Surface Tension Energy Research Articles

Model for atomization droplet size and energy distribution ratio at the distal end of an electrostatic nozzle

Electrostatic atomization minimum quantity lubrication (EMQL) employs the synergistic effect of multiple physical fields to atomize minute quantities of lubricant. This innovative methodology is distinguished by its capacity to ameliorate the atomization attributes of the lubricant substantially, which subsequently augments the migratory and infiltration proficiency of the droplets within the complex and demanding milieu of the cutting zone. Compared with the traditional minimum quantity lubrication (MQL), the EMQL process is further complicated by the multiphysical field influences. The presence of multiple physical fields not only increases the complexity of the forces acting on the liquid film but also induces changes in the physical properties of the lubricant itself, thus making the analysis of atomization characteristics and energy distribution particularly challenging. To address this objective reality, the current study has conducted a meticulous measurement of the volume average diameter, size distribution span, and the percentage concentration of inhalable particles of the charged droplets at various intercept positions of the EMQL nozzle. A predictive model for the volume-averaged droplet size at the far end of the EMQL nozzle was established with the observed statistical value F of 825.2125, which indicates a high regression accuracy of the model. Furthermore, based on the changes in the potential energy of surface tension, the loss of kinetic energy of gas, and the electric field work at different nozzle orifice positions in the EMQL system, an energy distribution ratio model for EMQL was developed. The energy distribution ratio coefficients under operating conditions of 0.1 MPa air pressure and 0 to 40 kV voltage on the 20 mm cross-section ranged from 3.094‰ to 3.458‰, while all other operating conditions and cross-sections had energy distribution ratios below 2.06‰. This research is expected to act as a catalyst for the progression of EMQL by stimulating innovation in the sphere of precision manufacturing, providing theoretical foundations, and offering practical guidance for the further development of EMQL technology.

On the size- and shape-dependence of integral and partial molar Gibbs energies, entropies, enthalpies and inner energies of solid and liquid nano-particles

In this paper the size- and shape dependences of 8 different integral and partial molar thermodynamic quantities are derived for solid and liquid nano-phases, starting from the fundamental equation of Gibbs: i) The integral molar Gibbs energies of nano-phases and the partial molar Gibbs energies of components in those nano-phases, ii) The integral molar enthalpies of nano-phases and the partial molar enthalpies of components in those nano-phases, iii) The integral molar entropies of nano-phases and the partial molar entropies of components in those nano-phases, and iv). The integral molar inner energies of nano-phases and the partial molar inner energies of components in those nano-phases. All these 8 functions are found proportional to the specific surface area of the phase, defined as the ratio of its surface area to its volume. The equations for specific surface areas of phases of different shapes are different, but all of them are inversely proportional to the characteristic size of the phase, such as the diameter of a nano-sphere, the side-length of a nano-cube or the thickness of a thin film. Therefore, the deviations of all properties discussed here from their macroscopic values are inversely proportional to their characteristic sizes. The 8 equations derived in this paper follow strict derivations from the fundamental equation of Gibbs. Only the temperature dependent surface energy of solids and surface tension of liquids will be considered as model equations to simplify the final resulting equations. The theoretical equations are validated for the molar Gibbs energy against the experimental values of liquidus temperatures of pure lead. The theoretical equations for the molar enthalpy are validated i). Against the experimental values of dissolution enthalpy differences between nano- and macro cobalt particles in the same liquid alloy and ii). Against the size dependent melting enthalpy of nano-indium particles. In this way, also the theoretical equations for the molar entropy and molar inner energy are validated as they are closely related to the validated equations for the molar Gibbs energy and molar enthalpy.

Thermodynamic characteristics and surface free energy analysis of bifonazole and lecithin with sodium dodecyl sulfate in hydroethanolic solvent systems

The thermodynamic investigations of the well-recognised antifungal drug bifonazole and lecithin with anionic surfactant sodium dodecyl sulphate have been established. The experiments were conducted using five distinct hydro-ethanolic concentrations, namely 0% v/v, 10% v/v, 30% v/v, 70% v/v, and 90% v/v ethanol, throughout a range of five temperatures (ranging 20 ℃, 25 ℃, 30 ℃, 35 ℃ and 40 ℃) with an increment of drug concentration. The study involved the determination of several parameters, including surface tension (σ), density (ρ), conductivity (κ), contact angle (θ) and surface free energy. Conductivity and surface tension data was used for calculating critical micelle concentration (CMC). CMC was utilised to calculate various thermodynamic properties, such as the standard entropy change (ΔS°m), standard Gibbs energy change (ΔG°m) and standard enthalpy change (ΔH°m) of micellization. This study represents a comparative analysis of the critical micelle concentration (CMC) by utilising surface tension and conductivity measurements. Contact angle is used to determine the hydrophobicity and hydrophilicity of the system. These investigations are valuable for examining the magnitude of hydrophobic interactions within the system, which might be used to ascertain an optimal concentration of bifonazole, lecithin and surfactant to prepare ethosomal formulations.

