Solidification treatment effect of wellsite waste mud based on physical adsorption of a composite curing agent

Zhikun Liu; Chaoqun Zhang; Qi Li

Journal & Issue Details

Applied Mathematics and Nonlinear Sciences

Journal Details

Format: Journal
eISSN: 2444-8656
First Published: 01 Jan 2016
Publication timeframe: 2 times per year
Languages: English

One of the focuses of current social research is wastewater treatment, which is currently a hotspot for scientific research [1]. The polyvinyl alcohol (PVA) nanofiber membrane was prepared by using electrospinning technology, the adsorption of Pb²⁺ and Cu²⁺ in wastewater was studied and the effects of different preparation processes on the diameter, uniformity and fibre morphology of PVA nanofibers were studied [2]. At the same time, the adsorption performance, model and adsorption kinetics of Pb²⁺ nanofiber membrane on Pb²⁺ and Cu²⁺, the regulation and characterisation of PVA nanofibers in water morphology and the characterisation of PVA-g-POSS nanofibers and the adsorption properties of Pb²⁺ and Cu²⁺ were also studied [3]. The research aims to address the shortcomings of traditional wastewater treatment technologies and further enhance the ability to treat wastewater.

The effects of the PVA nanofiber preparation process on fibre diameter, uniformity and fibre morphology were studied by an orthogonal experiment, and the effects of spinning voltage, spinning distance and PVA spinning solution concentration on the preparation process were analysed. The Pb²⁺ and Cu²⁺ ions in PVA nanofiber adsorption solution were studied, and the adsorption model was also proved to be a multi-layer adsorption process of the PVA nanofiber membrane.

Heavy metal ions in wastewater are highly toxic, are not easily degradable and exist in water for a long time, endangering human life and health [4]. Nowadays, the problem of water shortage in China is becoming more and more serious, and the cost of sewage treatment is relatively large. Therefore, water resources must be developed benign. In addition to water conservation, the recycling of wastewater must be paid attention to. The nanofiber membrane prepared by the adsorption of heavy metal ions in the wastewater is superior to the traditional water treatment method, achieving a high adsorption level with certain innovation [5].

The research is divided into three parts: the first part is literature review, the second part is the waste mud solidification treatment method of PVA nanofiber, including the electrospinning process of PVA nanofiber and the introduction of the adsorption performance method, and the third part is the analysis of experimental results.

Related work

Water is the source of life and the natural resource on which human beings depend. Elnemr et al. [6] believed that water pollution has become a global issue in recent years and has reached the point where it needs to be managed immediately. Wan et al. [7] proposed that the ever-changing social development has greatly improved the industrial level in human society, but this development has brought crisis to our living environment, and natural water resources are the biggest victims to this development. Mozaffari et al. [8] believed that large amounts of natural water are discharged into industrial wastewater, causing rapid accumulation of heavy metal ions such as lead, copper and chromium in natural waters. Wei and Yang et al. [9] proposed that heavy metal ions in wastewater are highly toxic, difficult to degrade and exist in water for a long time and finally enriched throughout the food chain, endangering human life and health. Therefore, water resources must be developed benign, and in addition to water conservation, the recycling of wastewater must be paid attention too. Lee et al. [10] believes that there are many methods for the treatment of heavy metal wastewater in China. The traditional methods include the precipitation method, filtration method, ion exchange method and membrane separation method. Membrane treatment is more commonly used, and the most used ones are reverse osmosis treatment and membrane treatment, which use special membranes to allow certain particles to pass smoothly and prevent some particles from flowing out. Sun et al. [11] proposed that the chemical treatment method is to effectively extend the life of the equipment and save water by effectively inhibiting scale corrosion. Piana et al. [12] proposed that the most common material used for water treatment is activated carbon, which is well known for its excellent adsorption properties. There are many adsorption methods for activating carbon, but the adsorption principle is consistent. The huge surface area of activated carbon and unique pore structure make it have strong adsorption performance. Wang et al. [13] used activated carbon fibre to remove Cr⁶⁺ from wastewater. The study shows that activated carbon fibres can adsorb Cr⁶⁺ quickly and efficiently, which is better than common activated carbon; so, it has practical application value. Wang et al. [14] proposed that, in recent years, various novel water treatment methods have emerged, such as aerogels for water treatment, which have been extensively studied. Aerogels can be used to remove toxic metals and organics such as Hg²⁺, Pb²⁺ and nitrophenol from water. Motavalizadehkakhky et al. [15] prepared some composite aerogels for water treatment. In 2013, they prepared metal composite magnetic carbon aerogels as adsorbent materials for adsorbing heavy metal ions in wastewater; solid-liquid separation can be achieved by magnetic separation after adsorption, which is an easy-to-implement method and environmentally friendly.

