio in several industrial applications.

An Investigation on the Profile of Microlens by the Thermal Reflow Process Due to Surface Tension and Gravity

2008 ◽  
Author(s):  
Jhy-Cherng Tsai ◽  
Yong-Sung Hsu
Keyword(s):  
Surface Tension ◽  
Critical Radius ◽  
Critical Size ◽  
Liquid Droplet ◽  
Bond Number ◽  
Diameter Ratio ◽  
Experimental Result ◽  
Critical Number ◽  
Reflow Process ◽  
Thermal Reflow

Microlens and its mold fabricated by thermal reflow using photoresist have been widely used for forming patterns in different scales. When the photoresist solidifies from melting condition, for example by the reflow process, its profile is formed based on the balance between surface tension and gravity. This research is aimed to investigate the influence of surface tension and gravity on the profile of microlens in thermal reflow process. Theoretical analysis based on the interaction between surface tension and gravity of liquid droplet is first investigated. The result showed that the height to diameter ratio (h/D), or the sag ratio, of the liquid droplet is affected by the Bond number (Bo), a number defined as the ratio of gravity to surface tension. The sag ratio is not sensitive to Bo when Bo is small but the ratio decreases as Bo increases if Bo is over the critical number. Based on the analysis, the critical number for the AZ4620 photoresist on a silicon substrate is 1, corresponding to the critical radius of droplet R = 2,500μm. When the size of the droplet is less then the critical size, the profile is mainly controlled by the surface tension and thus the sag ratio is about the same regardless the size. The profile, in contrast, is highly affected by the gravity if the size of the droplet is larger then the critical size. The sag ratio decreases exponentially with respect to Bo in this case. Experiments are also designed and conducted to verify the analysis. Experimental result showed that the sag ratio of the photoresist reduces to 0.065 from 0.095 when Bo increases from 0.0048 to 0.192. The results showed that the trend is consistent to the theoretical model.

Influence of nucleating agent type on the morphology of extruded polyetherimide foam for printed circuit boards*

2019 ◽  
Vol 56 (3) ◽  
pp. 317-341 ◽  
Author(s):  
Clemens Keilholz ◽  
Daniel Raps ◽  
Thomas Köppl ◽  
Volker Altstädt
Keyword(s):  
Surface Tension ◽  
Printed Circuit Boards ◽  
Particle Diameter ◽  
Nucleating Agent ◽  
Nucleating Agents ◽  
Circuit Boards ◽  
Printed Circuit ◽  
Foam Morphology ◽  
The Mean ◽  
Mean Particle Diameter

This work focuses on the development of foamed high temperature thermoplastic substrates for printed circuit boards. For this application it is necessary to achieve mean cell diameters smaller than 30 µm in order to be able to realize vias and high packaging densities (miniaturization). Different additives as nucleating agents, namely macro- and micro-crystalline talc, silica, calcium carbonate, and wollastonite, were melt-compounded with polyetherimide using a twin-screw extruder. Foamed samples are prepared by foam extrusion using a slit die and CO2 as physical blowing agent. The aim of this study is to analyze the influence of the mean particle size and the particle surface tension on the mean cell diameters. Therefore, the shape of the additives, the foam morphology, and the elongational viscosity were considered. The additives with a suitable particle size and surface tension exhibit a positive influence on the foam morphology, resulting in smaller cell diameters (<30 µm), a narrower cell size distribution and a foam density lower than 900 kg/m3. If the mean particle diameter of the nucleating agents is lower than 0.6 µm in this study, no nucleation effect could be observed. This is related to the fact that no heterogeneous nucleation occurs, if the particle diameter is too small. If the mean particle diameter of the used additives is larger than 1.5 µm, which could be demonstrated in this study in case of polyetherimide, then the additive acts as nucleating agent and heterogeneous nucleation occurs. Furthermore, it was observed that the mean cell diameter was affected by the different surface tensions of the studied nucleating agents.

