Capillary Force Model Research Articles

Analysis of wettability and oil-water separation mechanism of superhydrophilic/underwater superoleophobic mesh based on capillary force model

The Frequent oil spills at sea and large discharges of oily wastewater spills seriously jeopardize the ecological environment and lead to an increasing shortage of water resources, so the oil/water separation has become a hot spot of global research. As opposed to the conventional separation method, the membrane separation has received wide attention because of its advantages of green environmental protection, low energy consumption and easy operation. In this paper, Cu(OH)2 mesh with superhydrophilic and underwater superoleophobic properties were prepared by in-situ growth method using purple copper mesh as the substrate. Scanning electron microscopy, x-ray photoelectron spectroscopy and contact angle tests were used to evaluate the surface morphology, chemical composition and wetting behavior of the mesh. The results showed that the water contact angle was 0° in air and the contact angle was 155.4° for oil droplets underwater. The membrane exhibited high separation efficiencies (99%) and separation fluxes (3.67-6.54×104 L·m-2·h-1) for the five tested oils under gravity drive. The wettability of the mesh was unaffected after 20 separation experiments. The surface wettability and the oil/water separation mechanism were analyzed using the capillary force-based separation model combined with the Young and Cassie-Baxter equations.

Three-dimensional CFD simulation of geyser boiling in high-temperature sodium heat pipe

A deep understanding of the characteristics and mechanism of geyser boiling and capillary pumping is necessary to optimize a high-temperature sodium heat pipe. In this work, the Volume of Fluid (VOF) two-phase model and the capillary force model in the mesh wick were used to model the complex phase change and fluid flow in the heat pipe. Computational Fluid Dynamics (CFD) simulations successfully predicted the process of bubble nucleation, growth, aggregation, and detachment from the wall in the liquid pool of the evaporation section of the heat pipe in horizontal and tilted states, as well as the reflux phenomenon of capillary suction within the wick. The accuracy and stability of the capillary force model within the wick were verified. In addition, the causes of geyser boiling in heat pipes were analyzed by extracting the oscillation distribution of heat pipe wall temperature. The results show that adding the capillary force model within the wick structure can reasonably simulate the liquid backflow phenomenon at the condensation; Under the horizontal and inclined operating conditions of the heat pipe, the phenomenon of local dry-out will occur, resulting in a sharp increase in local temperature. The speed of bubble detachment and the timely reflux of liquid sodium (condensate) replenishment in the wick play a vital role in the geyser temperature oscillation of the tube wall. The numerical simulation method and the results of this study are anticipated to provide a good reference for the investigation of geyser boiling in high-temperature heat pipes.

Computational modelling of gas–liquid–solid multiphase free surface flow with and without evaporation

Gas–liquid–solid multiphase systems are ubiquitous in engineering applications, e.g. inkjet printing, spray drying and coating. Developing a numerical framework for modelling these multiphase systems is of great significance. An improved, resolved computational fluid dynamics-discrete element method (CFD-DEM) framework is developed to model the multiphase free surface flow with and without evaporation. An improved capillary force model is developed to compute the capillary interactions for partially floating particles at a free surface. Three well-known benchmark cases, namely drag coefficient calculation, the single sphere settling, and drafting-kissing-tumbling of two particles are conducted to validate the resolved CFD-DEM model. It turns out that the resolved CFD-DEM model developed in this paper can accurately calculate the fluid–solid interactions and predict the trajectory of solid particles interacting with the liquid phase. Numerical demonstrations, namely two particles moving along a free surface when the liquid phase evaporates, and particle transport and accumulations inside an evaporating sessile droplet show the performance of the resolved model.

CFD-DEM validation and simulation of gas–liquid–solid three phase high-speed jet flow

Gas–solid–liquid flows are central to many industrial and natural processes. This paper investigates high-speed particle-laden water jets using both numerical and experimental approaches. The study considers key parameters such as converging angles (from 5 to 60 degrees), solids mass fraction (from 0.1. to 0.3), and mean jet velocity (from 20 to 28 m/s) using a particle sample with a mean size of 200 μm. A CFD-VOF-DEM model was developed and validated against standard single-particle release into water and application-specific tests of high-speed jet flow. The effect of drag model selection was investigated and the Gidaspow drag model showed optimal results compared to other empirical models. Results of initial experimental work indicated limited jet spread of particle-barren and particle-laden jets. Integrating a capillary force model into the numerical framework ensured constrained jet spread and particle entrainment within the liquid phase. High-speed imaging and surface feature tracking methods provided data that supported the numerical findings. The research offers a practical approach to understanding three-phase jet behaviors with potential implications for optimizing industrial processes involving such flows.