Wastewater treatment is the focus of today's research, and traditional water treatment technologies have various drawbacks, such as high cost, cumbersome treatment process, inconspicuous treatment of low-concentration heavy metal ions and secondary pollution during treatment. The PVA nanofiber membrane was prepared by electrospinning technology, and the adsorption of Pb²⁺ and Cu²⁺ in wastewater was studied to further solve the shortcomings of traditional water treatment technology and enhance the ability to treat sewage.

Theory of solidification treatment of waste mud of polyvinyl alcohol nanofiber

3.1

Adsorption kinetics

The solution of Cu²⁺ and Pb²⁺ with 50 mL mass concentration of 100 mg/L was added to the conical bottle, and the pH was adjusted to 7.0 by NaOH or HCl. Then, 50 mg cell membrane or Cell-g-SAA membrane was added to the above solution, and the supernatant was filtered after shaking at a constant temperature in a water bath at 25°C for 10, 30, 60, 120, 240, 360, 480, 720, 960, 1200 and 1400 mins. The mass concentrations of Cu²⁺ and Pb²⁺ in the solution were measured by an atomic absorption phototypesetter, and the mass concentrations of Cu²⁺ and Pb²⁺ in the solution after adsorption were calculated. The adsorption capacity qe (mg/g) of Cu²⁺ and Pb²⁺ on the fibre membrane was calculated by Eq. (1). (1) $q_{e} = \frac{V (ρ_{0} - ρ_{e})}{m}$ {q_e} = {{V\left({{\rho _0} - {\rho _e}} \right)} \over m}

In the formula, ρ₀ and ρ_e are the mass concentrations of heavy metal ions in the solution before and after adsorption (mg/L), respectively, V is the solution volume (L) and m is the fibre membrane mass (g).

In order to further study the adsorption kinetics of Cu²⁺ and Pb²⁺ on nanofiber membranes, quasi-first-order and quasi-second-order models need to be used to fit the experimental data. The quasi-first-order Eq. (2) and quasi-second-order Eq. (3) kinetic equations are as follows: (2) $ln (q_{e} - q_{t}) = ln q_{e} - k_{1} t$ \ln \left({{q_e} - {q_t}} \right) = \ln {q_e} - {k_1}t (3) $\frac{t}{q_{t}} = \frac{1}{k_{2} q_{e}^{2}} + \frac{1}{q_{e}} t$ {t \over {{q_t}}} = {1 \over {{k_2}q_e^2}} + {1 \over {{q_e}}}t

The Corey diffusion equation in the solution has the following form: (4) $q = k \cdot t^{0.5}$ q = k \cdot {t^{0.5}}

The modified pseudo-first-order kinetic equation is as follows: (5) $\frac{dq}{dt} = K_{1} \frac{q_{e}}{q_{t}} (q_{e} - q_{t})$ {{dq} \over {dt}} = {K_1}{{{q_e}} \over {{q_t}}}\left({{q_e} - {q_t}} \right) when q is t, the adsorption amount is mg/g, t is the adsorption time and k is the internal diffusion rate constant of the particles mg·g⁻¹·min^−0.5. Second-order reaction model, (6) $\frac{c}{c_{0}} = \frac{1}{1 + k_{2} c_{0} t}$ {c \over {{c_0}}} = {1 \over {1 + {k_2}{c_0}t}}

The adsorption equilibrium of c₀ and c in the solution and the concentration of the solution at the initial t time, respectively. k₂ is a quasi-first-order adsorption rate constant.

