Mathematical Modeling of Dispersion Coefficient and Particle Density Bacterial Influence on Campylobacter spp Transport In Surface Water Environment Volume 4 - Issue 2

Ezeilo FE¹* and Eluozo SN²

• ¹Department of Civil Engineering, Rivers State University of Nkpolu Oroworukwo, Port Harcourt
• ²Department of Civil College of Engineering, Gregory University Uturu Abia State

Received: January 04, 2021   Published: January 22, 2021

Corresponding author: Ezeilo FE, Department of Civil Engineering, Rivers State University of Nkpolu Oroworukwo, Port Harcourt, Nigeria

DOI: 10.32474/TCEIA.2021.04.000182

Abstract PDF

Particle density bacterial and dispersions of Campylobacter deposition was monitor in surface water environment, the transport of these microbes were observed to decrease with respect to change in distance at various monitored locations, dispersion of the contaminant at initial point of discharge were examined in the study environment, this was influenced through the migration of the contaminant at various station point of discharge, it was based on the heterogeneous velocity in the surface water environment. Despite the application of one dimensional flow transport, the study experience the impact of dispersion as decrease in concentration were observed in all the figures, the spread of the contaminant are based on the velocity of flow subjecting it to fast spread of campylobacter in surface water environment, particle density bacterial influence was also examined in its different dimensions, the particle densities of the bacterial was through transient frequencies, while another was through a microfluidic channel of flow in surface water, thus the distribution of a population and its heterogeneous size particle were based on difference carrier fluids, these also affected the concentration through heterogeneous velocities of surface water flows at different station point, the decrease in the transport system were monitored based on these two predominant parameters in the simulation, the generated parameters of concentrations at different stationed point of transport ranged from 24.38700365-3.422646182, 21.54119013- 3.170336995, 23.47218199-3.56121468, 19.59794838-2.705873785, 14.78899765-1.873477905, 12.58403842-1.536910683. the study has express the behaviour of the system in terms of its rapid decrease of campylobacter based on these factors, the concentration implies that the surface water Pollution should be subjected to clean up to reduce the rate of contamination to the minimum required standard, this will definitely make the surface water environmentally friendly. The study is imperative because it has expressed the rate of these two predominant parameters that can influenced the spread and the deposition of campylobacter in surface water environment.

Keywords: Mathematical Modeling, Dispersion Coefficient Density Bacterial and Campylobacter Transport

Pathogens group of this type of species were Vibrio Cholera are from has such causes cholera, this has been observed to infect numerous human settlements, over millions of people each year Nelson et al., 2009 [1] Eluozo Afiibor 2018 [2]). For instance, records of the implementation of a suitable quantify to prevent the transmission of water borne pathogens (Colwell, 1996 [3]; Okun 1996 [4], Eluozo and Oba 2018 [5], Pandey 2012 [6]). Studies carried out in the Year past the application of geographic techniques has shown the spread and epicenter of cholera, this perception resulted to the locating of contaminated water body, because that it was observed to be responsible for spreading of the disease. Diseases such as Water borne (i.e., diarrhea, gastrointestinal illness) such rate are caused by various microbes such as bacteria, viruses, and protozoa, there are various reasons for numerous outbreaks as it stated by (Craun et al., 2006 [7] Eluozo and Ezeilo 2018 [8], Pandey 2012 [6]). Nigeria as a developing nation such as other Africa nations, waterborne diseases infect millions of people (Fenwick, 2006 [9]). Cryptosporadium, E. coli O157:H7, V. Cholera, and Salmonella was observed to be the fundamental outbreaks in this environment (Craun et al., 2006 [7], Eluozo and Ezeilo 2018a [10], Eluozo and Ezeilo 2018b [11], Eluozo and Ezeilo 2018c [12]). It was noted that in the mid late 18^th century; cholera, diseases have infected high percentage millions of people around the globe (Colwell, 1996 [3]). More so , in relative conditions, there are current research studies carried out such as Diffey (1991) [13], Brookes et al. 2004 [14] Eluozo and Ezeilo 2018d [15], Jamieson et al.(2004) [16], Gerba and Smith (2005) [17], Gerba and McLeod (1976), John and Rose (2005) [18], Hipsey et al. 2008 [14] Eluozo and Afiibor 2018b [19], Eluozo and Afiibor 2018a [2]), and Pachepsky and Shelton (2011) [20] these there is a comprehensive research the has thoroughly reviewed the current advancement in this area, precisely, freshwater and estuarine sediments. However, these research studies have developed some other areas that has not been done to improve on the existing works, numerous research is on specific water bodies, examples of these are research studies carried out by, John and Rose (2005) [18] it focuses on ground water, Brookes (2004) [14], other works carried out focuses on reservoirs and lakes, and Jamieson et al. 2004 [16], Eluozo and Amadi 2019a [21], Amadi and Eluozo 2019b [22] while others focuses on agriculture watershed.

