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Analysis of displacement of compounds used as pesticides in Annona Muricata through the simulation of a liquid chromatography column.


The Annona Muricata is commonly known as soursop, it is one of the most traded fruit in Latin America, due to its high content of bioactive compounds and pleasant aroma [12]. These features because the fruit is vulnerable to various pests, such as fruit punch wasp, the lace bug, etc. [4]. Currently, to combat this phenomenon is used chemical pesticides, which directly combat harmful organisms to the plant and the fruit.

The Environmental Protection Agency (EPA) classified as moderately toxic most of compounds used as chemical pesticides, however, the mixture of various compounds a cause of an incorrect synthesis, poor purification or inadequate application. That mixture can provoke that the toxicity increased [9].

In the preparation and purification of chemical pesticides are used dissociation techniques such as chromatography, which is a process widely used in industry for separation of reactants and products. Principally the mixtures to separate are: some natural compounds, enzymes, proteins, contaminants in crops such as pesticides, among others [3, 6, 8].

In this separation process, the separation of various components through their chemical and physical properties was performed, thus, this process had been used as a specific separation method [1]. This separation is achieved due to the interaction between the mobile phase which contains the sample and the stationary phase, this phase could be made of alumina, silica or ion exchange resins, through this phase the dissolved sample flows. Different types of chromatography are characterized by the state of the phases. In the case of liquid chromatography (LC), the mobile phase is liquid and the stationary phase is in solid state [6, 7, 11]. However, the chemical interactions between the sample and each one of the phases determine the degree of migration and separation of the compounds.

Chromatography is a technique widely used worldwide, despite this; the lack of specific experiments for each compound causes the cost of implementation at industrial level is high. Because of this, it is necessary to develop models that describe the behavior of compounds through the column of this technique. Wicke in 1939 posed a model of LC, which is known as the ideal model LC, Wilson complement this model a year later [16, 18]. The development of these models was carried out using the Langmuir isotherm for a single compound. This isotherm can describe the adsorption of molecules on a solid surface.

Due to the complexity of these models, few people have taken on the task of developing. However, the increasing in the use of this technique, It has increased the interest in developing these models. Tingyue Gu proposed in 1995 proposed a model based on dimensionless numbers using mass transfer and energy (Tingyue, n.d.). Which are implemented in the material balances of the system.

Therefore, it is given the need to find a method, which can predict the behavior of some pesticides used in the AnnonaMuricata through a liquid chromatography column. This seeks to observe the relationship of these pesticides, choose of the appropriate column and the elution pattern of the compound through the same.



In the preservation of the Annona Muricata specie, chemical pesticides were used, in order to decrease the losses in the crops (

Fig.). Of these pesticides, the Malathion and the Dimethoate are organophosphorus compounds. The main toxic feature of these compounds is that upon entering the human system can produce muscular atrophy, dizziness, excessive sweating and even death. The Carbendazim used to control wasps fruit punches, it was characterized as a nitrogenous compound, and in addition it has a benzene as base. In the degradation of this compound, nitrates and nitrites were produced, which act as fertilizer for plants. However, benzene was also produced, which is highly carcinogenic. Mancozeb is a polymeric compound, used to prevent anthracnose in the fruits. Unlike the first three compounds, the Mancozeb behaves in different way, due to their multiple polymeric bonds, thus the behavior in a liquid chromatography column is carried out by taking into account the characteristics of this product dissolved in water.


Development of the model:

The material balances for a liquid chromatography column were raised, where the system was considered as an isothermal process with uniform pore size for the liquid phase. Because the current columns are designed with a small diameter, there are not considered radial concentration gradients. This also promotes the formation of the equilibrium between the surface and the surrounding fluid.

The model can be derived from the equations of continuity from the book Transport Phenomena by Bird et al. [2]. In addition it is supplemented with material balances in dynamic state for the particle (Eq. 1) and the fluid passing through the column (Eq. 2).