3.2

Adsorption isothermal equilibrium

Initially, 50 mg fibre membrane samples were added to the solution of Cu²⁺ and Pb²⁺ ions with 50 mL concentrations of 40, 60, 80, 100, 120, 160 and 200 mg, respectively, and 1200 min was oscillated at a constant temperature in a water bath at 25°C. After the reaction, the supernatant was filtered, and the mass concentrations of Cu²⁺ and Pb²⁺ in the solution were measured by an atomic absorption phototypesetter, and the mass concentrations of Cu²⁺ and Pb²⁺ in the solution after adsorption were calculated. The parameters of the experimental data were estimated by Langmuir and Freundlich isothermal adsorption models. The equation expressions of the two models are as follows: (7) $\frac{1}{q_{e}} = \frac{1}{q_{max}} + \frac{1}{q_{max} K_{a} C}$ {1 \over {{q_e}}} = {1 \over {{q_{\max }}}} + {1 \over {{q_{\max }}{K_a}C}} (8) $lg q_{e} = \frac{lg C}{n} + lg K_{F}$ {\rm{lg}}{q_e} = {{{\rm{lg}}C} \over n} + {\rm{lg}}{K_F} q_max is the saturated adsorption capacity of the fibre membrane, q_e is the adsorption capacity of the fibre membrane with different initial concentrations, C is the initial concentration of the lysozyme, K_a is the Langmuir isotherm constant and n and K_F are Freundlich isotherm constants.

Adsorption thermodynamics mainly studies the change of energy in the adsorption process and the effect of temperature on adsorption. The following parameters can be obtained by isothermal adsorption at different temperatures: Gibbs free energy (ΔG⁰), enthalpy change (ΔH⁰) and entropy change (ΔS⁰). The relationship between them is shown in the Eqs (9)–(11): (9) $Δ G^{0} = - RT ln K_{D}$ \Delta {G^0} = - RT\ln {K_D} (10) $ln K_{D} = \frac{Δ S^{0}}{R} - \frac{Δ H^{0}}{RT}$ \ln {K_D} = {{\Delta {S^0}} \over R} - {{\Delta {H^0}} \over {RT}} (11) $K_{D} = \frac{q_{e}}{ρ_{e}}$ {K_D} = {{{q_e}} \over {{\rho _e}}} where K_D is the adsorption diffusion coefficient, T (K) is the adsorption temperature, R (J/(mol K)) is the gas constant and q_e (mg/g) is the adsorption equilibrium capacity. ρ_e (mg/L) is the mass concentration of heavy metals in the solution at adsorption equilibrium.

3.3

Adsorption thermodynamics

Initially, 50 mg Cell-g-SAA membrane samples were added to the solution of 50 mL Cu²⁺ and Pb²⁺ ions at 10°, 20°, 30°, 40° and 50°, and are left in a shaker for 1200 min. After the reaction, the supernatant was filtered, and the mass concentrations of Cu²⁺ and Pb²⁺ in the solution were measured by an atomic absorption spectrophotometer, and the mass concentrations of Cu²⁺ and Pb²⁺ in the solution after adsorption were calculated.

Exploration of solidification treatment of waste mud of polyvinyl alcohol nanofiber

4.1

Electrospinning process of polyvinyl alcohol nanofibers

The PVA nanofiber membrane has a large specific surface area and has a good effect on the adsorption of Pb²⁺ and Cu²⁺. The finer the diameter of the fibre, the larger the specific surface area and the better the theoretical adsorption efficiency, in order to obtain the PVA nanofiber with the best adsorption effect, three-factor and three-level orthogonal tests are designed based on the spinning voltage, spinning distance and PVA spinning solution concentration during spinning, and the effects of the process on the average diameter, diameter distribution and fibre morphology of PVA nanofiber membranes are investigated. The materials used in the experiment are shown in Table 1.

Table 1

Name, specifications and models of experimental raw materials and manufacturers

Name of raw material	Specifications and models	Manufacturer

Polyvinyl alcohol	117	Colerie Trading (Shanghai) Co., Ltd.
Deionised water	-	Laboratory self-control

The equipment and instruments used in the experiment are shown in Table 2.

Table 2

Experimental equipment and instruments

Instruments/equipment	Model	Manufacturer

Scanning electron microscope	QuantaFEG250	American FEI Company
Electrospinning machine	ESM-C01	Shanghai Yuyue Nanotechnology Co., Ltd.

The PVA powder was weighed and dissolved in deionised water and heated and stirred in a constant temperature water bath at 90°C for 2 h to obtain a uniform spinning solution of different mass concentrations for use. The spinning solution was poured into a syringe with a volume of 10 ml and a needle diameter of 0.8 mm, and air bubbles were extruded. The spinning voltage ranged from 10 kV to 20 kV, and the aluminium foil was fixed on a roller at a distance from 10 cm to 14 cm from the needle to collect the nanofibers. The nanofiber membrane was separated from the surface of the aluminium foil for further testing. A schematic diagram of electrospinning is shown in Figure 1.

