*4.6. Schmidt and Peclet Number Effects*

The Schmidt number *Sc* has a considerable influence on the mass distribution as it increases. Such influence on *φ*(*η*) and *χ*(*η*) is depicted in Figures 11 and 12. The Schmidt number describes the mass momentum transition. It is a physical number that is calculated as the proportion of kinematic viscosity to mass diffusivity in the flow regime, where mass and momentum diffusion circulation mechanisms occur simultaneously. From Figures 11 and 12, it is clear that increasing the Schmidt and bio-convection Schmidt numbers reduces the mass and the micro-organism diffusion and, as a result, *φ*(*η*) and *χ*(*η*) are decreased.

**Figure 11.** Influence of the Schmidt number on *φ*(*η*).

**Figure 12.** Influence of the bio-convection Schmidt number on *χ*(*η*).

Figure 13 demonstrates the effect of *Pb* on *χ*(*η*). The increment in Pb enhances *χ*(*η*). By using values greater than one and less than one, the estimated Peclet number establishes whether diffusion or convection is the dominant mode of mass movement. Diffusion is a process in which molecules move down a concentration gradient in a net flux. Despite convection being far faster than diffusion, diffusion is the most efficient mode of transport for very small volumes, such as in microfluidic systems. It is noticeable that the diffusion propagation transport is more dominant compared with the advection propagation rate. Hence, by increasing the values of the Peclet number, the motile micro-organisms' profile *χ*(*η*) increases.

**Figure 13.** Influence of the bio-convective Peclet number on *χ*(*η*).

*4.7. Effects of Various Parameters on Motile Microorganisms' Number*

Figures 14–17 are discussed to show the variations in the micro-organisms' number, *MnsRe*<sup>−</sup> <sup>1</sup> <sup>2</sup> *<sup>s</sup>* with *Nt*, *Nb*, *Pb*, and *Sb*. In Figure 14, *Sb* is varied between the range 5 ≤ *Sb* ≤ 7 along the thermophoresis parameter in the range 0.2 ≤ *Nt* ≤ 0.6. The variations clearly show that *MnsRe*<sup>−</sup> <sup>1</sup> <sup>2</sup> *<sup>s</sup>* decreases for *Nt* and increases for Sb. Similar effects are observed in Figure 15; by fixing the values of *Sb*, *Nb* is changed between 0.2 ≤ *Nb* ≤ 0.6. This is because the thermophoretic diffusion and Brownian motion diminish the concentration

of the motile micro-organism gradient of the flowing fluid, as the mobility of the microorganism increases. The fluctuations in the microorganisms' number with *Pb*, along with *Nt* and *Nb*, are described in Figures 16 and 17. We follow the same range of values for *Nt* and *Nb*, whereas *Pb* is changed between 0 ≤ *Pb* ≤ 1. As shown by the fluctuations, *MnsRe*<sup>−</sup> <sup>1</sup> <sup>2</sup> *<sup>s</sup>* decreases with *Nt*, *Nb*, and *Pb*. For the values *Pb* < 1 diffusion is more dominant than convection. Hence, we see the micro-organisms' number as a decreasing function.

**Figure 14.** Variation of the motile microorganisms' number with *Nt* and *Sb*.

**Figure 15.** Variation of the motile microorganisms' number with *Nb* and *Sb*.

**Figure 16.** Variation of the motile microorganisms' number with *Nt* and *Pb*.

**Figure 17.** Variation of the motile microorganisms' number with *Nb* and *Pb*.
