Root surface area

The uptake of water by a young root 1 mm in diameter (r = 0.5 x 10-3 m) is usually 1 x 1CT5 to 5 x 10-5m3 day-1 per meter of root length (0.1-0.5 cm3 day-1 per centimeter of length). This uptake occurs over a root surface area of 2nd, so the volume flux density of water at the root surface for a moderate water uptake rate of 3 x 10-5 m3 day-1 per meter of root length is... 

Let us designate the average volume flux density of water across area A3 of component j by 7y, which is the average velocity of the water movement (Chapter 2, Section 2.4F). A7 can be the root surface area, the effective cross-sectional area of the xylem, or the area of one side of the leaves. In the steady state, the product J v A7 is essentially constant, because nearly all of the water taken up by the root is lost by transpiration that is, the same volume of water moves across each component along the pathway per unit time. We will represent the drop in water potential across component j by AT7 defining the resistance of component j ( ) as follows ... 

Mycorrhizal associations with vascular plants apparently evolved about 400 million years ago and are present in about 80% of our plants (Simon et al., 1993 Remy et al., 1994). Ecto- and endomycorrhiza are common associations with roots they enlarge the root surface area and thus help to catch more... 

Note Tq is the root hair radius, the half-mean distance between root hairs, the influx into root hairs, and a the root surface area per unit volume of soil. 

The effects of data spread should be examined for all individual parameters. These individual effects usually take place simultaneously, and the combined effect is assessed using the root—sum—square (RSS) method. The total additional surface area required to obtain a certain level of design confidence is calculated from... 

The diametei of average mass and surface area are quantities that involve the size raised to a power, sometimes referred to as the moment, which is descriptive of the fact that the surface area is proportional to the square of the diameter, and the mass or volume of a particle is proportional to the cube of its diameter. These averages represent means as calculated from the different powers of the diameter and mathematically converted back to units of diameter by taking the root of the moment. It is not unusual for a polydispersed particle population to exhibit a diameter of average mass as being one or two orders of magnitude larger than the arithmetic mean of the diameters. In any size distribution, the relation ia equation 4 always holds. 

Chow demonstrated theoretically [143] that for anisodiametrical particles, the ultimate tensile stress is inversely proportional to square root of the effective or characteristic filler particle size (in this case by effective particle size the ratio of particle volume to surface area is implied). 

The nonlinear character of log has not often been discussed previously. Nevertheless, Jorgensen and Duffy [26] argued the need for a nonlinear contribution to their log S regression, which is a product of H-bond donor capacity and the square root of H-bond acceptor capacity divided by the surface area. Indeed, for the example above their QikProp method partially reflects for this nonlinearity by predichng a much smaller solubility increase for the indole to benzimidazole mutation (0.45 versus 1.82 [39, 40]). Abraham and Le [41] introduced a similar nonlinearity in the form of a product of H -bond donor and H -bond acceptor capacity while all logarithmic partition coefficients are linear regressions with respect to their solvation parameters. Nevertheless, Abraham s model fails to reflect the test case described above. It yields changes of 1.8(1.5) and 1.7(1.7) [42] for the mutations described above. 

Traditionally, nutrient uptake from solution culture was taken to depend on the concentration of the external mineral nutrient, C , the amount of nutrientabsorbing surface, and the kinetics of uptake per unit surface area or unit length of root (22). The flux of nutrients into the roots, J, is described by one of two functionally equivalent equations. ... 

Figure 12 The predicted changes in average root radius of maize root systems during 20 days of growth. The subscripts on the curves denote differing ways of calculating the average (by volume, by surface area or by root number). (From Ref. 38.)...

For small amounts of powder, dissolution of the particulate material can often be assessed (and compared with that of other compounds) by placing the powder in a calorimeter [68] and measuring the heat evolved as a function of time. The surface area must be assessed microscopically (or by image analyzer), and the data must be plotted by a cube root equation [39] ... 

Equation (1) predicts that the rate of release can be constant only if the following parameters are constant (a) surface area, (b) diffusion coefficient, (c) diffusion layer thickness, and (d) concentration difference. These parameters, however, are not easily maintained constant, especially surface area. For spherical particles, the change in surface area can be related to the weight of the particle that is, under the assumption of sink conditions, Eq. (1) can be rewritten as the cube-root dissolution equation ... 

Remediation with plants requires that the contaminants be in contact with the root zone of the plants. Therefore, root morphology and depth directly affect the depth of soil that can be remediated or the depth of groundwater that can be influenced. A fibrous root system such as that found in grasses has numerous fine roots spread throughout the soil and provides maximum contact with the soil because of the high surface area of the roots. A tap root system (such as in alfalfa) is dominated... 

The diffusion layer model satisfactorily accounts for the dissolution rates of most pharmaceutical solids. Equation (43) has even been used to predict the dissolution rates of drugs in powder form by assuming approximate values of D (e.g., 10 5 cm2/sec), and h (e.g., 50 pm) and by deriving a mean value of A from the mean particle size of the powder [107,108]. However, as the particles dissolve, the wetted surface area, A, decreases in proportion to the 2/3 power of the volume of the powder. With this assumption, integration of Eq. (38) leads to the following relation, known as the Hixon-Crowell [109] cube root law ... 

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