Schematic diagram of electrospinning principle

4.2

Characterisation method

The fibre structure of the PVA nanofiber membrane is observed by using a scanning electron microscope (SEM), including the average fibre diameter, diameter distribution and presence or absence of adhesion. The sample is adhered to the sample stage, and the test is carried out under high vacuum after the gold treatment, and the test condition is 10 kV. According to the SEM photograph of the PVA nanofiber membrane, the fibre diameter is measured using Image ProPlus software, and the fibre diameter measurement of not less than 100 is taken as the standard, the average diameter of the nanofibers is calculated according to Eq. (1): (12) $\bar{d} = \frac{\sum_{i = 1}^{n} d_{i}}{n}$ \overline d = {{\sum _{i = 1}^n{d_i}} \over n} $\bar{d}$ \overline d : the average diameter of fibres, μm; d_i: the diameter of the i-th fibre, μm; n: number of fibres in the SEM photograph.

4.3

Adsorption performance experiment

The raw materials used in the experiment are shown in Table 3.

Table 3

Names, specifications and models of raw materials and manufacturers

Name of raw material	Specifications and models	Manufacturer

Polyvinyl alcohol	One hundred and seventeen	Colerie Trading (Shanghai) Co., Ltd.
Deionised water	-	Laboratory self-control
Copper sulphate pentahydrate	Analytical purity	China Pharmaceutical Group Chemical Reagents Co., Ltd.
Lead chloride	Analytical purity	China Pharmaceutical Group Chemical Reagents Co., Ltd.

The equipment and instruments used in the experiment are shown in Table 4.

Table 4

Experimental equipment and instruments

Instruments/equipment	Model	Manufacturer

Electrospinning machine	ESM-C01	Shanghai Yuyue Nanotechnology Co., Ltd.
ICP emission spectrometer	PS3500DDII	Hitachi Manufacturing Institute

A batch test is performed, and 50 mg of the PVA nanofiber membrane is placed in a vacuum oven at 60°C for drying for 1 h. Then, it is immersed in 100 mL of 25–100 mg/L CuSO₄.5H₂O and PbCl₂ solution, and the adsorption at different contact times is carried out at a constant temperature of 20°C, and the supernatant is taken for dilution and acidification, and then, the amount of adsorption is tested. The supernatant is diluted and acidified, and the concentration of heavy metal ions in the solution is measured on an ICP emission spectrometer (inductively coupled plasma spectrometer), and the adsorption capacity of the nanofiber membrane at different initial ion concentrations of the adsorbed solution and at different contact times is calculated: (13) $q_{t} = (C_{0} - C_{t}) \frac{V}{m}$ {q_t} = \left({{C_0} - {C_t}} \right){V \over m} q_t (mg/g) is the adsorption amount at any time, C₀ (mg/L) is the initial ion concentration, C_t (mg/L) is the measured ion concentration, V (L) is the solution volume and m (mg) is the mass of the nanofiber membrane.

Experimental design and analysis

In the preparation of PVA nanofibers, the concentration of PVA spinning solution plays an important role in the average diameter, diameter distribution and fibre morphology of nanofibers. When the concentration of the PVA spinning solution is less than 6%, the viscosity of the solution is extremely low, and the molecular chains are not uniformly entangled, resulting in uneven distribution of charges, and the jet becomes unstable and cannot maintain continuity, and it is easy to obtain bead-shaped nanofibers, and the distribution of the diameter is very uneven. When the concentration of the PVA spinning solution exceeds 10%, the viscosity of the solution is large, and the spinning solution is easily condensed into a block at the nozzle due to the small amount of solvent and volatilisation, which causes the nozzle to be clogged and cannot be continuously spun. As the PVA concentration increased from 6% to 10%, the average fibre diameter increased from 0.24 μm to 0.44 μm. The average diameter of PVA nanofibers increases with the concentration of the spinning solution because as the concentration increases, the viscosity of the solution increases, and the PVA content in the fluid increases, and the ability of the fluid to differentiate in the electrostatic field is greatly diminished, and the average fibre diameter becomes larger. The spinning voltage directly affects the strength of the electrostatic field, the diameter of the fibre, the distribution of the diameter and the morphology of the fibre, and when the spinning voltage of the PVA nanofibers is lower than 10 kV, the PVA solution has less charge when forming a jet from the nozzle due to insufficient electric field strength and cannot form a Taylor cone to form a filament; when the spinning voltage is higher than 20 kV, the fluid carries too much charge, the repulsive force is too large after differentiation, the liquid disperses and splashes and the filament cannot be formed. The spinning voltage is increased from 10kV to 20kV, and the average diameter of PVA nanofibers is reduced from 0.48μm to 0.19μm. When the voltage is increased and the spinning distance is constant, the electric field strength is increased, the charge of the PVA solution jet increases, the charge repulsive force increases, the differentiation ability of the PVA spinning solution after being ejected from the nozzle is enhanced and the number of fibres is increased; so, the diameter of the PVA nanofiber is reduced.