To solve the problem, the following boundary conditions were required:

Z = 0 [delta] [C.sup.b]/[delta]Z = v/[D.sub.b] x ([C.sub.b] - [C.sub.f] (t)) 3

Z = L [delta] [C.sup.b]/[delta]Z = 0 4

R = 0 [delta] [C.sup.p]/[delta]R = 0 5


In the system, the time "0" was the time when the sample in the form of a single pulse, finishes of enter in the column. For analysis, the following dimensionless parameters are defined:

[C.sub.b] = [C.sub.b]/[C.sub.0] 7

[C.sub.p] = [C.sub.p]/[C.sub.0] 8

[tau] = vt/L 9

r = R/[R.sub.p] 10

z = Z/L 11

P[e.sub.L] = vL/[D.sub.b] 12

Bi = K[R.sub.p]/[[member of].sub.p][D.sub.p] 13

[eta] = [[member of].sub.p][D.sub.p]L/[R.sup.2.sub.p]v 14

Bi = 3 Bi[eta] (l - [[member of].sub.b])/[[member of].sub.b] 15

Of these dimensionless parameters, which identifying the behavior of the fluid, there was three parameters such as the Peclet number (P[e.sub.L]) that quantifies the axial dispersion, the Biot number (Bi) for mass transfer and a single dimensionless factor of each compound ([eta]).

Using the equations 7 to 15 in the equations 1 and 2, it was obtained for the particle (Eq. 16) and the fluid passing through the column (Eq. 17).

- 1/P[e.sub.L] [[delta].sup.z][c.sub.b]/[delta][z.sup.2] + [delta][c.sub.b]/[delta]z + [delta][c.sub.b]/[delta][tau] + [xi] x ([C.sub.b] - [C.sub.p,r=1] = 0 16

[delta]/[delta]tau [(1 - [[member of].sub.b])[C.sup.*.ub.p] + [[member of].sub.p][C.sub.p]] - [eta][1/[r.sup.2] [delta]/ [delta]r ([r.sup.2] [delta][c.sub.p]/[delta]r] = 0 17

Parameters for each compound and the column:
Table 1: Properties of the pesticides in Annona Muricata.

Property     Value for   Value for    Value for
             Malathion   Dimethoate   Carbendazim

[T.sub.Eb]   513,15      348,15       348,15
MW           330,35      229,00       191,18
[micro]      1,00E-03    6,08E-03     2,50E-01
Vm           0,2785      0,1788       0,7647

[rho]        1,186       1,281        0,25

Property     Value for    Units

[T.sub.Eb]   348,15       K
MW           541,00       g/mol
[micro]      6,00E-01     Pa s
Vm           0,2818       [m.sup.3]
[rho]        1,92         g/[cm.

To solve the model, physical properties of each molecule were required ( Tablel) and specific data for the column (Table 2).

The other parameters necessary for the solution of the equations 16 and 17 (

Table 3) were calculated using the initial values.

Solving the equations system:

From Equation 16, the concentration profile according to column length and duration of the chromatography was obtained. For the development of the derivatives, the method of central derivatives was used for the equations 28 and 29 for partial differential equations [15]. The subscripts of equations indicate the basis of the derivative, while the parameters h and k are the step sizes that advances in length (z) and time ([tau]) respectively. The same process is performed for the partial derivatives of equation 17 for the concentration of component depending on the particle radius and time.

[U.sub.zz] = [U.sub.Z+1,[tau]] - 2[U.sub.Z,[tau]] + [U.sub.Z-1,[tau]]/[h.sup.2] 28

[U.sub.z[tau]] = [U.sub.Z+1,j+1] - [U.sub.Z-1,[tau]+1] + [U.sub.Z+1,[tau]-1] + [U.sub.i-1,j-1]/2hk 29

Considering that for the variables "z" and "r" 20 points were defined, with step size h, and for the variable "[tau]" 6 points were defined, it had a matrix of equations, in which the solution of the system is when the equation is zero at each point.

A multivariable iterative method for solving equations were used, the zero equalization was used as restriction of each equation, where random variables values were assigned until all equations in the matrix are zero. These equations were solved with the help of Solver function of Microsoft Excel 2013.

To calculate the error of the equalization to zero, the mean, median and standard deviation was calculated. This procedure was realized for each one of the molecules studied to verify the performance of each pesticide.

This solution was repeated for each compound examined, taking into account the properties of each molecule.



In crops of Annona Muricata, the chemical pesticides were used to control pests, as shown in

Table 4, there are very toxic compounds as Dimethoate. This compound is used to combat lace bug, however the intrinsic toxicity of the compound is high, while the Carbendazim was used to attack moths and drilling wasps fruit, had low toxicity, thus can be applied to the fruit without causing adverse contamination by bioaccumulation.

Development of the model:

The filling or stationary phase of the column is one of the most controlled parameters during his production, because a high quality, form more uniform pores, whereby the system reach the equilibrium faster. The process of liquid chromatography is an isothermal process, due to the variation of the densities and the viscosities of the compounds tested. Whereupon the assumptions applied in the model did not generate significant differences with the real behavior.

The properties of the different pesticides used in the column for the simulation were shown in

Table1, the column configuration is carried out according to the proposed by Tingyue Gu, which were shown in Table 2.