Nanobubble-Induced Aggregation of Ultrafine Particles: A Molecular Dynamics Study.

Nanobubble-induced aggregation (NBIA) of fine and ultrafine particles in liquid is a promising method for enhancing floatation rates in mineral processing, cleaning contaminants from water, and reviving marine ecosystems. Although the current experimental techniques can measure the nanobubble capillary force between two surfaces with controlled approach speed, they are not capable of imaging NBIA dynamics of fine/ultrafine particles by real-time observation with nanoscale spatial resolution. In this work, we use molecular dynamics (MD) simulations to study dynamics of NBIA of Ag particles in a Lennard-Jones fluid system. The molecular-level modeling allows us to study microscopic details of NBIA dynamics that are inaccessible by current experimental means. Using MD simulations, we investigated the effects of NB size, surface wettability, surface roughness, and contact line pinning on NBIA dynamics. Our modeling results show that both concave NB bridges between two hydrophobic surfaces and convex NB bridges between two hydrophilic surfaces can result in an attractive nanobubble capillary force (NBCF) that causes the aggregation of Ag particles in liquids. The equilibrium separation between two fully aggregated particles can be well predicted by the improved capillary force model. We also observe that the change of contact angle after the contact line pinning occurs at the sharp edge of a particle, which slows the aggregation process. Our thermodynamics analysis shows that there is a critical contact angle below which the merged surface NBs will detach from the surface instead of causing aggregation. The prediction of the critical contact angle is corroborated by our MD simulation results.

Estimation Method for Residual Sodium Amount on Unloaded Dummy Fuel Assembly

This study has researched an estimation method for the amounts of residual sodium film and sodium lumps on dummy fuel pins in the Japanese prototype fast breeder reactor Monju by fundamental experiments and demonstration experiments. The residual sodium amounts on the pin surface were measured using three types of test specimens: (a) single pin, (b) 7-pin assembly, and (c) 169-pin assembly. The single pin and 7-pin assembly experiments revealed that the withdrawal speed of the pins and improvement of the sodium wetting drastically increased the residual sodium amounts. Furthermore, the 169-pin assembly experiments measured the practical amounts of the residual sodium in the Monju dummy fuel assembly and demonstrated sodium draining behavior through small gaps between the pins. The estimation method includes four models such as a viscosity flow model, Landau-Levich-Derjaguin (LLD) model, an empirical equation related to the Bretherton model, and a capillary force model in a tube. These calculation results were comparable to the residual sodium amounts obtained by the experiments. In the tests of improving sodium wetting, the amounts of residual sodium on the test specimen were close to 1.4 times larger than those of the thin sodium film estimated by the LLD model. The increased amount of residual sodium by improving the sodium wetting was explained by the ratio of the adhesion energy ( γ S O − γ S L ).

Numerical and experimental study on the vapor-liquid distribution of loop heat pipe with varying density of working fluid

Loop heat pipes (LHPs) are effective passive heat transfer devices that are used in the thermal management systems for satellite payloads and electronic devices. The vapor–liquid distribution in the LHP determines the LHP's operating characteristics and heat transfer mechanism. This work developed a two-dimensional transient model for an LHP based on CFD methodology. The model includes a capillary force model and a phase change model, and considers the change in vapor and liquid densities during LHP operation. The steady-state vapor–liquid distribution in the condenser under different heat loads can be simulated. To validate the calculation results, a visualization experiment was conducted on the condenser. The simulation and the experimental results agree well. It was discovered that when the LHP works in steady-state conditions, the increase in vapor density and decrease in liquid density at high heat loads is a major cause for the the growth of liquid volume fraction in the condenser. When the condenser is entirely filled with liquid, the LHP fails to operate. The simulation model can be employed for theoretical research and design optimization of LHP.