When the spinning distance ranged from 10 cm to 12 cm, the average diameter of the PVA nanofibers was reduced from 0.21 μm to 0.19 μm. Because as the spinning distance increases, the flight time of the PVA fluid in the electrostatic field increases, the solvent evaporation time becomes longer and the volatilisation is more sufficient, which optimises the differentiation environment of PVA nanofibers, and the differentiation time increases; so, the average fibre diameter decreases. However, as the spinning distance increased from 12 cm to 14 cm, the average diameter of the PVA nanofibers increased to 0.24 μm. This is because the continuous increase of the distance makes the differentiation environment of the PVA fluid superior, and the differentiation time increases.

Through orthogonal experimental analysis, the factors affecting the average fibre diameter, diameter distribution and fibre morphology were ranked as follows: PVA concentration > spinning distance > spinning voltage. The optimum level combination is determined to have a spinning voltage of 20 kV, a PVA concentration of 6% and a spinning distance of 12 cm. As the concentration of PVA spinning solution increases, the viscosity increases, and the greater the PVA content per unit volume, the weaker the ability of the fluid to differentiate in the electrostatic field, resulting in a larger average fibre diameter. With the increase of the spinning voltage, the electrostatic field strength increases when the distance is constant, the repulsive force of the static electricity in the PVA fluid increases, the tensile force of the fibre increases and the differentiation ability increases, which reduces the average diameter of the PVA nanofibers and improves the uniformity of the diameter distribution. Therefore, after the spinning solution concentration and the spinning voltage are determined, the spinning distance is not linear with the average diameter of the nanofibers and has an extreme value, which is a combination of two factors. In order to accurately measure the adsorption amount, a standard curve between the metal ion concentration and the absorption intensity of the inductively coupled plasma spectrometer (ICP emission spectrometer) is drawn; first, the standard Pb²⁺ solutions of 5.5 mg/L, 1 mg/L, 2 mg/L, 3 mg/L, 4 mg/L and 5 mg/L are prepared and acidified. Figure 2 shows the test to achieve the Pb²⁺ standard solution curve because the ICP emission spectrometer can simultaneously measure a variety of metal ions; there are different ion conversion procedures inside, and the Cu²⁺ standard curve can be converted by Pb²⁺; so, there is no need to draw a Cu²⁺ standard solution curve.

The Pb²⁺ standard solution curve is shown in Figure 2; the supernatant after adsorption is diluted, and after acidification, the super atomising device changes into an aerosol through the conduit into the plasma flame, and most of the state immediately becomes an excited state of atoms and ions. When an excited atom or ion returns to a stable ground state, a fixed energy is released and appears as a spectrum of a certain wavelength, the emission spectrometer obtains a standard curve by measuring the specific line and intensity of each element and the larger the ion concentration, the greater the absorption intensity. The correlation coefficient R2 of the Pb²⁺ standard curve is 0.99974, which conforms to the standard and guarantees the credibility of the subsequent actual test results. Figure 3 is a graph showing the adsorption amount of Pb²⁺ on the PVA nanofiber membrane, as shown in Figure 3. With the increase of contact time, the adsorption amount of Pb²⁺ by PVA nanofiber membrane gradually increases, and it becomes stable after reaching equilibrium, and the equilibrium time is 30h, the maximum adsorption amount of 100 mg/L at the initial concentration of the adsorbed solution reaches 168.3 mg/g. Pb²⁺ is free to move in the solution. When Pb²⁺ is immobilised on the PVA nanofiber membrane, the remaining Pb²⁺ takes time to continue to approach and be adsorbed by the PVA nanofiber membrane by the driving force of the concentration difference. At the same time, a small amount of adsorbed Pb ions is desorbed and re-entered into the solution, and at the beginning of the adsorption, the adsorption rate caused by the concentration difference is much larger than the desorption rate. Therefore, as the contact time increases, a large amount of Pb²⁺ is adsorbed and fixed on the PVA nanofiber membrane, and the adsorption amount gradually increases with time, and when the adsorption rate is equal to the desorption rate, the adsorption reaches equilibrium. It can also be observed from Figure 3 that the PVA nanofiber membrane adsorbs the adsorbed liquid at different initial concentrations, and the equilibrium adsorption amount is proportional to the initial Pb²⁻ concentration of the adsorbed liquid. For the PVA nanofiber membrane, the number of adsorption active sites is sufficient, but it takes a certain time for the Pb²⁺ to be adsorbed from the adsorbed liquid gradually close to the surface of the PVA nanofiber membrane by the concentration difference driving. When the adsorption rate is equal to the desorption rate, the adsorption equilibrium is reached. It is not because the PVA nanofiber membrane adsorbs insufficient active sites but because it is difficult to drive the remaining Pb²⁺ near the surface of the PVA nanofiber membrane for the concentration difference is insufficient. Therefore, for different initial concentrations of Pb²⁺ adsorbed liquid, the adsorption amount reaching the adsorption equilibrium is basically proportional to the initial concentration of Pb²⁺.