The main change in compounds were their density and their viscosity, which directly affect the calculation of the Peclet number, due to this number was the relationship between fluid advection and diffusion rate, while is was bigger indicates the system is mainly governed by fluid displacement. The porosity of the particle ([member of]p) and stationary phase ([member of]b) are predetermined for each column and depend on the material in which the column is manufactured. The tortuosity ([[tau].sub.tor]) is the degree of rotation that had the column, between longer is the column, a higher degree of tortuosity was required to store the column without affecting the volume occupied by it.

With the initial values, the parameters necessary for the resolution of the derivatives were calculated (

Table 5), it should be noted that the number of mass transfer Biot indicates the ease of molecular diffusion within the column, as the column has a smaller diameter; the diffusion intra-particle will be smaller. The viscosity is another factor that significantly affects the diffusion, so that the concentration inside the particle will have many variations. This dimensionless number depends directly on the mass transfer coefficient, it is intended that this value is as high as possible on any system to facilitate the exchange of molecules between the two phases, this factor depends on the Reynolds number, which characterizes the movement of a fluid, in liquid chromatography is intended that the fluid passing through the column is in laminar regime, as consequence the molecular transfer between the phases is facilitated.

The internal volume of the column is a very important factor in terms of operating cost, between the value is higher, it requires a larger quantity of mobile phase, leading to the existence of more waste when operating the equipment. Currently, in the columns this value is littler, this is achieved by making the column diameter smaller and internal pore diameters are much finer.

For each compound the dimensionless factor takes values between1x[10.sup.-2] and 1x[10.sup.-6], outside these values, the system is considered as non-equilibrium system. Whereupon for Carbendazim and Mancozeb, the value was outside the limits, reason why the system shows a lot of oscillation, and observed spikes not had a good definition.

Solving the model for each compound:

The step size for each of the variables was modifiable, to high step sizes, the system loses accuracy, while for a low steps, the error in each iteration builds up, so that the system will behave so oscillatory. To solve the system of equations were used steps from 0.0526 and 0.2000 for h and k respectively, the step size h, was defined for the change in the variable length "z" and radio "r", because they were the Main variables on which the studio is located, while the variable k, was assigned to the variable of time "[tau]".

To verify the system solution through the proposed method, the mean, median, and standard deviation was determined for each compound (

Table 6). These values were calculated using the data obtained from each point of the matrix, in total 240 spots.


The average data for the compounds was closer to the desired value, despite the high volume of data. This value is verified with the standard deviation, which shows the dispersion of data, which in this case is low, thus the 240 equations to solve the method tend to reach its desired value, giving credence to the results.

The system of equations for each compound was resolved (Equation 16 and 17), with these solutions, the displacement of the maximum concentration of the pesticide was determined (Fig. 1). Of the compounds tested, the greater variation in the data was the Malathion. This is mainly due to the two chains accompanying the phosphate group (

Fig.--Part A), these chains generate a drag force on the surface of the solid phase, for which, decreases the dispersion and diffusion within the column, this causes the oscillations generated by the model.

The change in concentration of Malathion depending on the length of the column (Fig. 1--Part A), is constant for low values of Tao, however to Taos of 0.8 and 1, the change was not apparent, this is due to the molecular interactions of the phosphate functional group and the sulfur radicals with the stationary phase. These groups attached to the chain, induce the formation of multiple peaks in the chromatogram, whereby the optimal travel time within the column, was for a maximum Tao of 0.8

For Carbendazim (Fig. 1,

Fig. 2--Part B), two large peaks for lower Taos (<0.2) and higher Taos (> 0.8) were generated, this is because the benzene function was very nonpolar, whereby the displacement of the pesticide within the column occur linearly. This shows that the interactions between the compound and the column were very low, because of this, the intermediate area of the chromatogram not present peaks as noticeable as in the ends. Malathion and Carbendazim, have low viscosity, this parameter promotes intra-particle diffusion, whereby the local balance between stationary phase and mobile phase is reached faster.

The Dimethoate (Fig. 1,

Fig. 2--Part C) presents an intermediate behavior between Malathion and Carbendazim due to the similarity with these two molecules. The chromatogram generated have defined peaks for different Taos. However the optimal time to perform the separation of this compound was for high Taos (0.9), in this point the resolution and the concentration increases.

The Mancozeb (Fig. 1,

Fig. 2--Part D) differs in behavior from the other compounds, mainly because of its polymeric property, which induces the formation of clusters of the compound. The intra-particle diffusion is low for the entire range of time analyzed. These clusters can cause blockages and inside the particles of the stationary phase, leading to greater drag force, this causes the system take long to reach a balance.