Extendibility Study of Conventional IPA Drying Process From Dynamic Fluid Model for Pattern Collapse

1. IntroductionIPA (iso-Propyl alcohol) has been widely used in semiconductor manufacturing for drying silicon wafer to mitigate water mark and keep the surface clean after wet cleaning process. Then, IPA process has been extended by combining with the other engineering techniques such as surface modification treatment to dry fragile nano-sized Si patterns [1]. As the scaling of advanced semiconductor devices continues, however, the pattern collapse is one of the most challenging issues for IPA drying process today. Capillary force model explains the pattern collapse in the earlier studies, where Laplace pressure originated from meniscus between patterns is a critical factor [2]. And the model has been well referred to and extensively studied in semiconductor industry [3]. Although, the model does not take dynamics of fluid into account, our experimental result suggests that drying rate is also critical, i.e., pattern collapse rate decreases as drying rate increases. This result is not explained by the reported models since the drying rate is not considered as a variable. In this report, a new model is suggested and verified by unique experiments. Our proposed model assumed that osmosis of metastable liquid to nano-size structures occurs from the triple line which is the air-liquid-solid interface, and the region of osmosis is less favorable for pattern collapse. The width of osmosis region would be determined by the drying rate. Also, based on this study, extendibility of IPA drying process to smaller device feature size for advanced node is discussed.2. ExperimentalWafer processing was conducted in spin process chamber on HVM equipment for drying experiment. IPA was dispensed on rotating wafer then dried at 0 or 1500 rpm. Nano-structured wafer used was with 34 nm-diameter of Si pillars, and aspect ratio (AR) of the pillar was 12:1. Pattern collapse was observed by top-view SEM, and collapse rate was calculated by automated image analysis with obtained SEM pictures. For osmosis observation at the triple line, FPM was prepared by mixing 49% HF, 30% H2O2 and H2O at volume ratio of 1:2:100. A droplet of FPM was dropped on the surface of Si pillar pattern wafer and observed by optical microscopy while the drop was drying out. After drying, pattern collapse of the pillar pattern was observed by X-SEM. To study effect of drying rate and to maximize it, IPA was dispensed on 10×12 mm2 coupon, then vaporized at 0 rpm with flash lamp annealing. AR of the pillar was 16:1. Observation of pattern collapse by top-view SEM was also conducted.3. Results and DiscussionIPA drying at 0 and 1500 rpm resulted in collapse rate of 91.1% and 46.9%, respectively, on the pillar AR = 12:1 (Fig. 1). IPA was dried out faster when wafer rotation speed was 1500 rpm. Thus, collapse rate decreases as drying speed increases. On osmosis observation, FPM droplet was sucked into between the pillars, causing osmosis at around droplet, and generated colored interference according to liquid film thickness. X-SEM inspection after the droplet drying indicated the most pattern collapse seemed to occur at the osmosis region where liquid thickness nearly equals to the pillar height. We assumed by increasing drying rate the osmosis region would be minimized and the pattern collapse would be suppressed. To verify this model, the following evaluation was conducted. With extremely high drying rate of IPA by flash lamp annealing, we obtained 0% of collapse rate even in the pillar AR = 16:1 (Fig. 2). This result indicates that there is some more process margin for the pattern collapse on IPA drying process.4. ConclusionIn the IPA drying process, collapse rate decreases as drying rate increases. Our proposed model assumed that osmosis region of metastable liquid to nano-size structures occurs from the triple line, and the pattern collapse happens there. That explains reasoning for lower collapse rate at higher drying speed is that osmosis is minimized when drying rate is maximized. Test result from maximized IPA drying rate by flash lamp annealing indicates that there is some more process margin for the pattern collapse. In our view, by this method IPA drying process might be extended to two more device nodes.

Rayleigh-Plateau Instability of a Particle-Laden Liquid Column: ALattice Boltzmann Study.

Colloidal particles known to be capable of stabilizing fluid-fluid interfaces have been widely applied in emulsion preparation, but their precise role and underlying influencing mechanism remain poorly understood. In this study, a perturbed liquid column with particles evenly distributed on its surface is investigated using a three-dimensional lattice Boltzmann method, which is built upon the color-gradient two-phase flow model but with a new capillary force model and a momentum exchange method for particle dynamics. The developed method is first validated by simulating the wetting behavior of a particle on a fluid interface and the classic Rayleigh-Plateau instability and is then used to explore the effects of particle concentration and contact angle on the capillary instability of the particle-laden liquid column. It is found that increasing the particle concentration can enhance the stability of the liquid column and thus delay the breakup, and the liquid column is most stable under slightly hydrophobic conditions, which corresponds to the lowest initial liquid-gas interfacial free energy. Due to different pressure gradients inside and outside the liquid column and the capillary force being directed away from the neck, hydrophobic particles tend to assemble in a less compact manner near the neck of the deformed liquid column, while hydrophilic particles prefer to gather far away from the neck. For hydrophobic particles, in addition to the influence of the initial liquid-gas interfacial free energy, the self-assembly of particles in a direction opposite to the liquid flow also contributes to opposing the rupture of the liquid column.

