Three-dimensional Diagram Research Articles

Solid–Liquid Phase Equilibria in the Quinary System NaCl-KCl-MgCl2-SrCl2-H2O at 273 K

To realize the comprehensive utilization of underground brines, this work focuses on the research of phase equilibria in salt–water systems containing potassium, sodium, magnesium, strontium, and chlorine. The solid–liquid phase equilibria in the quinary system NaCl-KCl-MgCl2-SrCl2-H2O at 273 K were determined by the isothermal dissolution equilibrium method. X-ray powder diffraction was used to identify the equilibrium solids in invariant points, and the XRD diffraction patterns of equilibrium solids in invariant points were obtained. Based on the experimental data, the three-dimensional equilibrium phase diagram was constructed. The results show that no solid solution is formed in the quinary system, while the double salt KCl·MgCl2·6H2O and corresponding hydrates SrCl2·6H2O and MgCl2·6H2O are formed. The three-dimensional equilibrium phase diagram of this quinary system at 273 K contains two invariant points, seven isothermal solubility curves, and five single salt crystallization regions corresponding to NaCl, KCl, MgCl2·6H2O, SrCl2·6H2O, and KCl·MgCl2·6H2O. In addition, two-dimensional projection phase diagrams with the saturated surfaces of NaCl, KCl, and SrCl2·6H2O were also analyzed, and the dry-salt phase diagrams were also obtained. When NaCl is saturated, there are two invariant points, five univariant curves, and four crystallization regions (KCl, MgCl2·6H2O, SrCl2·6H2O, and KCl·MgCl2·6H2O) in the dry-salt phase diagram. When KCl is saturated, the dry-salt phase diagram consists of only one invariant point, three univariant curves, and three crystallization regions (NaCl, SrCl2·6H2O, and KCl·MgCl2·6H2O). When SrCl2·6H2O is saturated, the dry-salt phase diagram contains two invariant points, five univariant curves, and four crystallization regions corresponding to NaCl, KCl, MgCl2·6H2O, and KCl·MgCl2·6H2O.

Performance of warm asphalt mixtures containing reclaimed asphalt pavement, an anti-stripping agent, and recycling agents: A study using a balanced mix design approach

This research aims to use a balanced mix design (BMD) approach to investigate the effect of recycling agents (RAs) and an anti-stripping agent on the mechanical properties of warm-mix asphalt (WMA) containing different levels of reclaimed asphalt pavement (RAP). The BMD used three RAs (aromatic extract, triglycerides and fatty acids, and tall oil), an amidoamine WMA additive (PAWMA®), and an anti-stripping agent (Zycotherm®). The Dynamic Creep (DC), Indirect Tensile Strength (ITS), and Semi-Circular Bending (SCB) fracture tests were respectively used to evaluate the rutting, moisture susceptibility, and cracking resistance of mixtures. In addition, two-dimensional and three-dimensional (2-D and 3-D) performance interaction diagrams were developed as typical approaches for the BMD of asphalt mixtures. For mixtures with RAP, the results indicated that the aromatic extract and tall oil RAs decreased the moisture susceptibility, while triglycerides and fatty acids increased the moisture susceptibility. In addition, the RAs generally decreased the rutting resistance of mixtures while they increased the cracking resistance. This effect was more noticeable in the mixtures treated with triglycerides and fatty acids. The results also showed that introducing PAWMA® and Zycotherm® to the mixtures improved their resistance to moisture damage, cracking, and rutting.

Study of Dynamic Evolution of the Shear Band in Triaxial Soil Samples Using Photogrammetry Technology

In order to avoid the influence of end restraint on triaxial stress and strain measurements, this study combines photogrammetry and computer technology to apply to the unconsolidated undrained test of triaxial soil samples. The novel method can establish an intuitive shear band evolution model of soil samples and help attain a clear and intuitive shear band evolution law. On the basis of the conventional triaxial test, this new method needs to paste the RAD (Ringed Automatically Detected) code points on the rubber film, plexiglass cover and brackets and then take pictures of the RAD code points in the loading process in a surrounding manner, with which the 3D shape of the restored soil samples can be determined. After eliminating the influence of refraction, the coded point cloud coordinates measured in the experiment can be used to calculate the axial deformation and radial deformation of the soil sample in the deformation process and determine the local stress–strain curve and three-dimensional displacement field diagram of the soil sample. The test shows that the new method can clearly determine the peak value and inflection point of the stress–strain curve in the middle region of soil samples, enabling it to reflect the shear change process of the soil sample more accurately. In addition, the displacement field can be used to directly observe the formation, development and penetration process of the shear band in soil samples.