Effect of CaO/MgO on rheological properties and structure of CaO–MgO–SiO2–Al2O3-50 % TiO2 slag with SiO2/Al2O3=1.0

The rheological properties, including viscosity, melting temperature, surface tension, density, and viscous activation energy (Eη) were systematically investigated in the CaO–MgO–SiO2–Al2O3-50 % TiO2 slag system with SiO2/Al2O3 = 1.0. The effect of CaO/MgO on the structure and phase composition of the slag was studied using Raman spectroscopy and X-ray diffraction (XRD). The results of viscosity properties indicate that as the CaO/MgO ratio in the slag increase, viscosity and the viscous activation tend to decrease. Melting temperature and surface tension decreases with increasing CaO/MgO, while density increases. As the CaO/MgO ratio in the slag increases, polymerization decreases, leading to the dissociated basic oxides into metal cations and oxygen anions. This addition of basic oxides provides more O2−, increasing the O/Si ratio, disintegrating complex silica-oxygen composite ions into simple silica-oxygen composite anion, and reducing viscosity. Anosovite (MgTi2O5), CaAl2Si2O8, Mg (Al, Ti)2O4, spinel (MgAl2O4), augite (Ca (Mg, Fe, Al) (Al, Si)2O6) and Ca12Al14O33 were identified as the primary phases in slag. The appropriate CaO/MgO should not exceed 0.76. These findings will serve as a valuable technical foundation to support the development of the direct reduction smelting process for the comprehensive utilization of vanadium titanomagnetite.

Magnetic field assisted centrifugal acceleration thin-layer chromatography: An approach to investigate the magnetic field effects on separation parameters including retention factor difference, selectivity factor, and resolution

The effect of internal and external magnetic fields on the separation of antifungal drugs by centrifugal acceleration thin-layer chromatography was reported for the first time. External and internal magnetic fields were applied using neodymium magnets and CoFe2O4@SiO2 ferromagnetic nanoparticles. Separation of ketoconazole and clotrimazole was performed using a mobile phase consisting of n-hexane, ethyl acetate, ethanol, and ammonia (2.0:2.0:0.5:0.2, v/v). The influence of the magnetic field on the entire chromatographic system led to changes in the properties of the stationary and mobile phases and the analytes affecting the retention factor, shape, and width of the separated rings. The extent of this impact depended on the structure of the analyte and the type and intensity of the magnetic field. In the presence of the external magnetic field, there were more significant changes in the chromatographic parameters of the drugs, especially the width of the separated rings, and ketoconazole was more affected than clotrimazole. The changes are conceivably due to the effect of the magnetic field on the analyte distribution between the stationary and mobile phases, which is also caused by the possibility of the magnetic field affecting the viscosity, surface tension, and surface free energy between the stationary and mobile phases.

Shear-Induced Fabrication of Cellulose Nanofibril/Liquid Metal Nanocomposite Films for Flexible Electromagnetic Interference Shielding and Thermal Management.

To address electromagnetic interference (EMI) pollution in modern society, the development of ultrathin, high-performance, and highly stable EMI shielding materials is highly desired. Liquid metal (LM) based conductive materials have received enormous amounts of attention. However, the processing approach of LM/polymer composites represents great challenges due to the high surface tension and cohesive energy of LMs. In this study, we develop a universal one-step fabrication strategy to directly process composites containing LMs and cellulose nanofibrils (CNFs) and successfully fabricate the ultrathin, flexible, and stable EMI shielding films with an average specific EMI shielding efficiency (EMI SE) value of 429 dB/mm and small thickness of only 70 μm in the wide frequency range of 8.2-18 GHz. In addition, the resulting films also exhibit excellent mechanical performance and flexibility, which endow the film with the ability to withstand repeated folding, bending, and folding into complex shapes without producing cracks or fractures. Besides, the resulting films display excellent thermal conductivity with a λ of 4.90 W/(m K) and an α of 3.17 mm2/s. Thus, the presented approach shows great potential in fabricating advanced materials for EMI shielding applications.