Adsorption of lead ion by contact time and initial concentration

Figure 4 is a graph showing the equilibrium adsorption capacity of the PVA nanofiber membrane to Cu²⁺. As shown in Figure 4, as the contact time increases, the adsorption amount of Cu²⁺ by the PVA nanofiber membrane continues to increase, and the equilibrium time is 15 h; the equilibrium adsorption amount of the initial concentration of Cu²⁺ at 100 mg/L reaches 62.3 mg/g. Similar to Pb²⁺, Cu²⁺ moves freely in the adsorbed solution. When most of the Cu²⁺ is immobilised on the PVA nanofiber membrane, the remaining Cu²⁺ requires a longer contact time to drive closer to and be adsorbed by the PVA nanofiber membrane by the difference in concentration until the adsorption equilibrium is reached. It can also be seen from Figure 4 that the value of the equilibrium adsorption amount of the PVA nanofiber membrane to the adsorbed liquid at different initial concentrations is substantially proportional to the initial Cu²⁺ concentration of the adsorbed liquid, which is still caused by the concentration difference drive. However, compared with Pb²⁺, the time for Cu²⁺ to reach equilibrium adsorption is only half of that of Pb²⁺, and the adsorption amount is also far from Pb²⁺. In order to study the differences, the adsorption mechanism and adsorption kinetics are studied.

Effect of contact time and initial concentration on copper ion adsorption capacity

In order to further study the adsorption mechanism of PVA nanofibers, the adsorption isotherms of Pb²⁺ and Cu²⁺ were fitted by Langmuir and Freundlich theoretical models, respectively. The Langmuir theoretical model equation is one of the commonly used adsorption isotherm equations and is widely used in the field of adsorption. Langmuir theoretical model is written as follows: (14) $q_{e} = \frac{K_{L} q_{m} C_{e}}{1 + K_{L} C_{e}}$ {q_e} = {{{K_L}{q_m}{C_e}} \over {1 + {K_L}{C_e}}} q_e is the equilibrium adsorption amount (mg/g), C_e is the equilibrium solution concentration (mg/L), q_m is the saturated adsorption amount (mg/g) and K_L is the constant (L/mg) of the Langmuir theoretical model. The Langmuir theoretical model believes that the adsorbent surface contains a large number of active adsorption centres. When the active adsorption centre is fully occupied, the adsorption amount reaches the saturation value, and the adsorbate exhibits a monolayer distribution on the surface of the adsorbent. The equilibrium constant K_L of Langmuir is related to the physical properties of the adsorbent and the adsorbate as well as the temperature. The larger the K_L value, the stronger the adsorption performance of the adsorbent. Figure 5 is a map of the Langmuir adsorption model fit.

Langmuir adsorption model fitting diagram: Lead Yuzi (left) Tongyuzi (right)

The Freundlich theoretical model has no practical physical meaning but is applied to the adsorption theory as an empirical formula, and it satisfies the Freundlich theoretical model, which represents the PVA nanofiber membrane adsorption model as a multilayer adsorption model. Freundlich theoretical model is written as follows: (15) $q_{e} = K_{F} C_{e}^{\frac{1}{n}}$ {q_e} = {K_F}C_e^{{1 \over n}} q_e is the equilibrium adsorption amount (mg/g), C_e is the equilibrium solution concentration (mg/L), qm is the saturated adsorption amount (mg/g) and K_F is the constant of the Freundlich theoretical model [(mg/g) (Mg/L)-n], representing the adsorption capacity of the adsorbent, and the n value is often used to judge the preferential performance of adsorption performance, n>l is the preferential adsorption, n = l is linear adsorption and n<l is non-preferential adsorption. The Freundlich theoretical model describes a multi-layer adsorption model and is widely used for physical adsorption, chemical adsorption and solution adsorption because it has no saturated adsorption value. K_F indicates the strength of the adsorption capacity of the adsorbent. Figure 6 is a Freundlich adsorption model fit.