Chaos Analysis of Single-Stage Spur Gear System Considering Backlash Fractal

PurposeConsidering the time-varying pressure angle and dynamic clearance, the effects of rotational speed, tooth surface friction, and tooth surface morphology on the system’s dynamic response are studied.MethodAn improved gear nonlinear model is proposed, which considered nonlinear factors such as time-varying pressure angle, position angle, tooth surface morphology, and tooth surface friction. The time-varying dynamic backlash is deduced, and the nonlinear dynamic equation of the gear is established. The nonlinear dynamic response of the gear system is obtained based on Runge–Kutta method.ResultsThe influence of the rotational speed and tooth surface friction on single-stage spur gear system response is analyzed through the analysis of the bifurcation diagram, the three-dimensional spectrum diagram, the proportion of the meshing state, and the largest dynamic meshing force (LDMF). Dynamic response differences between the three different model are compared. In addition, by changing the tooth surface roughness and fractal dimension, the influence of tooth surface morphology on the dynamic response of the system is studied.ConclusionCompared with the traditional model, when the dynamic center distance and dynamic pressure angle are considered, the system response may enter a chaotic state earlier. When the tooth surface friction is further considered, the chaotic state of the system response is suppressed. At the same time, the velocity of the dynamic transmission error is significantly reduced, and the fluctuation amplitude of the dynamic pressure angle is increased. The value of LDMF rose overall. The stability of the system response decreases with the increase of tooth surface roughness and fractal dimension. Compared with the fractal dimension, the tooth surface roughness has a more obvious effect on the dynamic response of the system.

Dynamic pedestrian traffic assignment with link transmission model for bidirectional sidewalk networks

Planning assessment of urban walking infrastructure requires appropriate modeling methodologies that capture the time-dependent and unique microscopic characteristics of bidirectional pedestrian streams. In this paper, we develop a simulation-based dynamic pedestrian traffic assignment (DPTA) model specifically formulated for walking networks (e.g. sidewalks) with bidirectional links. The model consists of a dynamic user equilibrium (DUE) based walking route choice and a link transmission model (LTM) for network loading. The formulated DUE adopts a pedestrian volume delay function (pVDF) taking into account the properties of bidirectional pedestrian streams such as self-organization. The adopted LTM uses a three-dimensional triangular bidirectional fundamental diagram as well as a generalized first-order node model. The applicability and validity of the model is demonstrated in hypothetical small networks as well as a real-world large-scale network of sidewalks in Sydney. The model successfully replicates formation and propagation of shockwaves in walking corridors and networks due to bidirectional effects.

Multicritical phase diagram of PrMn1−xSb2 with two interacting magnetic elements

We carried out systematic magnetotransport measurements to study the magnetic phase diagram of ${\mathrm{PrMn}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{2}$, where two antiferromagnetic orders associated with the moments of Pr and Mn coexist. When the magnetic field ($H$) was applied parallel to the crystallographic $c$ axis, we found a tricritical point where a first-to-second order changeover takes place as in ordinary metamagnets. On the other hand, the metamagnetic transition field decreased unexpectedly with decreasing the temperature at low temperatures for $H\ensuremath{\parallel}[110]$. Further, the transition line associated with the metamagnetic transition terminated at low temperature, where a multicritical point was formed. Starting from a three-dimensional phase diagram predicted from a simple model and modifying it to fit our experimental results, we argue that the magnetic interaction between the two magnetic elements is responsible for forming the new critical point and influences the shape of the phase boundaries.