Validation study on a toroidal approximation-based capillary force model in the discrete element method simulation

Comprehension of wet particle behavior is of great importance in science and engineering. In the past two decades, modeling and simulation for wet particles have been extensively studied because of their various industrial applications. The discrete element method (DEM) is extensively employed to simulate the wet particle behavior. To calculate the wet particle behavior, several capillary force models have been developed so far. Roughly speaking, the capillary force models are classified into two types, namely, the analytical model and the geometrical approximation model. The analytical model is most frequently employed because of its simplicity, though only a small amount of the liquid volume is applicable. The geometrical approximation model has significant advantages because of no theoretical limitation of the liquid volume as well as its high accuracy. Incidentally, the geometrical approximation model usually expresses the liquid bridge shape by the toroidal approximation. However, validation tests for the geometrical approximation model have hardly been performed due to difficulty in incorporating the complex algorithm into the DEM. From the background, this paper aims to prove the superiority and adequacy of the geometrical approximation model in the DEM simulation for wet particles. First, the superiority of the geometrical approximation model to the analytical model is examined in a two-body system. Afterward, the following two types of validation tests are performed: granular collapse and wet powder mixing in a twin-screw kneader. In the granular collapse, the liquid content is set to be less than 4 vol. %. In the twin-screw kneader system, the liquid content is more than 5 vol. %. Through the validation tests, the adequacy of the geometrical approximation model in the DEM is proved because of the agreement between the computational and experimental results in the above systems. Consequently, this study will significantly contribute to a better understanding of wet particle behavior in science and engineering.

Nanobubble capillary force between parallel plates

The aggregation of fine or ultrafine particles in liquid due to the nanobubble (NB) bridging capillary force is a key process for many industrial applications. The magnitude and direction of the NB capillary force (NBCF) are directly affected by the geometry of the NB gas bridge between two adjoining particles. Although the NBCF can be accurately measured using experimental techniques, it is very challenging to monitor the images of a NB capillary bridge in nanoscale spatial resolution in NBCF measuring experiments. As a result, the capillary force model that predicts the dependence of the NBCF on the geometry of the NB bridge has never been explicitly verified using experimental means. In this work, molecular dynamics (MD) simulations are carried out to study the NBCF between two parallel plates. MD simulations can readily measure both the NB bridge geometry and the resulting NBCF, which allows us to explicitly verify the predictions from the capillary force model. Our modeling results show that the capillary force model gives a good prediction of the NBCF for both concave and convex NB capillary bridges. Furthermore, with the assumption of constant contact angle and number of gas atoms inside the capillary bridge, we develop an improved capillary force model, which predicts the variation of the bridge geometry and the NBCF with the separation between two parallel surfaces. The continuum predictions from the improved capillary force model are corroborated by the MD simulation results and are consistent with the existing experimental data on NBCFs between two solid surfaces.

A new relative permeability model of coal reservoir considering interface effect

During the process of gas and water production in coal reservoirs, the interface effect between gas and water should not be ignored. In this study, based on nuclear magnetic resonance technology, the unsteady displacement experiment was carried out with coal samples to monitor the interface effect, and a new relative permeability model (with a specific benchmark) is established and verified which considering the interface effect. The results show that the NMR method can be used to monitor the interface effect effectively, and in the experiment movable water controlled by the pressure difference is limited (11% and 20%), and that controlled by the interface effect is dominant (89% and 80%), which means the interface effect plays a dominant role in the two-phase flow. In the flow, the gas phase drives the water phase, and this additional driving effect results in that the relative permeability of water phase is greater than 1. The verified results show that the new model can effectively describe the driving effect which can not be achieved by the capillary force model.

