Atmospheric aerosols are extremely small, finely distributed, liquid or solid particles suspended in a gaseous medium. Both natural and anthropogenic aerosol particles have been playing a major role in the global climate for several years. Due to coagulation, aerosols bind each other and deforms in the atmosphere resulting in either larger or smaller particles than its original size and shape. The particles that are formed due to coagulation, have a direct impact on fog formation, cloud physics, reduction of visibility, etc. Thus, there is a requirement of evaluating the concentration of the mixture of aerosols and atmospheric fluid using mixture theory.

A handful of research work was attempted in the field of mixture theory. Barry et al

Many studies were conducted in the coagulation of aerosols in particular. Anand et al

Different analytical approaches are existing to solve the derived partial differential equations. Dettman

Meenapriya and Ratchagar

These studies urge to study about aerosol mixture in a channel bounded by porous beds with the externally applied electric and magnetic fields. The concentration of the aerosol mixture is evaluated both in the presence and absence of homogeneous first-order chemical reaction. Numerical calculations are computed using MATHEMATICA and the results are portrayed graphically by varying parameters like Hartmann number, electric number, reaction rate parameter, porous parameter. The potrayed graphical results helps to analyze the effects of air visibility through the concentration of aerosol mixture.

A two-dimensional turbulent flow of chemically reactive aerosols in a poorly conducting atmospheric fluid bounded by porous layers is modelled as shown in

Uniform magnetic field of strength

Basic governing equations are based on poro-elasticity and are derived using mixture theory and Reynolds averaging procedure.

Equation of continuity

Equation of Momentum

Where

Equation of Species

For

To derive a cartesian form of governing equations let the components of velocity be

The Cartesian form of equations (1) to (3) are,

Continuity equation

x-momentum equation

y-momentum equation

Species equation

For

Boundary conditions for velocity are

For Concentration

Where

The reaction rate parameter is

x- momentum solid phase

x- momentum fluid phase

y- momentum solid phase

y- momentum fluid phase

Concentration

The dimensionless boundary conditions for velocity are given by,

For Concentration

To determine the velocity of the fluid, we need to evaluate the value of

Conservation of charges

Maxwell’s equation

In a poorly conducting fluid, the induced magnetic field is negligibly small compared to an electric field and hence the current density is

So (26) reduces to

Where

Using this value in (31), we get

Now consider,

Since

Hence

After substituting

To evaluate the values of velocity and concentration of the aerosol mixture, Perturbation technique is used. Disintegrating the flow variables into steady base state quantities denoted by upper case and two-dimensional linear perturbed quantities denoted by tilde (

After decomposing the above equation into base and perturbed parts, the solution of the base part are obtained analytically and that of the perturbed part are obtained numerically. Let the perturbation parameter

Base part equations

Perturbed part equations

where

The base part boundary conditions are

and perturbed part boundary conditions are,

Base part solutions

For equations (34) and (35) the solution is

Also the derivatives of

The values of integration constants A,B,C,D are calculated using (43) to (46). The perturbed part equations (38) to (41) are simplified using (51) to (54) as given below,

Where

The above four perturbed equations (55) to (58) are solved for

The base part of

Using boundary conditions (43) to (46) the values

For solid phase:

Equation (42) becomes,

Using (51) and (60), the above equation becomes,

For fluid phase:

Equation (42) becomes,

Using (52) and (60), the above equation becomes,

These perturbed equations (63), (65) are solved numerically subject to the boundary conditions prescribed in (47) to (50). Graphs are plotted for concentration with chemical reaction (

The base part of

and its solution is given by,

Using boundary conditions (43) to (46) we get,

For solid phase:

Equation (42) becomes,

Using (51) and (69), the above equation becomes,

For fluid phase:

Equation (42) becomes,

Using (52) and (69), the above equation becomes,

These perturbed equations (71) and (73) are solved numerically subject to the boundary conditions prescribed in (47) to (50). Graphs are plotted for the concentration without the effects of chemical reaction (

The velocity directions are exposed to get a better perception of the flow. The velocity profile for aerosols and atmospheric fluid for parameters including Hartmann number (

Concentration profiles for different values of parameters are discussed as two cases in the proceeding sub-sections.

The concentration of aerosols and atmospheric fluid in the presence of chemical reaction by varying some parameters are illustrated in

The concentration of aerosols and atmospheric fluid without the effect of a chemical reaction by varying some parameters are depicted in

In the presence of chemical reaction,

The concentration of aerosols in the aerosol mixture is reduced by enhancing electric, magnetic and porous effects.

The concentration of atmospheric fluid in the aerosol mixture is reduced by increasing the rate of the reaction, and by improving electric, magnetic and porous effects.

In the absence of chemical reaction,

The concentration of aerosols in the aerosol mixture is reduced by enhancing magnetic field effects.

The concentration of atmospheric fluid in the aerosol mixture is reduced by increasing electric, magnetic field effects.

The concentration of the aerosol mixture is evaluated both in the presence and absence of homogeneous first-order chemical reaction under the presence of electric and magnetic field. The concentration of aerosols in the mixture when chemically reactive, reduces when enhancing the electric, magnetic, and porous effects. The same results hold for the concentration of atmospheric fluid in the presence of chemical reaction. Atmospheric fluid concentration in the mixture reduces while increasing the rate of the reaction, electric, magnetic and porous effects. In the absence of chemical reaction, aerosol concentration reduces when improving the magnetic field and fluid concentration reduces when maximizing the effects of both electric and magnetic fields. Hence it is concluded that both in the presence and absence of chemical reaction concentration of the mixture is minimized when electric, magnetic and porous effects are enhanced.