| Droplets widely exist in the advanced metal processing and manufacturing processes,such as the manufacturing of immiscible alloys,high-precision welding and spray forming,selective laser melting or ablation,plasma metal atomization,etc.The knowledge of the fundamental data of droplet surface tension and its curvature,temperature,and alloy concentration dependencies,is the key for optimizing and regulating these critical processes.Mastering such knowledge meets our country's long-term needs in advancing the fields of metal processing and manufacturing.Because direct measurement on the surface tension of liquid droplets in experiments is difficult,many research works have been devoted to the development of ”computer experiment” measurement techniques and thermodynamic theories for accurately predicting the surface tension of droplets in recent years.However,the existing computational studies focused on the model system liquid-vapor droplets/bubbles,rather than realistic alloy droplet systems with practical application values;the state-of-the-art Morphometric Thermodynamics(MT)theory has been only validated in the hard-sphere droplet model system and has not been successfully validated in the realistic droplet systems.The current thesis adopts the equilibrium simulation technique for droplets using the Molecular-Dynamics simulation method.We choose the immiscible aluminum-lead alloy(bearing alloy)liquid droplets with practical application value as our research systems,systematically calculate a series of crucial thermodynamic properties of these droplet systems,and determine the high-precision relationships between these thermodynamic properties and the droplet sizes and temperatures.The validity of the MT theory in a realistic metal droplet system and the accurate prediction of the aluminumlead alloy droplet surface tensions are realized through the above calculations.Besides,a quantitative understanding of the critical behaviors of the liquid surface stiffness coefficients is obtained.The detailed works include:1.For a liquid-liquid interface droplet system,a set of integrated simulationcharacterization-analysis-calculation methodology has been developed.The IrvingKirkwood method coupling the spherical or cylindrical coordination for calculating the local pressure tensor components is applied.The methodology is applied to the immiscible Al-Pb alloy liquid droplet system to study the temperature and droplet size effects on the droplet radial distributions of thermodynamic properties,the densities,mutual miscibilities within spherical droplets,and the pressure components,and the stresses across the curved liquid-liquid interfaces.The temperature and droplet size dependencies of the thermodynamic quantities are obtained,such as the mutual solubilities within spherical(cylindrical)droplets and the inner pressure.Noticeable changes in mutual miscibilities in the droplet phases are seen,which correspond to the shifts of the solvus lines toward lower solubilities as temperature increases or the droplet size decreases.2.The curvature dependence of the surface tension of the aluminum-lead liquidliquid interface droplets with different temperatures and radii and the liquid column system is calculated with high precision.We found that the surface tensions of the aluminum spherical(cylindrical)droplets increase with increasing the radius,while the surface tensions of the lead spherical(cylindrical)droplets decrease with increasing the radius.This variation trend originates from the particle size mismatch between lead and aluminum and particle packing pattern as the interface is bent.With a uniform set of parameters,the MT theory can perfectly describe the calculation results of the surface tension of the spherical and the cylindrical droplets at the same time,which verifies the validity and the universality of the MT theory,with high confidence,in realistic metal droplet system with capillary wave fluctuations.By employing the MT theory to fit the calculated surface tension data,we further extracted the previously rarely reported bending stiffness and Gaussian curvature stiffness and their temperature dependencies.The magnitude of the bending stiffness of the liquid-liquid interface decreases with increasing temperature,and it is found that when the temperature reaches1300 K,the bending stiffness changes from a positive value to a negative value,which corresponds to the change of the stability of the droplet system,from a stable state at low temperature to an unstable state at high temperature.The Gaussian curvature stiffness of the liquid-liquid interface is negative at all temperatures and increases its magnitude.The magnitudes and the signs of bending stiffness and Gauss curvature stiffness can be explained analogously with the classical elastic membrane theory,yet the quantitative statistical mechanics theory is still lacking.3.The obtained bending stiffness and Gauss curvature stiffness data allow us to reveal the higher-order coefficients' critical behavior in the aluminum-lead liquid-liquid interface's surface tension.By fitting the temperature dependencies of the four surface tension coefficient parameters,i.e.,surface tension,Tolman length,bending stiffness,and Gaussian curvature stiffness with four power functions,quantitative descriptions of the critical behaviors for the four parameters are calculated.For the first time,the critical exponents of bending stiffness and Gaussian curvature stiffness are calculated as5.98 and 2.49,respectively.This calculation predicts that far from the critical temperature,the bending stiffness changes faster than the Gaussian curvature stiffness;near the critical point,as the surface tension diminishes,the bending stiffness and the Gaussian curvature stiffness gradually decrease to zero,which is in contrast to the Tolman length,which diverges as the critical point is approached from below.4.A computational method that maps out the instantaneous surface morphology of the droplet is developed.According to the instantaneous droplet morphology,the intrinsic interfacial statistical analysis has been carried out,yielding the determination of the probability distribution for the local curvatures of the investigated liquid droplets,the construction of the local curved interface ensemble,and the elucidation of the mechanism behind the curvature dependence of the mean surface tension from a more fundamental perspective.The validation of the MT theory in the realistic metal droplet system makes it possible to accurately predict the surface tension of the liquid interface of any temperature and any shape.Combining the calculated interface thermodynamic properties for the aluminum-lead alloy system,we could: i)harvest new ideas that fine-tuning the interfacial particle packings and alloy mutual miscibilities via adjusting local pressure in the liquids,ii)provide theoretical guidance for the improvement of the manufacturing/processing of immiscible alloys with high-quality dispersed soft phase,iii)and facilitate the development of the thermodynamic theory/modeling of the nano-sized alloy phase diagram.The integrated simulation-characterization-analysis-calculation methodology developed in the current thesis can be widely applied to the metallic droplet system involved in various advanced manufacturing processes.It can be extended to investigate nano-sized systems such as crystallization nucleation,liquid-phase inclusions,soft matter droplets,and other systems.The critical behaviors of the two surface stiffness coefficients reported here enrich the research field of the phase transitions and critical phenomena,and they also raise the new need to develop related statistical physics theoretical models. |
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