For the separation of these compounds through a liquid chromatography column, it requires analyzing the chromatogram for a maximum time (Tao = 1) (Fig. 3). Mancozeb because its physicochemical properties can be easily separated in a column length of 0.24, the remaining peaks of this compound were not a significant portion, due to this, they did not present problems. In the case of Malathion two peaks were presented in 0.58 and 0.70, these peaks were due to the polar parts of the molecule, with which two different drags were generated depending on the orientation of the molecule, the separation of this compound was not as efficient as the Mancozeb. For Dimethoate and Carbendazim their concentration peaks are at 0.93 and 0.94 respectively, these are partially superimposed. This effect produces instability in the system, reason why generated noise for high Taos was.



The model was developed based on the material balances for the column of liquid chromatography system. Due to the model complexity, the ideal step sizes were selected according to the importance of the analyzed variable. With these steps, the accumulated error decreases through each point of the matrix.

The solution of the equations depends on the initial values taken, however, the pore diameter and the molecular diffusivity, greatly affect the dimensional parameters of mass transfer, which dictate the behavior of the pesticide in the column. It should be noted that these parameters also depend on the physicochemical properties of the molecule worked. Also, it should take in account the flow requirements inside the column.

The diffusion and the dispersion of the pesticide in the column depends primarily on the physicochemical characteristics of the compound. For the same column configuration, the separation is efficient For Mancozeb and Malathion, due to it had retention times of 0.24 and 0.73 respectively, whereas the Dimethoate and the Carbendazim had similar times (about 0.93), which this separation has little performance.

Bi             Biot Number
c              Dimensionless Malathion concentration
C              Malathion concentration {mol/L)
d              Diameter (cm)
[d.sub.c]      Inner diameter of a column (cm)
[D.sub.m]      Molecular diffusivity for Malathion ([cm.sup.2]/s)
[D.sub.p]      Effective diffusivity for Malathion ([cm.sup.2]/s)
[[member of]
  .sub.b]      Bed void volume fraction
[[member of]
  .sub.b]      Particle porosity
[xi]           Dimensionless mass transfer constant
h              Step size for z and r
K              Mass transfer coefficient for Malathion
K              Step size for [tau]
L              Length of study area(cm)
MW             Molecular Weight (g/mol)
n              Dimensionless constant for Malathion
Pe             Peclet number
Q              Mobile phase volumetric flow rate (mL/min)
[tau]          Dimensionless time
t              Time (s)
r              Dimensionless particle radio
R              Radial coordinate (cm)
v              Interstitial velocity (cm/s)
[V.sub.m]      Atomic volume ([m.sup.3]/kgmol)
V              Volume ([cm.sup.3])
Z              Column length (cm)
Z              Dimensionless column length


0              Initial point
b              Mobil phase
c              Column
in             Inner part
L              Axial column coordinate
P              Particle phase


The authors would like to offer their special gratitude to the Research Vice-chancellorship of Nueva Granada Military University for financing the research project IMP_ING 1777 titled: "Analisis de residuos de plaguicidas en frutas tropicales en Colombia para la prediction de posibles efectos en la salud humana", 2015.


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[5] Giacometti, J. and D. Josic, 2013. Chapter 7--Protein and Peptide Separations. In S. F. R. H. F. P. S. Lloyd (Ed.), Liquid Chromatography pp: 149-184. Amsterdam: Elsevier. Retrieved from

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[8] Hernandez, F. and M. Ibanez, 2013. Chapter 12 - Multiresidue Methods for Pesticides and Related Contaminants in Food. In S. F. R. H. F. P. S. Lloyd (Ed.), Liquid Chromatography (pp. 319-336). Amsterdam: Elsevier. Retrieved from http://www. sciencedirect. com/ science/article/pii/B9780124158061000127

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[13] Striegel, A.M., W.W. Yau, J.J. Kirkland and D.D. Bly, 2009. The Column. In Modern Size-Exclusion Liquid Chromatography (pp. 130-144). John Wiley & Sons, Inc. Retrieved from

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Jorge Eliecer Buitrago Salazar, Olga Lucia Ramos Sandoval, Dario Amaya Hurtado

Engineering in mechatronics, Faculty of Engineering, Military University Nueva Granada, Bogota D. C., Colombia

Received 12 April 2016; Accepted 10 May 2016

Address For Correspondence:

Jorge Buitrago, Engineering in mechatronics, Faculty of Engineering, Military University Nueva Granada, Bogota D. C., Colombia.Tel:+57-1650000 Ext: 1280, E-mail:
Table 2: Initial values for calculating the parameters
of the column.