Freundlich adsorption model fitting figure: lead (left) and copper (right)

In this study, the two adsorption models are fitted according to the equilibrium adsorption amount, and the fitting data are analysed. For the Langmuir model, the Ke values of Pb²⁺ and Cu²⁺ are 0.0129 and 0.0023, respectively, indicating that the PVA nanofiber membrane has a higher adsorption capacity for Pb²⁺ than Cu²⁺. Both of them have R2 of 0.98 or more, indicating that they conform to the single-layer adsorption model. For the Freundlich model, Pb²⁺ and 0: the & value of 112+ is 14.88 and 1.399 respectively, indicating that the adsorption capacity of PVA nanofibers to Pb²⁺ is greater than that of Cu²⁺, and the n values of both are about 1.1, indicating that the adsorption modes are preferential adsorption, that is, adsorption is easier to carry out. Since the R2 of the Freundlich model is larger than the R2 of the Langmuir model, the nanofiber membrane belongs to multilayer adsorption. In order to study the difference of the equilibrium adsorption amount of Pb²⁺ and Cu²⁺ at the same initial concentration, the adsorption kinetics of Pb nanofiber membranes adsorbing Pb²⁺ and Cu²⁺ are studied by using quasi-first-order and quasi-second-order kinetic equations. In the kinetic study of chemical reactions, scientists derived the chemical reaction kinetics equation based on the relationship between the reaction rate of the substance and the concentration of the participating substances. The number of chemical reactions is the sum of the individual reactant concentration indices of the kinetic equation. The quasi-first-order dynamic equation is a new model obtained by the modified method, which is equivalent to the dynamic model of the first-order reaction. According to the quasi-first-order dynamic equation, the system is mainly based on physical adsorption, that is, adsorption plays a major role in electrostatic and van der Waals forces. For Pb²⁺, both the quasi-first-order kinetic equation and the quasi-second-order kinetic equation have R2 exceeding 0.98, indicating that both physical adsorption and chemisorption act simultaneously. For Cu²⁺, the R2 of the quasi-second-order kinetic equation is much larger than the quasi-first order; so, chemisorption plays a major role. This is because Cu²⁺ can form a complex structure with the hydroxyl groups on the PVA molecular chain; so, Cu²⁺ is fixed on the fibre membrane mainly through complexation, and the adsorption equilibrium time is short. However, because 4 mol –OHs are required to reach the complex equilibrium with each mole of Cu²⁺ ions, some of the hydroxyl groups on the surface of the PVA nanofiber membrane can no longer be complexed with Cu²⁺. The increase of the surface degree of the PVA nanofiber membrane weakens the driving force, and the adsorption amount is reduced. For Pb²⁺, although it has no complexation with hydroxyl groups, it is more easily adsorbed by the PVA nanofiber membrane through the action of static electricity and Howard force, and the concentration driving force is greater than Cu²⁺ ion, but the adsorption equilibrium time is relatively long, and the adsorption amount is larger than Cu²⁺ ions.

With the increase of contact time, the adsorption amount of Pb²⁺ and Cu²⁺ showed an increasing trend, and finally, it became equilibrium. The time for Pb²⁺ to reach equilibrium was 30 h, and the time for Cu²⁺ to reach equilibrium was 15h. As the initial concentration of the adsorbed liquid increases, the amount of adsorption also increases, and the final amount of adsorption is proportional to the treated concentration. By fitting the Langmuir model, the K_L values of Pb²⁺ and Cu²⁺ for PVA nanofiber membranes were 0.0129 and 0.0023, respectively, indicating that the adsorption capacity of the PVA nanofiber membrane for Pb²⁺ is much larger than that of Cu²⁺, and both of them have R2 of 0.98 or more, indicating that they conform to the single-layer adsorption model. For the Freundlich model, the K_F values of Pb²⁺ and Cu²⁺ are 14.88 and 1.399, respectively, indicating that the adsorption capacity of PVA nanofibers to Pb²⁺ is much larger than that of Cu²⁺, and the n values of both are greater than 1; so, it is a multi-layer adsorption model that is easy to adsorb. However, because the R2 of Freundlich is larger than the R2 of the Langmuir model, the nanofiber membrane belongs to multilayer adsorption. For Pb²⁺, the R2 of the quasi-first-order and quasi-second-order kinetic equations is close, and the chemisorption and physical adsorption are performed simultaneously; for Cu²⁺, the R2 of the quasi-second-order kinetic equation is greater than that of the quasi-first order, indicating that chemisorption plays a major role.