Understanding mono- and bi-metallic Au and Ni nanoparticle responses to fast heating.

Nanoparticle assembly, alloying and fragmentation are fundamental processes with significant implications in various fields such as catalysis, materials science, and nanotechnology. Understanding these processes under fast heating conditions is crucial for tailoring nanoparticle properties and optimizing their applications. For this, we employ molecular dynamics simulations to obtain atomic-level insights into nanoparticle behavior. The performed simulations reveal intricate details of sintering, alloying and fragmentation mechanisms shedding light on the underlying physical phenomena governing these processes. The calculation results help to visualize nanoparticle evolution upon undercritical and supercritical heating elucidating not only the role of temperature, but also of nanoparticle sizes and composition. In particular, it is shown that surface tension and surface energy play important roles not only in nanoparticle melting but also in its fragmentation. When the added energy exceeds a critical threshold, the nanoparticle begins to experience alternating compression and expansion. If the tensile stress surpasses the material's strength limit, fragmentation becomes prominent. For very small particles (with radius smaller than ∼10 nm), this occurs more rapidly, whereas sub-nano-cavitation precedes the final fragmentation in larger particles, which behave more like droplets. Interestingly, this effect depends on composition in the case of AuNi alloy nanoparticles, as expected from the phase diagrams and excess energy. The heating level required to overcome the mixing barrier is also determined and is shown to play an important role in the evolution of AuNi nanoparticles, in addition to their size. Furthermore, our findings provide insights into controlling nanoparticle synthesis for various applications in numerous nanotechnological domains, such as catalysis, sensors, material analysis, as well as deseas diagnostics and treatment. This study bridges the gap between experimental observations and theoretical predictions paving the way for designing advanced nanomaterials with enhanced functionalities.

The Shape of a Compressible Drop on a Vibrating Solid Plate

The influence of high-frequency vibrations on the shape of a compressible drop placed on an oscillating solid substrate is studied in this paper. Due to the significant difference in characteristic temporal scales, the average and pulsating motions of the drop can be considered separately. For nearly hemispherical drop, the solution to the problem of pulsating motion is found in the form of series in Legendre polynomials. Frequencies of natural sound oscillations of hemispherical axisymmetric drop are obtained. Resonances of the acoustic mode of drop oscillations are found. The problem of forced oscillations of hemispherical drop in the limit of weakly compressible liquid is considered. It is found that drop oscillation amplitude grows with vibration intensity according to quadratic law, which is consistent with the solution of the pulsation problem for finite compressibility assumption. A variational principle for calculation of average drop shape is formulated based on minimization of energy functional for the case, so the compressibility of the liquid should be taken into account. It is shown that the functional (the sum of the kinetic and potential energies of the pulsating flow, the kinetic energy of the averaged flow, and the surface tension energy of the drop) decreases and reaches a minimum value at quasi-equilibrium state, in which the average shape of the drop becomes static. The influence of vibrations on the drop shape is studied for small values of the vibrational parameter. The surface of the drop in the absence of vibrations is assumed to be hemispherical. Calculations showed that under vibrations, drop height decreases, while the area of the base increases.

Formation and elimination mechanisms of prior particle boundaries in a new powder metallurgy superalloy

The formation of prior particle boundaries (PPBs) in a new powder metallurgy superalloy during hot isostatic pressing (HIP) is investigated. Also, the impact of subsequent hot deformation on the elimination of PPBs is systematically studied. The PPBs involves large γ′ phases, carbides (MC and M6C) and oxides (Al2O3, SiO2 and ZrO2). The reactions among the superficial oxides, the adsorbed C and O elements on the particle surface and internally-migrated alloying elements are the dominant reasons for the formation of PPBs during HIP. Besides, the existence of surface tension and surface energy induces the carbon segregation, as well as the formation of PPBs. Thus, the density of PPBs decreases when the spacing between powders is shrunk by a rapid deformation. In hot forming process, the PPBs can be efficiently eliminated via raising deformation temperature/true strain or reducing strain rate. The interactions between dislocations and PPBs, as well as the occurrence of dynamic recrystallization (DRX) induced by the strain/orientation gradient, lead to the elimination of PPBs. The thermodynamic stability of carbides declines with the raised temperature. It indicates that the dissolution of carbides and the elimination of PPBs can be accelerated via raising the deformation temperature. The breakage or deformation behavior of PPBs during hot extrusion is investigated by numerical simulation. The deformation degree of PPBs increases with the raised extrusion ratio. The above important findings are useful for developing hot extrusion processing to effectively eliminate PPBs.