Parameter             Value    Unit

MW                    10000    g/mol
Q                     1,0000   mL/min
L                     10,000   cm
[d.sub.c]             1,0000   cm
[R.sub.p]             0,0113   cm
[[member of].sub.b]   0,4000
[[tau].sub.tor]       4,0000
[d.sub.p]             300,00   [Angstrom]
[[member of].sub.p]   0,5000

Table 3: Equations used to calculate the parameters.

Parameter           Equation                             Number

[]          [] = [pi] x [R.sup
                      .2.sub.c] * L
v                   v= Q/[pi]/4 [d.sup.z.sub.c]          22
                      [[member of].sub.b]
[d.sub.m]           [d.sub.m]=1.44 [(MW).sup.1/3]        23
[D.sub.m]           [D.sub.m]=9.96x[10.sup.-16]T/[mu]    24
  (Polson, 1950)      x [V.sup.1/3.sub.m]
[D.sub.v]           [D.sub.p]=[D.sub.m][1 - 2.104 x      25
  (Striegel, Yau,     ([d.sub.m]/[d.sub.p]) + 2.09
  Kirkland, &         [([d.sub.m]/[d.sub.p]).sup.3]
  Bly, 2009)          - 0.95 [([d.sub.m]/[d.sub.p])
K(E. J. Wilson &    K= 0.687[v.sup.1/3][([[member of]    26
  Geankoplis,         .sub.b][R.sub.p]/[D.sub.m])        27
  1966)               .sup.-2/3]

Parameter           Units

[]          [cm.sub.3]
v                   cm/S
[d.sub.m]           [Angstrom]
[D.sub.m]           [cm.sup.2]/S
  (Polson, 1950)
[D.sub.v]           [cm.sup.2]/S
  (Striegel, Yau,
  Kirkland, &
  Bly, 2009)
K(E. J. Wilson &    cm/S

Table 4: Toxicological properties of pesticides.

Compound      Formula                  CAS Number   Toxicity (Oral
                                                    LD50 Rat)

Malathion     [C.sub.10][H.sub.19]     121-75-5     5500 mg/kg
Dimethoate    [C.sub.5][H.sub.12]N     60-51-5      967 mg/kg
Carbendazim   [C.sub.9][H.sub.9]       10605-21-7   > 15000 mg/kg
Mancozeb      [C.sub.4][H.sub.8]Mn     8018-01-7    > 5000 mg/kg

Table 5: Parameters calculated for each compound.

Parameter    Equation   Value for   Value for
                        Malathion   Dimethoate

[]   22         7,8540      7,8540
v            23         0,0531      0,0531
[d.sub.m]    24         9,9546      8,8100
[D.sub.m]    25         3,24,E-11   1,01,E-10
[D.sub.p]    26         7,53,E-12   2,38,E-11
K            27         9,62,E-07   2,06,E-06
[Pe.sub.L]   12         222,2222    222,2222
[eta]        14         5,61,E-06   1,77,E-05
Bi           13         2874,8444   1948,8070
[xi]         15         0,0725      0,1552

Parameter    Value for     Valor for   Units
             Carbendazim   Mancozeb

[]   7,8540        7,8540      [cm.sub.3]
v            0,0531        0,0531      cm/S
[d.sub.m]    8,2956        11,7335     [Angstrom]
[D.sub.m]    1,52,E-12     8,82,E-13   [cm.sup.2]/S
[D.sub.p]    3,57,E-13     2,02,E-13   [cm.sup.2]/S
K            1,25,E-07     8,71,E-08   cm/S
[Pe.sub.L]   222,2222      222,2222
[eta]        2,66,E-07     1,51,E-07
Bi           7876,4682     9685,3012
[xi]         0,0094        0,0065

Table 6: Error calculated for solving the system of equations.

Parameter     Value for   Value for    Value for     Value for
              Malathion   Dimethoate   Carbendazim   Mancozeb

Mean          0,3547      -0,2187      -0,3502       -0,1385
Median        3,8E-06     9,7E-06      0,0E+00       7,9E-06
Standard      1.2449      0.8531       0.7438        2,4238
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Author:Salazar, Jorge Eliecer Buitrago; Sandoval, Olga Lucia Ramos; Hurtado, Dario Amaya
Publication:American-Eurasian Journal of Sustainable Agriculture
Article Type:Report
Geographic Code:0LATI
Date:Jun 1, 2016
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