Hydrodynamic Models for Packed Beds with Low Tube-to-Particle Diameter Ratio

2008 ◽  
Vol 6 (1) ◽  
Author(s):  
Carlos O. Castillo-Araiza ◽  
Felipe Lopez-Isunza
Keyword(s):  
Experimental Data ◽  
Effective Viscosity ◽  
Particle Diameter ◽  
Packed Bed ◽  
Diameter Ratio ◽  
Packed Beds ◽  
Hydrodynamic Models ◽  
Viscous Term ◽  
Measured Velocity ◽  
Viscosity Parameter

In the last decade it has been a special interest to incorporate the hydrodynamics in packed bed reactor models. This seems to be important in the case of highly exothermic partial oxidation reactions normally performed in packed beds with low tube/particle diameter ratio (dt/dp< 5) because of the large void distributions in the radial and axial directions, which have a direct impact on the magnitude of radial, angular and axial profiles of the velocity field, and consequently on both, the temperature and concentration profiles in the catalytic reactor. A successful reactor model needs an adequate hydrodynamic description of the packed bed, and for this reason several models additionally incorporate empirical expressions to describe radial voidage profiles, and use viscous (Darcy) and inertial (Forchheimer) terms to account for gas-solid interactions, via Ergun's pressure drop equation. In several cases an effective viscosity parameter has also been used with the Brinkman's viscous term. The use of these various approaches introduce some uncertainty in the predicted results, as to which extent the use of a particular radial voidage expression, or the use of an effective viscosity parameter, yield reliable predictions of measured velocity profiles.In this work the predictions of radial velocity profiles in a packed bed with low tube to particle diameter ratio from six hydrodynamic models, derived from a general one, are compared. The calculations show that the use of an effective viscosity parameter to predict experimental data can be avoided, if the magnitude of the two parameters in Ergun's equation, related to viscous and inertial energy losses, are re-estimated from velocity measurements, for this particular packed bed. The predictions using both approaches adequately fit the experimental data, although the results are analyzed and discussed.

Superhydrophobicity-Enabled Interfacial Microfluidics on Textile

2013 ◽  
Vol 1569 ◽  
pp. 115-120
Author(s):  
Siyuan Xing ◽  
Jia Jiang ◽  
Tingrui Pan
Keyword(s):  
Surface Tension ◽  
Capillary Force ◽  
Three Dimensional ◽  
Liquid Volume ◽  
Driving Mechanism ◽  
Chemical Analyses ◽  
Skin Model ◽  
Liquid Motion ◽  
Liquid Flows ◽  
Hydrophilic Materials

ABSTRACTCapillary-driven microfluidics, utilizes the capillary force generated by fibrous hydrophilic materials (e.g., paper and cotton) to drive biological reagents, has been extended to various biological and chemical analyses recently. However, the restricted capillary-driving mechanism persists to be a major challenge for continuous and facilitated biofluidic transport. In this abstract, we have first introduced a new interfacial microfluidic transport principle to automatically and continuously drive three-dimensional liquid flows on a micropatterned superhydrophobic textile (MST). Specifically, the MST platform utilizes the surface tension-induced Laplace pressure to facilitate the liquid motion along the fibers, in addition to the capillary force existing in the fibrous structure. The surface tension-induced pressure can be highly controllable by the sizes of the stitching patterns of hydrophilic yarns and the confined liquid volume. Moreover, the fluidic resistances of various configurations of connecting fibers are quantitatively investigated. Furthermore, a demonstration of the liquid collection ability of MST has been demonstrated on an artificial skin model. The MST can be potentially applied to large volume and continuous biofluidic collection and removal.

Computing Profiles of Porosity and Surface/Volume Ratio in a Packed Bed Using Monte Carlo Method

2013 ◽  
Author(s):  
Genong Li
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Particle Diameter ◽  
Volume Ratio ◽  
Packed Bed ◽  
Diameter Ratio ◽  
Accuracy Requirement ◽  
Radial Profiles ◽  
Novel Method ◽  
Rigorous Error

Porosity and surface/volume ratio are two important parameters for a packed bed. In cylindrical packed beds at low tube-to-particle diameter ratio, they vary greatly in the radial direction. In the existing literature, radial profiles of porosity and surface/volume ratio have been computed using some analytical equations which involve elliptic integrals. In this paper, a Monte Carlo method is used to compute those profiles. To the authors’ knowledge, the method has never been employed in this context. The procedure of using this novel method is explained in detail. Through a rigorous error analysis based on statistics, the accuracy of the simulation result can be controlled. Before any simulation, the number of sampling points needed in the Monte Carlo simulation can be determined given an accuracy requirement. The method is completely general and can be used to compute profiles of porosity and surface/volume ratio in any packed bed with any shape of packing elements.

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