Magnetoelastic primary resonance and bifurcation of an axially moving ferromagnetic plate under harmonic magnetic force

The magnetoelastic primary resonance and bifurcation of an axially moving ferromagnetic plate under harmonic magnetic force are investigated. In harmonic magnetic field, the ferromagnetic plate is subjected to harmonic magnetic force generated by magnetization. Based on the Hamilton principle, the nonlinear magnetoelastic transverse vibration equation of the plate under the combined action of mechanical load and harmonic magnetic force is derived. For simply supported boundary conditions, the discretized vibration differential equation is obtained by Galerkin method. The multi-scale method is used to solve the nonlinear primary resonance, and obtain the resonance characteristic equation under steady-state response. According to Lyapunov stability theory, the stability criterion of constant solutions is determined. Through numerical calculation, two-dimensional and three-dimensional characteristic diagrams of amplitude are plotted, and the parameter ranges corresponding to multivalued solution regions and stable solution regions are determined. Global bifurcation diagrams and maximum Lyapunov exponent spectrums are plotted for different control parameters, and the effects of control parameters on the dynamic response and stability of the system are analyzed. The results show that magnetic field strength, axial velocity and mechanical load have significant effects on the vibration characteristics of the system, and tiny variation of control parameters can lead to the dramatic change of system motion characteristics.

Strain glass in Ti50-x-yNi50+yNby alloys exhibiting a boson peak glassy anomaly

Strain glass, which is a type of ferroic glass with lattice strain short-range ordering, has been found in many shape memory alloy systems, while its unique properties still await to be investigated. Here we report a strain glass found in Ti50-x-yNi50+yNbx due to the synergistic effect of Ni and Nb atoms and its boson peak glassy anomaly. It is found that Nb atoms can only slightly suppress the martensitic transformation, but with the help of 1 at% excess Ni atoms (y=1), 2% Nb atoms (x=2) are enough to lead the system to the strain glass state. A three-dimensional phase diagram is established accordingly. Moreover, a boson-peak-like glassy feature is also found in the strain glass state, which resembles the boson peak in metallic glass. This work provides more clues to understand the glass nature of strain glass.

Dynamic modeling and response analysis of rub-impact rotor system with squeeze film damper under maneuvering load

With the development of the aero-engine rotor system towards accurate modeling, it is necessary to establish a general rotor system model considering many important strong nonlinear factors. In this paper, based on the finite element method, a 6-node rub-impact rotor system model including the newly-built blade-casing rub-impact force, climbing maneuvering load, nonlinear Hertz contact force of rolling bearing, rotor eccentric unbalance force, gravity field and squeeze film damper oil film force is established. The dynamic responses of the system under different rub-impact stiffness, different oil film clearance and different bearing clearance are analyzed in detail by means of bifurcation diagram, three-dimensional spectrum diagram and axis trajectory diagram. Through comparative analysis, it is found that the change of the oil film clearance has the greatest influence on the rub-impact response of the system, followed by the bearing clearance, and the change of the rub-impact stiffness has the least influence on the rub-impact response of the system. The study of this paper can provide a theoretical basis for the rub-impact response of the rub-impact rotor system with squeeze film damper under climbing maneuvering flight.

Phase portraits and optical soliton solutions of coupled Sasa–Satsuma model in birefringent fibers

The main purpose of this paper is to discuss the optical soliton solutions and phase portraits of the coupled Sasa–Satsuma model in nonlinear optics. This model is usually used to describe the propagation of femtosecond pulses in optical fibers. By using traveling wave transformation, the coupled Sasa–Satsuma model is simplified into the coupled nonlinear ordinary differential equations. After that, the coupled nonlinear ordinary differential equations are transformed into two-dimensional planar dynamic system with the Hamiltonian system. According to the bifurcation theory of planar dynamical system, the phase portrait of two-dimensional dynamical system is drawn. What is more, some very important optical soliton solutions are also constructed. In order to explain the propagation of optical solitons, three-dimensional diagrams, two-dimensional diagrams and the contour plots of the obtained solutions are drawn by using Maple software.

Dynamic Force and Moment Characteristics of Annular Gaps—Simulation Results and Evaluation of the Relevance of the Tilt and Moment Coefficients

Abstract Nowadays, most studies of the dynamic characteristics of annular gaps focus only on the force characteristics due to translational motions, while the tilt and moment coefficients are less well studied. To expand the knowledge of the additional coefficients, we investigate both the dynamic force and the dynamic and moment characteristics of annular gaps. First, the rotordynamic influence of annular gaps is recapitulated. Second, a new simulation method is presented, using a perturbed integro-differential approach in combination with a Hirs’ model and power law ansatz functions for the velocity profiles to calculate the dynamic force and moment characteristics. Subsequently, an extensive parameter study is carried out. To evaluate whether the hydraulic tilt and moment coefficients need to be considered, an effective stiffness is defined and the influence of the annulus length, an eccentrically operated shaft, the center of rotation, a modified Reynolds number, the flow number, and the pre-swirl is investigated. It is shown that despite the annulus length, the flow number as well a modified Reynolds number are crucial for the relevance of the additional coefficients. This leads to a simple three-dimensional diagram, which makes it possible to assess the necessity of including the additional coefficients on the basis of the three variables.