A new capillary force model implemented in lattice Boltzmann method for gas–liquid–solid three-phase flows

A lattice Boltzmann method is developed for the direct numerical simulation of gas, liquid, and solid three-phase flows. The liquid–gas two-phase flow with a high density ratio is solved using a phase-field model where the interface evolution is described by the conservative Allen–Cahn equation, and the dynamics of the solid particle is captured by the momentum exchange method. By distributing the surface tension over the entire diffuse interface, a new model is proposed to account for the capillary force exerted on the particle, which not only is suited for curved boundaries but can also be implemented in a simple and accurate manner. Several typical benchmark cases, including the wetting behavior of a particle on the liquid–gas interface, a bubble adhering to a particle that can move freely, and the sinking of a horizontal cylinder through an air–water interface, are used to validate the present method. Results show the necessity to incorporate the capillary force on the contact lines, especially when the surface tension is a dominant factor, and that the new capillary force model is able to calculate the capillary force accurately and suppress the oscillations of the capillary force. In addition, the capability of the present method for particle interactions is further demonstrated by studying the self-assembling behavior of three hydrophilic particles on a liquid–gas interface.

Modeling of capillary force between particles with unequal contact angle

When two particles with a thin liquid film are colliding toward each other, liquid films merge to form a pendular liquid bridge, which may induce a strong capillary force. The capillary force is determined by the particle size as well as contact parameters, such as liquid volume, contact angles of liquid on each particle, and the separation distance. Upon considering all these impacting factors, a general and explicit capillary force model was established in this study with a minimal energy method by using the software-Surface Evolver. The developed model was validated by comparing results with those obtained through an analytical expression and previous closed-form models. The developed capillary force model is capable of predicting the capillary force between two particles with different diameters and contact angles (≤50°) with an error of less than 15%.

Lattice Boltzmann model for ternary fluids with solid particles

On the basis of phase-field theory, we develop a lattice Boltzmann model for ternary fluids containing solid. We develop a modified bounce-back method to describe the interactions between the solid and N-phase (N≥2) fluids. We derive a wetting boundary condition for three-phase flows from the point of mass conservation and propose a scheme for implementing the wetting condition on curved boundaries. We develop a diffuse interface method to compute the capillary force acting on the moving solid objects at the ternary fluids-sold contact lines. In addition, this model can deal with problems involving high density and viscosity contrasts. The proposed method is examined through several test cases. We test the modified bounce-back scheme, wetting boundary condition, and capillary force model in three different cases, and the numerical results agree well with the analytical solutions. Finally, we apply the model to two three-dimensional problems to assess its numerical accuracy and stability.

Capillary forces on wet particles with a liquid bridge transition from convex to concave

The transition of a liquid bridge profile from convex to concave and the associated capillary forces are experimentally studied via particle-particle and particle-plane pairs. The results demonstrate that a convex liquid bridge appears at a relatively large water volume and small separation distance, where the capillary force remains approximately constant. As the separation distance increases, the liquid bridge is stretched from convex to concave, and the capillary force initially doesn't change much but increases to the maximum value and then decreases gradually. By combining analytical analysis and experimental data, a framework is proposed for predicting the evolution of liquid bridge profiles. Additionally, a capillary force model that is applicable to both convex and concave liquid bridges is formulated. The applicability of this force model to multiple-particle systems is demonstrated by comparing DEM predictions of repose angles of sandpile and hopper flow discharge rates with experimental measurements at various water contents.

Agglomeration Mechanism of Complex Ti-Al Oxides in Liquid Ferrous Alloys Considering High-Temperature Interfacial Phenomenon

This work presents the agglomeration mechanism of complex Ti-Al oxides in the liquid ferrous alloy. Cluster characteristics were investigated using Al and Ti/Al-complex deoxidation method in lab scale. The time-dependent size distribution, total number per volume, average size, and circularity of the clusters were quantitatively analyzed. Furthermore, high-temperature confocal laser scanning microscopy was utilized to directly observe the cluster formation of Ti-Al oxides. A capillary force model including wettability parameters was applied to compare the agglomeration capabilities of different types of non-metallic inclusions. When a low Ti is added into melt, the agglomeration of TiOx·FeO liquid inclusions is one of the key factors to decrease the frequency of cluster formation. When the Al is added into melt, the heterogeneous precipitation on TiOx·FeO surfaces is the main reaction process. Ti-Al oxides have lower agglomeration ability than that of Al2O3, which in turn, contribute to a low agglomeration frequency as well.