Conclusion

The Pb²⁺ and Cu²⁺ in the PVA nanofiber adsorption solution were studied, and the results show that when the initial concentration of the adsorbed liquid increases, the adsorption amount also increases. The study of the adsorption model proves that the PVA nanofiber membrane belongs to multilayer adsorption, and the theoretical model is supported by the Freundlich theorem. By fitting the Langmuir model, the K_L values of Pb²⁺ and Cu²⁺ for PVA nanofiber membranes were 0.0129 and 0.0023, respectively, indicating that the adsorption capacity of the PVA nanofiber membrane for Pb²⁺ is much larger than that of Cu²⁺. Both of them have R2 of 0.98 or more, indicating that they conform to the single-layer adsorption model. For the Freundlich model, the K_F values of Pb²⁺ and Cu²⁺ are 14.88 and 1.399, respectively, indicating that the adsorption capacity of PVA nanofibers to Pb²⁺ is much larger than that of Cu²⁺, and the n values of both are greater than 1; so, it is a multi-layer adsorption model that is easy to adsorb. However, because the R2 of Freundlich is larger than the R2 of the Langmuir model; the nanofiber membrane belongs to multilayer adsorption. For Pb²⁺, the R2 of the quasi-first-order and quasi-second-order kinetic equations is close, and the chemisorption and physical adsorption are performed simultaneously; for Cu²⁺, the R2 of the quasi-second-order kinetic equation is greater than that of the quasi-first order, indicating that chemisorption plays a major role.

Figures & Tables

Names, specifications and models of raw materials and manufacturers

Name of raw material	Specifications and models	Manufacturer

Polyvinyl alcohol	One hundred and seventeen	Colerie Trading (Shanghai) Co., Ltd.
Deionised water	-	Laboratory self-control
Copper sulphate pentahydrate	Analytical purity	China Pharmaceutical Group Chemical Reagents Co., Ltd.
Lead chloride	Analytical purity	China Pharmaceutical Group Chemical Reagents Co., Ltd.

Experimental equipment and instruments

Instruments/equipment	Model	Manufacturer

Electrospinning machine	ESM-C01	Shanghai Yuyue Nanotechnology Co., Ltd.
ICP emission spectrometer	PS3500DDII	Hitachi Manufacturing Institute

Name, specifications and models of experimental raw materials and manufacturers

Name of raw material	Specifications and models	Manufacturer

Polyvinyl alcohol	117	Colerie Trading (Shanghai) Co., Ltd.
Deionised water	-	Laboratory self-control

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Applied Mathematics and Nonlinear Sciences

Solidification treatment effect of wellsite waste mud based on physical adsorption of a composite curing agent

Zhikun Liu,
Zhikun Liu,
Chaoqun Zhang and
Chaoqun Zhang and
Qi Li
Qi Li

Published Online: 15 Jun 2022

Volume & Issue: AHEAD OF PRINT

Page range: -

Received: 28 Jan 2022

Accepted: 27 Mar 2022

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Applied Mathematics and Nonlinear Sciences

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Applied Mathematics and Nonlinear Sciences

Solidification treatment effect of wellsite waste mud based on physical adsorption of a composite curing agent

Zhikun Liu,Zhikun Liu,Chaoqun Zhang andChaoqun Zhang andQi LiQi Li

Published Online: 15 Jun 2022

Volume & Issue: AHEAD OF PRINT

Page range: -

Received: 28 Jan 2022

Accepted: 27 Mar 2022

Journal & Issue Details

Applied Mathematics and Nonlinear Sciences

PDF Preview

Article

Fig. 1

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Fig. 3

Fig. 4

Fig. 5

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References

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Zhikun Liu,
Zhikun Liu,
Chaoqun Zhang and
Chaoqun Zhang and
Qi Li
Qi Li