Governing equation

Nomenclatures

C = Concentration Campylobacter SPP
B = Particle density of bacterial
K = Dispersions. Velocity of flow
A = Fluid Density
X = Distance
Multiplying the equation through byC[x], we have:

Then Equation (2), we have:

Differentiate 2nd term on the left hand side of (6) with respect to x, we have

Applying separation of variables, by dividing through by C(x) and cross multiply by dx, gives:

Taking exponent of the both side of the equation

Standard laboratory experiment where performed to monitor Campylobacter using the standard method for the experiment at different sample at different station, the water sample were collected in sequences base on specification stipulated at different locations, this samples collected at different location generated variations at different distance producing different Campylobacter concentration through physiochemical analysis, the experimental result were compared with the theoretical values for model validation [23].

Tables 1-6 & Figure 1-6.

Figure 1-6 explained the behaviour of Campylobacter Concentration in surface water environment, the study through its expression on graphical representations, shows the rate of concentration from the initial point of discharge to the final monitored distance in the study environment, the figures from various location in studied environment experienced high to low concentration, but with different concentration between the initial point source of discharge to the final monitored distance in the study area, gradual decrease with respect to change in distanced was observed in all the studied locations, the rate of decrease in concentration was observed to be attributed to the dispersion coefficient and the particle densities of the bacterial, in surface water environment, the system developed monitor the influenced based on the imperative factors in surface water environment, the variation of velocity affected the dispersions of the microbes in terms of discharge in different point source, this implies that the dispersion influence on the transport of Campylobacter Concentration were based on the observed heterogeneous velocities in various point source of discharge in the study environment , while the particle density bacterial are observed through its mass transient frequency through the channel flow, it is monitored based on the discharge rate of population observed in its rate of heterogeneity particle size, while particle densities measured from carried fluids through its frequencies, this implies the shapes of the microbes that also determined the densities are affected by the microfluidic channel on the variation of heterogeneous fluid velocities, this system were influenced by these parameters as observed from the study carried out, the trend of the graph despite the variation of velocities in various station point source experience the effect from particle density of the bacterial, the predictive and the experimental values in all the figures developed best fits correlation.

Figure 1: Predictive and Experimental Values of Campylobacter Concentration at Different Distance.

Figure 2: Predictive and Experimental Values of Campylobacter Concentration at Different Distance.

Figure 3: Predictive and Experimental Values of Campylobacter Concentration at Different Distance.

Figure 4: Predictive and Experimental Values of Campylobacter Concentration at Different Distance.

Figure 5: Predictive and Experimental Values of Campylobacter Concentration at Different Distance.

Figure 6: Predictive and Experimental Values of Campylobacter Concentration at Different Distance.

Table 1: Predictive and Experimental Values of Campylobacter Concentration at Different Distance.

Table 2: Predictive and Experimental Values of Campylobacter Concentration at Different Distance.

Table 3: Predictive and Experimental Values of Campylobacter Concentration at Different Distance.

Table 4: Predictive and Experimental Values of Campylobacter Concentration at Different Distance.

Table 5: Predictive and Experimental Values of Campylobacter Concentration at Different Distance.

Table 6: Predictive and Experimental Values of Campylobacter Concentration at Different Distance.

The study of Campylobacter transport in surface water environment has been carried out applying modeling and simulation; the study expressed the behaviour of the Campylobacter transport in terms of influence from dispersion coefficient and particle densities of the bacterial in study area. The application of one dimensional flow system monitored the rate of migration at different point source of discharge, these are based on the predominant parameters that was monitored in the surface water environment, despite the application of one dimensional flow transport system, the dispersions in various location of discharge was examined to determine its rates of concentration at different station point of discharge, the dispersion on the contaminant are basically from the heterogeneity of the velocities that experience variations in various point sources, this condition examined affected the concentration of the contaminant in these stations point of discharge, the variation level of concentration were observed to experience some negative impact on it decrease with respect to change in distance, while that of the particle densities of the bacterial was through transient frequencies, while another was through a microfluidic channel of flow in surface water, thus the distribution of the population in heterogeneous size particles based on difference carrier fluids. These were also affected based on the heterogeneous velocities of surface water flows at different station point, these two predominant parameters examined has expressed in detail there impacts on the decrease of the contaminant with respect to change in distance, the study has definitely determined the impacts of these two parameters in Campylobacter transport in surface water environment.

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