Temperature-Dependence of Mixing Properties of Cu-Ti Liquid Alloy

In this study, the temperature-dependence of thermodynamic and surface properties of Cu-Ti binary liquid alloy were studied. In thermodynamic properties, excess Gibbs free energy of mixing, enthalpy of mixing, excess entropy of mixing, and activity of the system were computed at 1873 K. The surface properties were analyzed by computing the surface tension and surface concentration of the system. Thermodynamic properties were computed in the framework of the Redlich-Kister polynomial, and the surface properties were computed using the Butler model. At its melting point, the system exhibited a tendency for the formation of compounds, and as the Cu concentration was increased, the surface tension of the system gradually decreased. The excess Gibbs free energy of mixing, activity and surface tension of the system were also computed at different temperatures, in the range 1873-2173 K. With the increase in temperature of the system, the compound forming tendency of the system gradually decreased.

Interface characteristics and stability mechanisms of bubbles in high-concentration bentonite slurry

Foam and slurry are important materials for preventing spewing of the earth pressure balance (EPB) shields, but their interaction at the interface level is not entirely understood. Herein, an anionic surfactant was used to foam bentonite slurry with a concentration of 10–30 wt%. The mechanism of the slurry on the foamability of the surfactant and the bubbles stability were analysed through surface viscoelastic modulus, ζ-potential, FT-IR, surface tension, contact angle, and microscopic observation. The results show that the bentonite slurry forms a stable three-dimensional grid structure, which increases the surface tension and free energy required for the formation of the gas–water interface. Surfactants are adsorbed on the bound water layer on the surface of bentonite particles. This increases both the electrostatic repulsion of system and the hydrophobicity of the particle and forms a multi-layered gas–water interface with high viscoelasticity, thus slowing down the drainage, coarsening, and coalescence.

Influence of the Filtration Velocity on the Local Oil Distribution of Oleophilic Coalescence Filter Media

Fibrous nonwoven coalescence filters are commonly utilized in gas-cleaning processes to separate liquid droplets from a gas stream, e.g., oil mists. These filters are mainly composed of micro glass fibers and in some cases, small amounts of synthetic fibers. The shape of the deposited oil on filter fibers of the filter media depends on several factors, including the oil saturation, wettability, roughness, diameter of the fibers and fiber arrangement. The oil deposits can take the form of, e.g., axially symmetric barrel-shaped droplets or larger structures, such as oil sails between adjacent fibers. Understanding the initial state of the coalescence filtration process and the impact of the deposited oil structures on the separation efficiency requires characterizing these structures. X-ray microtomography (µ-CT) and artificial intelligence tools for segmentation can be utilized to visualize, identify and analyze deposited oil structures in the micrometer region. To quantify and compare oil structures formed at three distinct filtration velocities (10, 25 and 40 cm s−1) commonly utilized in industrial applications and one defined oil saturation of oleophilic coalescence filter media, applying X-ray microtomography is the main emphasis of this work. The results indicate that there is no significant influence of the filtration velocity on the local saturation (determined via µ-CT), the number- and volume-based fractions of the identified deposited oil structures on or between adjacent fibers as well as the droplet concentrations and distributions of deposited oil droplets. It is assumed that the structure of the deposited oil formed by coalescence in the filter medium is dominated by the wetting properties of the fibers (surface tension and surface energy) and the saturation, independent of the filtration velocity.