Directional diagrams of acoustic radiation from unmanned aerial vehicles

When solving the urgent task of detecting small unmanned aerial vehicles (UAVs) by their acoustic radiation (AR), there is a need to study the AR characteristics of UAVs. Therefore, considerable attention is paid in the literature to theoretical and experimental studies of the structure and parameters of the sound field created by UAVs.
 This article is devoted to the experimental study of the directional diagrams of the acoustic radiation from the DJI Phantom 3 unmanned aerial vehicle. The UAV AR recording experiment was conducted in a "silenced" chamber, the walls of which are covered with sound-absorbing panels with a surface of a special geometric shape. The experimental setup includes the UAV mounted on a boom, a microphone for sound recording, and a boom for the microphone.
 Studies of the structure and parameters of the sound field of the quadcopter have shown that the spectra of the emitted signal have pronounced harmonic components with frequencies multiples of the propeller rotation frequency. The spectral components have the greatest power in the frequency range up to 500 Hz, where the first harmonic has the largest amplitude, and then the spectrum components decrease to the ambient noise level.
 Obtained two-dimensional and three-dimensional directional diagrams of the UAV AR with and without propellers when only the aircraft engine is operating. It is shown that in the absence of screws, the acoustic radiation is much weaker in level. The experimental data was also presented in the form of three-dimensional AR diagrams for the four harmonics of the acoustic signal, and it was analyzed what changes in the spatial orientation of the UAV AR are observed based on changes in the three-dimensional figure for each of the radiation harmonics.
 It is shown that the spatial distribution of both the total energy (over the entire frequency range) of the acoustic signal and the energy of its individual spectral (harmonic) components is significantly anisotropic. It follows from this conclusion that the range of UAV detection and observation in real conditions is a statistical value that depends on the angle of its observation.

Petrogenesis of siliciclastic sediments and sedimentary rocks explored in three-dimensional Al2O3–CaO*+Na2O–K2O–FeO+MgO (A–CN–K–FM) compositional space

Quantitatively determining the amount of chemical weathering within sedimentary rocks (and weathering profiles) took a major step forward with the creation of the chemical index of alteration (CIA) 40 years ago. The CIA relates the proportion of immobile aluminum to the mobile cations of calcium, sodium, and potassium and is grounded in empirical and modeled geochemical data for mineral reactions that occur during hydrolysis. However, the CIA should be applied cautiously because it is a one-dimensional value that in the most complex situations, as with clastic sedimentary rocks, homogenizes the compositional inputs of source, weathering, sorting, and diagenesis. Subsequently developed two-dimensional (2D) ternary diagrams (Al2O3–CaO*+Na2O–K2O; Al2O3–CaO*+Na2O+K2O–FeO+MgO) permitted the capacity to explore mineralogical-geochemical pathways in data sets that may separate those inputs, but interpreting the ternary diagrams may be complicated because they differentiate and group certain elements. Here we develop a three-dimensional tetrahedral diagram (Al2O3–CaO*+Na2O–K2O–FeO+MgO, A–CN–K–FM) that incorporates the same critical elements and permits the simultaneous assessment of felsic and mafic rocks and minerals on the same diagram while retaining the ability to separate plagioclase from alkali feldspar and monitor post-depositional potassium changes. Using the tetrahedral plot, we show that both the CIA value and positions on the 2D ternary diagrams can generate potentially misleading interpretations without properly budgeting the ferromagnesian components in parallel. We first show how the tetrahedron works, then use it with numerous previously published examples to identify how the competing mafic and felsic inputs shape the composition of source rocks, weathering profiles, actively transporting sediment, paleosols, and sedimentary rocks in sedimentary petrogenesis.