Numerical simulation of wet particle flows in an intensive mixer

Simulations of wet particle flow in an intensive mixer were conducted based on three-dimensional discrete element methods (DEM). Mikami capillary force model was introduced to mimic the complex effects of pendular liquid bridges in the granular flow. Lacey mixing index was adopted to evaluate the dynamic process of particle system. Experiments of intensive mixer tester were carried out for validating the simulation model during the mixing process. It was found that the blade torque increases with higher liquid fraction due to the damping action of capillary forces. Bigger particle size, high blade, and vessel speed can also increase the blade toque as the pronounced velocity fluctuation. Our results indicate the contact number decreases with higher blade speed and vessel speed, while it is little affected by the liquid fraction. The analysis of mixing quality shows that high homogeneity of particles distribution is obtained with higher blade speed and small particle size, while liquid fraction and vessel speed have little influence during the dynamic equilibrium stage.

Experimental Investigation of the System Nonmetallic Inclusion-Molten Steel-Refractory System at High Temperatures

In continuous casting, the buildup of particles in the flow control system is called clogging. Clogging may be caused by preexisting nonmetallic inclusions attached to the refractory wall, interrupting or disturbing the fluid flow conditions. The interfacial properties of the nonmetallic inclusion-molten steel-refractory system are believed to play a key role in the clogging tendency of selected steel grades in contact with ceramics. The combination of a high-temperature laser scanning confocal microscope (HT-LSCM), which is employed for in situ observation of inclusions’ behavior in the liquid steel or at the steel/ceramic interface, and a high-temperature drop shape analyzer (HT-DSA), which is utilized for contact angle measurements, enabled the investigation of reactions and interactions in the described system at experimental temperatures of approximately 1600 °C. The objective of this study was to develop a method to obtain qualitative information on the deposition of nonmetallic inclusions (NMIs) in the submerged entry nozzle (SEN) during casting. The behavior of solid NMIs from a calcium-treated steel at the interface between liquid steel and Al2O3 or MgO was investigated by means of HT-LSCM. During the test evaluation, inclusions were found to separate at the steel/ceramic interface due to an attractive force. This force increased with the NMIs’ size as well as with the ceramic particle change. The HT-DSA provided contact angle data between molten steel and the ceramic used for implementation into the theoretical capillary force model. A clear correspondence between the estimated and calculated capillary forces was observed. The change in the wettability of the system, as induced by the change in the ceramic from MgO to Al2O3, showed a reduction of the attractive forces, indicating a weaker separation toward the SEN for the same inclusion type. This study confirmed the strong potential of wettability investigations to predict the clogging tendency of certain steel grades.

In situ observation of deformation behavior of chain aggregate inclusions: a case study for Al2O3 at a liquid steel/argon interface

Particle aggregation is a widespread phenomenon spontaneously occurring in nature, and it is also widely explored in industry, for instance, metallurgical engineering and colloid chemical engineering. In this work, deformation behavior of Al2O3 aggregates in liquid steel is investigated as a case study. Using high-temperature confocal laser scanning microscopy, the morphologies of Al2O3 chain aggregates during their deformation are observed in situ at liquid steel/Ar interface. Thereafter, the change of morphology of aggregates over time is quantitatively investigated, and the results show that circularity of aggregates increases during deformation. This fact indicates that the morphology of aggregates tends towards spherical with time. The bending forces between the particles in an aggregate during the deformation are calculated based on the experimental data obtained from in situ observations. The force exerted to cause bending is predicted by the capillary force model established for attractive capillary force of inclusions. It is found that the bending force is slightly lower than the capillary force, and this indicates that the capillary force plays a significant role in the bending of aggregates during deformation. Moreover, the difference between the two forces is due to a resistance force existed from inflection part of the aggregate during deformation. The residence is quantitatively evaluated, and there is a clear tendency showing that the resistance force increases with decreasing distance between two particles during bending. In addition, initial sintering between contacted particles after bending is reported, and the radius of neck formed between sintered particles is evaluated. Finally, the effects of inclusion size and steel flow velocity in actual steelmaking process on the radius of neck and shear stress exerted on the sintered neck during deformation are discussed.