Particle flux total mass

Figure 9. A log-log plot of the annual average ( Paxs/ °Thxs) as a function of sediment trap particle composition, and as a function of total mass flux. Note the importance of particle composition on the ( Paxs/ °Thxs) of trapped material, with a high opal fraction leading to higher ratios. Note also the poor relationship between ( Paxs/ °Thxs) and mass flux. This data was compiled by Chase et al. (in press-b) and includes data from that study, as well as from Lao et al. (1993), Scholten et al. (2001), and Yu et al. (2001a).

In a study of sediment trap samples collected at a depth of 3,200 m in the Sargasso Sea, Bacon et al. (1985) found that the fluxes of several radionuclides exhibited a seasonal cycle in phase with the total mass flux of particles. Mass flux, in turn, was found to be closely coupled to the seasonal cycle of primary production in surface waters of this region (Deuser et al., 1981). Seasonally varying fluxes of radionuclides produced in the deep sea (e.g., Th, Pa, and °Pb) are inconsistent with the view that these nuclides are removed by scavenging to small particles which constitute the bulk of particle mass in the deep sea and which are inferred to sink at an average rate of several hundred meters per year (Section 6.09.3). A seasonal cycle in the flux of these nuclides implies that scavenging in the deep sea responds rapidly to changes in the export of particles from surface waters. 

Problem 9-15. Evaporating Spherical Particle for Pe C 1. A spherical particle at temperature Ts is evaporating into a gas whose temperature far from the particle is T. The total mass flux from the particle due to evaporation is m. Although the particle shrinks in size as it evaporates, the density of the vapor exceeds that of the liquid, and the evaporation generates a net motion in the surrounding gas. The mass flux is related to the rate of evaporation, which is in turn dependent on the net heat flux to the drop. Recall that the boundary condition at the drop surface is... 

Particle or mass flux Number of particles or mass of substance crossing a unit surface per unit time. The appropriate units (SI) are particles m 2s 1 or kg m 2s 1, but particles cm 2s 1 or g cm-2s—1 are often used. Total mass flux of a substance (emitted, for example, at the Earth s surface) is often expressed in Tg yr-1 (1012 g yr 1). 

For comparison with the data in Fig. 7-28, it is instructive to calculate tropospheric residence times resulting exclusively from dry deposition. We confine the calculation to the size range 0.05-1.0 xm, where the deposition velocity is roughly size-independent. For continental aerosols this size region contains approximately one-half of the total mass of all aerosol particles. The residence time is then given by the tropospheric column content of such particles divided by their flux to the ground,... 

Adding the above two equations, we obtain the total mass balance equation (9.2-lb), which basically states that the total hold-up in both phases is governed by the net total flux contributed by the two phases. This is true irrespective of the rate of mass exchange between the two phases whether they are finite or infinite. Now back to our finite mass exchange conditions where the governing equations are (9.4-3a) and (9.4-3b). To solve these equations, we need to impose boundary conditions as well as define an initial state for the system. One boundary is at the center of the particle where we have the usual symmetry ... 

The dispersion term is absent since dividing the reach into Ax completely mixed segments accomplishes dispersion numerically. In equation 1 t is time (t), Ct is soluble, particulate, and colloidal, concentration (M/L ), U is average water velocity (M/t), Ds is particle deposition flux (M/L t), h is water column depth (L), m v is suspended solids concentration (M/L ), fp and fd are fractions chemical on particles and in solution, kf is the soluble fraction bed release mass-transfer coefficient (L/t), Cs is the total, soluble and colloidal, concentration at the sediment-water interface (M/L ), Rs is particle resuspension flux (M/L t), ms is the particulate chemical concentration in the surface sediment (M/L ), fps Cts is the fraction on particles and total chemical concentration in the surface sediment (M/L ), Kl is the evaporation mass-transfer coefficient (L/t), Ca is chemical vapor concentration in air (M/L ), H is Henry s constant (L / L ) and Sx is the chemical lost by reaction (M/L t). It is conventional to use the local or instantaneous equilibrium theory to quantify the dissolved fraction, fd, particulate fraction, fp, and colloidal fraction, fooM in both the water column and bed. The equations needed to quantify these fractions appear elsewhere (4, 5, 6) and are omitted here for brevity. 

Since m is the mass of solid remaining at time t, the quantity m/m0 is the fraction undissolved at time t. The time to total dissolution (m/m0 = 0) of all the particles is easily derived. Equation (49) is the classic cube root law still presented in most pharmaceutics textbooks. The reader should note that the cube root law derivation begins with misapplication of the expression for flux from a slab (Cartesian coordinates) to describe flux from a sphere. The error that results is insignificant as long as r0 8. 

Model simulations of particle volume concentrations in the summer as functions of the particle production flux in the epilimnion of Lake Zurich, adapted from Weilenmann, O Melia and Stumm (1989). Predictions are made for the epilimnion (A) and the hypolimnion (B). Simulations are made for input particle size distributions ranging from 0.3 to 30 pm described by a power law with an exponent of p. For p = 3, the particle size distribution of inputs peaks at the largest size, i.e., 30 pm. For p = 4, an equal mass or volume input of particles is in every logaritmic size interval. Two particle or aggregate densities (pp) are considered, and a colloidal stability factor (a) of 0.1 us used. The broken line in (A) denotes predicted particle concentrations in the epilimnion when particles are removed from the lake only in the river outflow. Shaded areas show input fluxes based on the collections of total suspendet solids in sediment traps and the composition of the collected solids. 

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