Nonlinear dynamics analysis of a dual-rotor-bearing-casing system based on a modified HB-AFT method

This paper presents a modified harmonic balance-alternating frequency/time domain (HB-AFT) method to analyze the nonlinear dynamics of a dual-rotor-bearing-casing system. The motion equations of a dual-rotor-bearing-casing system subjected to the unbalanced excitations of the two rotors are formulated with 284 degrees of freedom, in which, the complex nonlinear factors of the inter-shaft bearing such as exponential nonlinear restoring force, radial clearance and varying stiffness excitation are taken into consideration. The HB-AFT method is modified by applying the AFT procedure to obtain the harmonic expending coefficients of the harmonic balance residuals rather than that of the nonlinear terms, hence, the Jacobian matrix is calculated programmatically and efficiently, as a result the performance of the HB-AFT method is improved greatly. The primary resonance of the system is analyzed by employing the three-dimensional diagrams of amplitude-frequency responses of each node of the system, including the inner casing and the outer casing. In addition, the amplitude-frequency response curves with separated frequencies and orbits of the two rotors are also discussed. Furthermore, the pseudo-arclength continuation procedure is introduced into the modified HB method, then all periodic solution branches of the system including the unstable solutions are obtained. The results show that there are two resonant peaks in the amplitude-frequency response curves of the system and the vibration of each part of the system, i.e., LPC, LPT, HPC, HPT, inner casing and outer casing, is synchronous. Besides, the nonlinear dynamic behaviors such as vibration jumping, bi-stable and resonance hysteresis are revealed. Accordingly, the dynamic load of the inter-shaft bearing is calculated. The results show that the evolution of the inter-shaft bearing’s dynamic load is associated with the vibration responses of the two rotors. The nonlinear characteristics of the force-frequency responses of the inter-shaft bearing are consistent with that of the two rotors and casings. In addition, with the increase of the inter-shaft bearing clearance, the nonlinear characteristics of the force-frequency responses of the inter-shaft bearing are more significant. In comparison with the Newmark method, the modified HB-AFT method proposed in this paper has a great advantage in computing efficiency, and it can also grasp all solution branches of the system including the unstable solutions. Consequently, it has great potential to deal with high-dimensional systems with complex nonlinearities and multifrequency excitations in practical engineering.

Evaluation of fatigue and creep-fatigue damage levels on the basis of engineering damage mechanics approach

Progressive degradation of material mechanical properties in the low cycle fatigue (LCF) and creep-fatigue (CF) interaction at high temperature affects the safe operation of in-service materials. By considering material degradation, the present work aims to establish a method for evaluating LCF and CF damage levels with wide applicability. Material-level data accumulations as well as theoretical foundations of LCF and CF are presented, including interrupted LCF and CF tests, subsequent tensile tests and energy-based damage models. A damage variable representing the degradation of material mechanical properties is then defined based on the tensile plastic strain energy density (TPSED), the physical mechanism of which is reflected in the microstructure evolution and fracture appearance. By taking into consideration the material degradation threshold in the traditional damage summation rule, a new three-dimensional (3D) damage interaction diagram is established, where the additional third axis indicates the material degradation level. Finally, taking GH4169 alloy and P92 steel as examples, this work demonstrates the implemented procedures of damage level evaluation, which has been validated via the experimental data.

Extending the Black diagram of bitumen to three dimensions

• The Black diagram of bitumen is extended to three dimensions. • A temperature axis is added to Black diagram to indicate temperature-dependency. • Frequency dimension is incorporated indirectly to indicate time-dependency. • Common technical criteria are harmonised in three-dimensional Black diagram. The ordinary Black diagram of bitumen has only two dimensions. Thus, it does not differentiate the complex shear modulus and phase angle measured under different temperature and frequency conditions. This study proposes to extend the Black diagram to three dimensions by adding a temperature axis. It leads to the combination of multiple necessary ordinary plots in the same three-dimensional (3D) space. In this 3D space, the location, shape, and eventually colour of the plot (either curve or surface) can together indicate the unique temperature-dependency and time-dependency of the bituminous binder’s rheological properties, even the interplay between them. Hence, polymer-modified bitumen is distinguished from neat bitumen and harder bitumen is distinguished from softer bitumen. Furthermore, the additional temperature axis in the 3D Black diagram also enables direct visualisation and precise quantitative evaluations of bitumen properties by various current technical criteria in the same space, avoiding the inconvenient use of multiple ordinary plots. This may lead to the development of a practical tool towards more effective and efficient evaluation of rheological properties of bitumen.

