ES/RP 531 Fundamentals of Environmental Entomology Fall 2003ESRP531 Lect 19 MassTran[1].do Page 1 of 21November 12, 2003Lecture 19 Mass Transfer (Transport) PhenomenaI. Mass Transfer PhenomenaA. In part I of Environmental Chemodynamics, we discussed the movement ofchemicals as they disperse from themselves (water solubility and vapor pressure)and as they move across compartmental interfaces (phase transfers or partitioning;e.g., KH, Kow, Kd or Koc).1. Wherever the chemicals are as they approach equilibrium between one phase (orcompartment) are and another, their biological effect will depend partly on theirconcentration.2. However, this concentration is quite dynamic rather than static.3. In this lecture we will discuss the processes that remove the chemical furtheraway from their source points (mass transfer) and in the next lecture we willdiscuss the processes that lower a contaminants concentration in situ(degradation).4. First, we will differentiate molecular scale movement from mass transfer.II. Molecular Diffusion--the molecular scale movement of a chemical within a medium(i.e., soil, air, water)A. Can be conceptualized as a spontaneous mixing process1. Loss of spatial unevenness in the distribution of mass (or concentration), heat, orother attributes of a system is a manifestation of the second law ofthermodynamics, i.e., in the absence of an external energy source, entropy of asystem increases until equilibrium is reacheda. In other words, molecules will tend to rearrange themselves so that thesystem has the lowest energy.b. Molecules thus move from regions of high chemical potential to regions oflow chemical potential.2. In the case of a mass of substance, the random movement of molecules is due toBrownian motion, the kinetic energy of the molecule that causes it to move andexchange places with other moleculesa. The movement is directed from higher concentration of molecules to lowerconcentrationsB. Visual Model (Figure 1)1. A dye is added to one end of a narrow tube filled with water2. The dye will eventually spread throughout the tube (via diffusion)Figure 1. Model for diffusion. At time = 0, a chemical is released into one end ofthe narrow tube filled with water. The time = t, the chemical will havemoved through the water filled tube. No net movement occurs when thesystem has reached equilibrium (entropy is maximized; free energy isminimized)3. When the dye has become constant everywhere in the tube, net fluxes of dyeacross any section of the tube will be zero4. As long as the dye distribution is not homogeneous, net fluxes will proceedacross any interface such that transport is directed from the higher to the lowerconcentrationES/RP 531 Fundamentals of Environmental Entomology Fall 2003ESRP531 Lect 19 MassTran[1].do Page 2 of 215. The net flux of dye is proportional to the concentration difference between anyone point and an imaginary (or real) interface it crosses, ora. The flux term is given as mass (or moles) per square cm per unit of time (forexample, moles/cm2/secC. Diffusivity is related to molecular size and viscosity of the medium1. Larger chemicals progress more slowly because the mean velocity of theirthermal motion is reduced and their increased cross-sectional area reduces theirmean free path, i.e., their ability to slip through a crowd of other molecules2. Media exhibiting more crowding or viscosity will inhibit the Brownianmovements of moleculesa. Air is less densely packed than water, which means much higher diffusivitiesfor a given chemical in air than in water1. General diffusivity (i.e., the diffusion coefficient) in air is about 0.1cm2/sec; for aqueous media, the general diffusivity is about 104 timesless3. Another variable affecting diffusivity is temperaturea. Elevated temperatures result in more vigorous Brownian motion andconsequently more rapid random movementb. Because heated media are less densely packed, "percolation" of chemicalsthrough them is facilitatedIII. Turbulent DiffusionA. Molecular diffusion is important mainly on the microscopic scale; it brings reactantsinto contact with each other and causes transport of chemicals across boundaries(e.g., across a cell membrane; from water onto a particle surface; across the air-waterinterface)1. On a macroscopic scale (rivers, lakes, aquifers), molecular diffusion is extremelyslow in causing transport;a. Diffusion occurs very quickly (seconds or less) in water over distances lessthan 100 µm and in air across distances less than 1 cm; but to diffuse as faras a meter requires a long time2. Over large distances, transport is caused by the motion of the fluid itself, i.e.,advection; only at very short distances, where viscosity inhibits fluid motion,does transport by molecular diffusion become relevant (such areas exist in thepore space of sediments and at the various interfaces)a. There is a critical distance at which molecular diffusion and advection playequal roles in chemical transport3. Fluids are turbulent, making description of transport by currents complicated;turbulence can be thought of as the fine structure of the fluid motion, as opposedto the flow pattern of large-scale currents (i.e., small scale motion within largescale motion)4. Differences between molecular diffusion coefficient (called D) and turbulent(eddy) diffusion coefficient (called Ex):a. Ex depends only on the fluid motion (turbulence structure of the fluid) andnot on the substance described by the concentration C; D depends on thephysicochemical properties of the substance and the medium (e.g., themedium’s viscosity)1. Because the intensity of turbulence must strongly depend on forces likewind, solar radiation, river flow, etc., driving the currents, the coefficientsof turbulent diffusion constantly vary in space and timeb. Visual model (Figure 2)--a dye is placed at a single point in a body ofturbulent water; large scale fluid motion moves the dye patch center of massto a new location; at the same time, the patch grows in size because of smallES/RP 531 Fundamentals of Environmental Entomology Fall 2003ESRP531 Lect 19 MassTran[1].do Page 3 of 21(turbulent) eddies (i.e., eddies with size similar to or smaller than the dyepatch size) (remember that molecular diffusion is also causing the moleculesto spread out in a normal distribution over small distances);1. With increasing time, the growth of the patch will continue at anincreasing rate since larger and larger eddies will