Investigations on wetting and structural behavior using CaF2-SiO2-CaO-22.5%TiO2 SMAW electrode coating for AUSC applications

This study investigates the structural behavior and high-temperature wettability of a CaF2-SiO2-CaO-22.5%TiO2 shielded metal arc welding electrode coating for advanced ultra-supercritical power plant applications. The wettability parameters were measured, including contact angle, spread area, adhesion energy, and surface tension. Extreme vertices mixture design approaches were used to develop 13 different electrode coatings. To determine the contact angle at solid/liquid interface, circular pellets were made from powder samples and heated inside the furnace at 1125°C at a constant heating rate. Young's and Boni's equations are used to calculate the surface tension value for 13 coated samples using the calculated contact angle. Adhesion energy for 13 coated samples is calculated using Dupre's equation. Phases and structural behavior of coating samples were measured by Fourier transform infrared spectroscopy and X-ray diffraction. The developed regression model estimates the impact of primary ingredients and their interaction on the calculated wettability characteristics. CaF2.SiO2, CaO.SiO2, and CaO.CaF2 binary mixture is the more favorable and substantially impacts contact angle, whereas ternary interactions of CaO.SiO2.CaF2 shows an opposite effect on contact angle. Coating numbers 2 and 10 give better wetting behavior and spread area due to the low value of contact angles. Individual ingredient shows an increasing effect on surface tension and adhesion energy. Ternary component of CaO.CaF2.SiO2 is favorable and shows an increasing impact on adhesion energy.

Molecular Dynamic Modeling of Magnesium in the Scheme of the Embedded Atom Model

Potentials of the embedded atom model (EAM) for solid and liquid magnesium are proposed. Properties of magnesium are studied by means of molecular dynamics (MD) at binodals of up to 1500 K, and under conditions of static and shock compression. The main characteristics of bcc and liquid magnesium (structure, density, energy, compressibility, speed of sound, and coefficients of self-diffusion) are calculated. The static compression isotherm at 298 K up to a pressure of 108 GPa and the Hugoniot adiabat up to a pressure of 80 GPa are calculated with allowance for electron contributions. Values of the excess energy of the surfaces of magnesium nanoclusters with 13 to 2869 particles are found, and the Gibbs–Helmholtz equation for the relationship between surface tension and surface energy is estimated.

Fe3O4@SiO2 Core–Shell Nanoparticles: Synthesis, Characterization Prepared by Green Method for Iraqi Aloe Vera Extract

In this work, a green approach was used to create Fe3O4 nanoparticles. After that, ferrous chloride tetrahydrate and ferric chloride hexahydrate solutions were mixed with various quantities of Iraqi Aloe Vera gel and sodium hydroxide solution to achieve pH(8). Then, in the scale synthesis of silica-coated iron oxide NPs utilizing nontoxic and low-cost materials, tetraethyl orthosilicate (TEOS) was employed as a precursor to silica. (UV–Vis), FT-IR, XRD, AFM, EDS, TEM, Zeta Potential, VSM, FESEM and VSM were used to characterize the as-prepared silica-coated (Fe3O4@SiO2 CSNPs) and Fe3O4 NPs. UV–Vis exhibits an absorption band in the ultraviolet region at approximately 300 nm in Fe3O4NPs and 310[Formula: see text]nm in Fe3O4@SiO2 CSNPs, this means red shift occurs successively. Results of (XRD) and (EDS) analyses demonstrate that magnetite nanoparticles were effectively coated using this easy process. FESEM and TEM measurements demonstrate that the particle size of iron oxide nanoparticles and iron oxide NPs CSNPs increases before and after coating with spherical particles in form. AFM evaluates surface tension and surface energy. It is found that the surface roughness of magnetite nanoparticles NPs is 49.31[Formula: see text]nm and root mean square (RMS) is 319.8[Formula: see text]nm, whereas in core–shell it is 25.45[Formula: see text]nm and 166.7[Formula: see text]nm, respectively, it was raised in the case of the core–shell. This means decrease in particle size. Magnetic properties from (VSM) test demonstrate that the magnetization of the as-synthesized TEOS-coated magnetite NPs is lower than that of freshly created bare magnetite NPs, demonstrating the formation of Fe3O4@SiO2 CSNPs. The stability was around [Formula: see text][Formula: see text]mV, and the addition of magnetic and optical features improved their biocompatibility. The antibacterial activity of Fe3O4 NPs and Fe3O4@SiO2 CSNPs was investigated using the agar well diffusion method agains t Staphylococcus aureus Gram-positive and Escherichia coli Gram-negative bacteria, which exhibited a wide spectrum of antibacterial potency inhibiting the growth of both Gram-negative (8[Formula: see text]mm, 10[Formula: see text]mm) and Gram-positive (7[Formula: see text]mm, 12[Formula: see text]mm), respectively.

