Studies On The Treatment Of Coal And Brewery Wastewater Using Adsorption And Coagulation– Flocculation Techniques

CHAPTER THREE

3.0 THEORETICAL BACKGROUND
3.1 KINETICS OF RAPID COAGULATION

The quantitative interpretation of the kinetics of rapid coagulation on the basis of Brownian motion (diffusion) of particles were proposed by Smoluchowski in 1916.
Smoluchowski’s theory explains perikinetic flocculation with the particles aggregation brought about by random thermal motion (Brownian motion). The driving force for particles movement is the thermal energy of the fluid.
Most likely, it occurs when at least one of the particles is quite small normally less than approximately 1mm in diameter (Yan Jin, 2005). In his theory, smoluchowski made some assumptions. They are:
a) The particles are monodespersed. This means that they are all of the same size.
(b) No breakage of floc occurs.
(c) The fluid motion undergoes laminar shear.
d) The shape of all particles and flocs are spherical.
e) Collision involves only two particles.

According to smoluchowski, the region of rapid coagulation is defined as one in which all collision are effective. The rate of coagulation for this region is simply calculated because it consists in counting the number of collisions. This rate of coagulation becomes zero when the electrolyte concentration, C is low. Also within a narrow range, concentration increases rapidly up to a certain value that does not change with a further increase or growth in C. The rate of coagulation is a function of the particle concentration and the intensity of Brownian motion characterized by the diffusivity, D. An expression for the rate of decrease in the particle number, on the basis of Fick’s equation yields:

Equation (3.17) shows that the coagulation period, j depends only on the antiparticle concentration, C0, the viscosity of the medium n(brewery
water effluent in this case) and the absolute temperature, T.

The most complicated particles an expressed in the same way. Its
analysis shows that eqn (3.17) i.e.

3.2 EQUILIBRIUM, KINETICS, ISOTHERMS AND THERMODYNAMIC STUDIES OF ADSORPTION.
From the batch adsorption experimental results, the absorbance values are converted to concentration values by multiplication (Nath et al, 2006).
Concentration = 1100Ao (mg/l) …..(3.1)
where
A0= Absorbance.
The amount of total suspended particles (TSP) adsorbed per grain of adsorbent is later calculated as follows (Nath et al, 2006; Kushwaha et al,
2008):
q = Co-C …… (3.2)
m
where
C0= initial concentration of TSS mg/l
C = concentration of TSS at varying masses of adsorbent mg/l
m= mass of adsorbent g/l
q = amount of TSS adsorbent per gram of adsorbent (mg/g).
The equilibrium amount of TSP adsorbed per gram of adsorbent is also calculated as follows (Nath et al, 2000, Kushwaha et al,2008).

qe = Co-Ce/m ……. (3.3)

where
Co= initial concentration of TSP mg/L
Ce = equilibrium concentration of TSP at varying masses of adsorbent mg/l
m = mass of adsorbent mg/l
qe = equilibrium amount of TSP adsorbed per gram of adsorbent (mg/g)

qe= amount of (TSP) adsorbed per unit weight of adsorbent mg/g.
Ce = equilibrium concentration of the adsorbate, mg/l.
The constants Q and b are Langmuir constants and are calculated from
the intercept and slope of the plot of Ce/qe versus Ce (Nath et al, 2006). The linear plot between 1/Ce and 1/qe indicates the validity of langmuir adsorption isotherm (Kushwaha et al, 2008).