SCRUBBERS FOR PARTICLE COLLECTION Background To understand how scrubbers work, we must first define some terms. Single droplet efficiency, ηd, is similar to single fiber efficiency. It is the fraction of particles in the gas upstream of a spherical droplet that collect on that droplet as the droplet moves through the gas. Although the same mechanisms contribute to single droplet efficiency that contribute to single fiber efficiency, and include impaction, interception, and diffusion, impaction alone usually dominates. For particle collection due to impaction on a droplet, the following equation is often used: 2d35.0StkStk⎟⎟⎠⎞⎜⎜⎝⎛+=η (1) where Stk is the Stokes number for the drop moving through gas that contains particles. The particles are assumed to be “embedded” in the gas; that is, they do not move relative to the gas except to cross streamlines by impaction. Inspection of Eq (1) shows that ηd is zero if Stk is zero, and approaches a value of unity as Stk becomes large. dCg/dp2d18CVdStkµρ= . (2) Here, d is particle diameter, ρp is particle density, Vd/g is the velocity of the droplet relative to the gas (see below) CC is the Cunningham slip correction factor, µ is gas viscosity, and dd is droplet diameter. Because droplets are liquid, particle collection on liquid droplets will depend on some mechanisms that do not operate for collection on dry spheres or on dry fibers. For example, diffusiophoresis and Stefan flow can be important. If the droplets are water, Stefan flow will enhance particle collection under conditions when water vapor condenses on the droplets, but will reduce particle collection for evaporating droplets. Diffusiophoresis for condensing water vapor will tend to drive particles away from the droplet, and toward an evaporating droplet; however, this effect is usually less important than Stefan flow. Liquid holdup, Hd, is the fraction of the scrubber volume that is filled with droplets. It is analogous to solidity for a filter. If, for example, all the droplets in a scrubber were made of ice, then the ice all melted, then Hd would be the volume of the water from the ice divided by the volume of the scrubber. -1-A difference between holdup and solidity is that holdup is a dynamic situation whereas solidity is a stationary situation. The value for scrubber holdup depends on the rate that liquid is fed into the scrubber and the velocity with which the droplets move through the scrubber. w/dLw/dLVAQZAVZQscrubberofvolumescrubberindropletsofvolumeHd === , (3) where Hd is holdup, or volume fraction comprised of droplets, QL is liquid volumetric flow into the scrubber, Vd/w is the velocity of the droplets relative to the scrubber wall (see below) A is the cross sectional area of the scrubber, and Z is scrubber length, measured perpendicular to A. Droplet velocities within the scrubber can be expressed in several ways. Sometimes the important concept is the velocity of the droplets relative to the gas, Vd/g. This velocity would be important, for example, if we are interested in the impaction of particles that are in the gas on droplets that move through the gas. At the same time that droplets move through the gas, the gas itself is moving through the scrubber with a certain velocity that should be taken relative to the scrubber wall, Vg/w. This velocity is important, for example, if we are interested in the residence time of the gas in the scrubber. A final velocity of interest is the velocity of the droplets relative to the wall of the scrubber, Vd/w. This velocity is the vector sum of the velocity of the drops relative to the gas, and the velocity of the gas relative to the wall w/gg/dw/dVVVrrr+= . (4) Consider a spray tower in which the gas enters at the bottom and leaves at the top. Water is sprayed downward into the top of the rising gas. If, for example, the droplets fall through the gas with a downward terminal settling velocity of 200 cm/s relative to the gas, and the gas itself flows upward through the scrubber with a velocity of 50 cm/s relative to the scrubber wall, then the downward velocity of the droplets as seen through a window in the side of the scrubber, or Vd/w, is - 200 + 50 = -150 cm/s or 150 cm/s in the downward direction. If the gas happened to flow upward at the exact same velocity that the droplets fell downward through the gas, then the droplets would appear stationary when seen through that window, or Vd/w = 0. If the upward gas velocity had a higher numerical value than the downward droplet velocity, Vd/g Vg/w Vd/w -2-then the drops would be blown out the top of the scrubber, even though they continue to settle downward through the rising gas. Relative velocity is important as we consider particle collection in scrubbers. Bear in mind that the important velocity for particle collection is the velocity of the droplets relative to the gas, or Vd/g whereas the important velocity for droplet motion through the scrubber is the velocity of the droplets relative to the wall, or Vd/w. Liquid Evaporation will occur if the gas stream is not saturated with vapor. Liquid that evaporates is not available to collect particles, so evaporation must be considered as we investigate scrubber performance. This study can be done using the psychrometric chart; see a link to such a chart on the course website. Similar charts are available in many books and at many websites. Use of the psychrometric chart can be shown through an example. Consider a case where 100,000 cfm of air at 150 F, and relative humidity of 20%, is to be scrubbed. Assuming that the air becomes saturated, determine the exit gas temperature and the flow of water required to replace the water lost due to evaporation. First, locate the point on the psychrometric chart that corresponds to 150 F, 20% RH. Read to the left to find absolute humidity of about 0.033 lb water/lb dry air. At this point (150 F, 20% humidity) read humid volume to be about 16.3 ft3/lb dry air. From this initial point, follow the adiabatic saturation line up and to the left to determine the dew point or wet bulb temperature, Twb. For these conditions, Twb = 103 F; 0.045 lb water/lb dry air; 15.2 ft3/lb dry air. With these data we can solve the problem. The key is to express air conditions on a basis of pounds of dry air, as that quantity does not change as we add (or subtract) water vapor. a. Determine pounds of dry