Molecular Dynamics Model of Liquid Tin in the Scheme of the Embedded Atom Model

Results from calculating the properties of liquid tin using the EAM (Embedded Atom Model) interparticle potential are analyzed, and the surface properties of tin are calculated according to molecular dynamics (MD). Calculations based on the EAM generally agree better with experiments for the properties of liquid tin than ones based on the MEAM. The accuracy of the Gibbs–Helmholtz equation for the relationship between surface tension and surface energy is evaluated.

A thermodynamic model to predict the minimum energy required for engulfment of linearly aggregated spherical nanoparticles by tubular vesicles

Understanding the interaction of nanoparticles (NPs) with fluid membranes is important to achieve safe and improved performance of NPs in various biomedical applications. Studies show that fluid membranes can drive linear attraction between spherical NPs adsorbed on it, and forms tubular vesicles (membrane tubes) to engulf (wrap) multiple particles. The present work shows the theoretical investigation of the minimum total energy for wrapping of linearly aggregated multiple spherical NPs by a low-tense membrane tube by developing a thermodynamic model that accounts for membrane bending energy, adhesion energy between particles and the membrane, and surface tension energies of the membrane in the low tension regime. The model illustrates that the minimum total energy (negative) decreases with an increasing number of particles undergoing wrapping because of the increasing contact area between the membrane and the particles; resulting in a large adhesion energy gain compensating for the deformation energy costs of the membrane. The large adhesion energy gain results in the spontaneous wrapping and high stability of multiple spherical particles filled in a membrane tube. In addition, the model predicts the critical and the minimum adhesion strength of particles required for the initiation and completion of the wrapping process, respectively. Furthermore, the model demonstrates the wrapped states (non-wrapped, partially wrapped, deeply wrapped, and completely wrapped state) of multiple particles in a membrane tube as a function of the wrapped area of particles. Thus, the developed thermodynamic model provides insights into the understanding of how the spontaneous and simultaneous wrapping of multiple spherical NPs takes place in a low-tense membrane tube.

Theoretical analysis of thermo-responsive behavior of microgels loaded with silver nanoparticles

Temperature is one of the extremely significant factors which is responsible for modifications mostly in physical but also in chemical properties of some particular matter. In present study, we carried out theoretical analysis of thermo-responsive behavior of Ag-p (N-isopropylmethacrylamide) hybrid microgels. We employed the classical Maxwellian distribution function with respect to the velocity of spherical silver nanoparticles inside the microgel’s network. The behavior of distribution function relative to the temperature represents that the distribution function still obeys the Maxwell-Boltzmann law even at low temperatures. Further, the diffusion coefficient, probability density, surface tension and surface energy of silver nano-particles are numerically evaluated and then graphically illustrated.

Thermodynamic study of superoxide dismutase adsorption processes over cysteine-gold electrode

Modification of gold electrodes with cysteine, improve superoxide dismutase (SOD) electron transfer for superoxide quantification in a typical third-generation electrochemical biosensor. However, a thermodynamic study that describes the adsorption processes of this type of assemble, has not been reported. Hence in this work, differential capacitance studies of Au/Cys, Au/SOD and Au/Cys/SOD electrodes are reported to describe the adsorption process during the different steps of the enzyme immobilization, through the calculation of charge density, surface tension, surface excess and adsorption energy. Theoretical electrostatic potential calculations of the protein using X-ray diffraction data were carried out, to rationalize the adsorption orientation of SOD according to experimental data.

A study of micro-scale solder bump geometric shapes using minimizing energy approach for different solder materials

Demand for more interconnection joints between semiconductor devices can be realized with solder bump technology. Surface tension and density are usually material properties related factors that affect solder bump geometric shape. Therefore, to cope with this fast-changing microarchitecture design in semiconductor technology, a better understanding of the solder bump geometric shape is needed. This study used a static equilibrium force approach to integrate the surface tension and gravitational energy into the solder energy content. Surface Evolver software was used to perform calculations and deliver the final solder bump shape. Perfect agreement with less than 10 % comparison between previous studies and the current Surface Evolver results was found. According to statistical analysis using SPSS, the maximum width of solder shape is closely related to the surface tension. In contrast, the maximum standoff is highly correlated with the solder density. By changing the solder volume, the solder bump changes from standard flip-chip bump to Cu pillar bump with consistency in maximum width to maximum standoff height ratio of 1.5. This study shows that the bumping technology can produce various sizes of solder bumps to meet new electronic packaging requirements.