Optical solitons to the coupled cubic-quartic Sasa–Satsuma equation with Kerr law nonlinearity in birefringent fibers

This paper mainly studies the optical soliton solutions of the coupled cubic-quartic Sasa–Satsuma equation with Kerr law nonlinearity describing the propagation of femtosecond pulses in optical fibers. Firstly, using traveling wave transformation, the coupled cubic-quartic Sasa–Satsuma equation with Kerr law nonlinearity in birefringent fibers is simplified into the coupled nonlinear ordinary differential equations. Secondly, according to the trial method of polynomial of rank homogeneous equation, the optical soliton solutions of coupled cubic-quartic Sasa–Satsuma equation with Kerr law nonlinearity can be obtained. Finally, in order to explain the propagation of optical solitons, three-dimensional and two-dimensional diagrams of the obtained solutions are drawn.

Phase portraits and optical soliton solutions of coupled nonlinear Maccari systems describing the motion of solitary waves in fluid flow

The coupled nonlinear Maccari systems are very important equations which have been developed vigorously in the fields of the nonlinear optics, deep water theory, plasma physics, nonlinear optics and so on. The main work of this paper is focus on the bifurcation analysis and single optical soliton solutions of the coupled nonlinear Maccari systems describing the motion of solitary waves in the nonlinear optics. Firstly, the coupled nonlinear Maccari systems are reduced to the nonlinear ordinary differential equations by employing traveling wave transformation and linear transformation. Secondly, the phase portraits of coupled nonlinear Maccari systems are drawn. Moreover, the optical soliton solutions of the coupled nonlinear Maccari systems are obtained by using the planar dynamic system method and the polynomial complete discriminant system method, respectively. The Jacobian function solutions, the hyperbolic function solutions, the trigonometric function solutions and the rational function solutions are constructed. Finally, three-dimensional diagram and two-dimensional diagram of the coupled nonlinear Maccari systems are drawn.

Modelling drying pathways of an evaporating soft matter droplet

Micro-droplets of soft matter solutions have different morphologies upon drying, and can become wrinkled, buckled or cavitated particles. We investigate the morphology evolution of a drying soft matter droplet in this work: at the early stage of drying, wrinkling or cavitation instability can occur in the droplet, depending on the comparison between the critical wrinkling and cavitation pressure; at a later stage of drying, no wrinkles will appear if cavitation happens first, while cavitation can still occur if wrinkling happens first. A three-dimensional phase diagram in the space of elastic length, gel layer thickness and weight loss is provided to illustrate the drying pathways of a soft matter droplet. This diagram can help guide future fabrications of micro-particles with desired morphologies.

Simultaneous effect of multi-walled carbon nanotube and Span85 on the extraction of Ibuprofen from aqueous solution using emulsion liquid membrane

The Pickering emulsion stabilized by special nanoparticles, such as carbon nanotubes, due to their longer stability, cost-effectivity, and less toxicity has been developing as a matter of great interest for researchers. In this study, the extraction of the Ibuprofen (IBP) drug as a kind of pollutant at the simultaneous presence of the nanoparticle and surfactant has been investigated. In the Pickering Emulsion Liquid Membrane (PELM) process used in this study, the multi-walled carbon nanotube (MWCNTs), Span 85, Aliquat 336, Kerosene, and Sodium chloride solution were used as the nanoparticle, surfactant, carrier, solvent, and internal phase. Using the response surface methodology in Design-Expert software and based on the central composite design, the optimization of the concentrations of MWCNTs, Span 85, feed, and Aliquat 336 and the mixing time and stirring speed were performed. The significant and non-significant of these six parameters and their interactions with each other have been evaluated. A second-order regression model was obtained for measuring the extraction efficiency of IBP. The one-dimensional and three-dimensional diagrams were developed for investigating the effect of different variables on extraction efficiency. The maximum extraction efficiency of IBP obtained by the response surface method was 93.64%, which was achieved at the concentrations of 0.071 %wt/v, 5.06 v/v%, 73.53 ppm, and 1.68 v/v% for the MWCNTs, Span 85, feed, and carrier, respectively, mixing time of 6.42 min, and stirring speed of 246 rpm. Ultimately, the results obtained through this study have demonstrated that the MWCNTs nanoparticle plays an important role in the ELM system to improve the extraction efficiency of IBP.