PLANT BIOPHYSICS - Y. I. Posudin - 2004

II. TRANSPORT PROCESSES IN THE SOIL-PLANT-ATMOSPHERE SYSTEM

8. MASS TRANSPORT OF PARTICLES

Particles are individual portions of solid, liquid, or gaseous matter whose dimensions exceed 1 nm. A special place among particles is occupied by aerosols—dispersed (colloidal) systems consisting of particles ranging in size from 10^-5 m to 10^-7 m suspended in a gaseous medium. The primary source of biological aerosols is plants, which release spores and pollen into the atmosphere. The latter are dispersed by air currents. Bioaerosols also include Viruses, Bacteria, and insect fragments. All of them are capable of causing diseases and allergic reactions in humans, as well as affecting animals and plants. Furthermore, these aerosols act as Condensation nuclei and, consequently, influence cloud formation processes. Additional sources of bioaerosols include agricultural production, municipal activities, and numerous bodies of Water. The dimensions of aerosols of biological origin vary within the following ranges: viruses—0.005–0.25 µm; bacteria and spores—greater than 0.5 µm; pollen—greater than 5 µm; plant debris, insect parts, and human or animal epithelium—about 1 mm. The concentration of biological aerosols depends on specific conditions; for instance, in wastewater Treatment zones, their concentration reaches 10⁴–10⁵ cm^-3; in urban air—7500 cm^-3; and in park atmospheres—290 cm^-3. The main Methods for measuring aerosol parameters (size, size distribution, number, and velocity) are detailed in [Posudin, 2000; 2003].

Let us consider a particle of mass m and density ρ, immersed in a liquid medium with a density ρ_n. This particle is acted upon by the gravitational force:

Class="center">

which is directed downwards, and the buoyant force (Archimedean force):

which is directed upwards and is numerically equal to the weight m₀g of the liquid displaced by the particle. Here, V is the volume of the particle. The resultant force is equal to:

If ρ < ρ₀, the resultant force is directed upwards (flotation process); if ρ > ρ₀, the resultant force is directed downwards (sedimentation process).

At the same time, the liquid medium is characterized by viscosity (internal friction). Let us examine cases that depend on the ratio between the particle radius r, the mean free path λ of gas molecules, and the Reynolds number Re.

a) r > λ, but Re = 2rV/v < 0.1 (where V is the velocity of the particle, and v is the kinematic viscosity). In this case, for a spherical particle of radius r, the drag force caused by viscosity is determined by Stokes' law:

where η is the internal friction coefficient (dynamic viscosity η = ρv), and the sedimentation velocity is determined as follows:

b) r > λ, but Re = 2rV/v > 1. In this situation, form drag dominates, and the resistance force is equal to:

where S is the cross-sectional area of the particle, and ρ is the gas density.

In this case, the balance of forces acting on the particle is calculated using the formula:

For bioaerosols, ρ > ρ₀, so the latter equation can be rewritten as:

From this, the sedimentation velocity of the particle is:

where v is the kinematic viscosity.

The dependence of the Sedimentation Rate of plant particles on radius r and the Reynolds number Re_p at a particle density of ρ ≈ 10^-3 kg·m^-3 is shown in Fig. 8.1. It can be seen that Stokes' law holds for values of Re_p < 0.1 (r = 30 µm and V_sed = 0.1 m·s^-1).

Fig. 8.1. Dependence of the sedimentation rate of plant particles on radius r and the Reynolds number Re_p at a particle density of ρ = 10³ kg·m^-3.

Review Questions

1. Define particles and aerosols.

2. What forces act on a particle immersed in a medium?

3. State Stokes' law.

4. What factors determine the sedimentation rate of plant particles?