Root products diffusate

Root products are all the substances produced by roots and released into the rhizo.sphere (Table 2) (17). Although most root products are C compounds, they include ions, sometimes O, and even water. Root products may also be classified on the basis of whether they have either a perceived functional role (excretions and secretions) or a nonfunctional role (diffusates and root debris). Excretions are deemed to facilitate internal metabolism, such as respiration, while secretions are deemed to facilitate external proces.ses, such as nutrient acquisition. Both excretion and secretion require energy, and some exudates may act as either. For example, protons derived from CO2 production in respiration are deemed excretions, while those derived from an organic acid involved in nutrient acquisition are deemed secretions. 

Under conditions leading to a porous shell of magnetite, the kinetic curve displayed an induction period corresponding to formation of nuclei and the subsequent reaction followed the cube root law. Diffusion of the reducing gas to the reactant/ product interface took place readily with a porous product. Whether chemical or diffusion control predominated depended on reaction conditions. With small crystals... 

Provided that external diffusion is not limiting, P depends linearly on S and the ratio of the substrate and product diffusion coefficients (/> and Dp), and nonlinearly on a square-root expression, the so-called Thiele modulus (the square of which is the enzyme loading factor, 4). 

Figure 1. Graph of the Reciprocal of the Diffusivity against the Product of the Cube Root of the Molar volume and the Square Root of the Molecular Weight...

It is seen that if the diffusivity is to be correlated with the molecular weight, then a knowledge of the density of the solute is also necessary. The result of the correlation of the reciprocal of the diffusivity of the 69 different compounds to the product of the cube root of the molecular volume and the square root of the molecular weight is shown in Figure 1. A summary of the errors involved is shown in Figures 2 and 3... 

It is seen that the magnitude of (r(opt)) will vary as the square root of the product of the viscosity and diffusivity. As the solute diffusivity and the viscosity of a gas tend... 

The diffusion current Id depends upon several factors, such as temperature, the viscosity of the medium, the composition of the base electrolyte, the molecular or ionic state of the electro-active species, the dimensions of the capillary, and the pressure on the dropping mercury. The temperature coefficient is about 1.5-2 per cent °C 1 precise measurements of the diffusion current require temperature control to about 0.2 °C, which is generally achieved by immersing the cell in a water thermostat (preferably at 25 °C). A metal ion complex usually yields a different diffusion current from the simple (hydrated) metal ion. The drop time t depends largely upon the pressure on the dropping mercury and to a smaller extent upon the interfacial tension at the mercury-solution interface the latter is dependent upon the potential of the electrode. Fortunately t appears only as the sixth root in the Ilkovib equation, so that variation in this quantity will have a relatively small effect upon the diffusion current. The product m2/3 t1/6 is important because it permits results with different capillaries under otherwise identical conditions to be compared the ratio of the diffusion currents is simply the ratio of the m2/3 r1/6 values. 

It is thus seen that the kinematic viscosity, the thermal diffusivity, and the diffusivity for mass transfer are all proportional to the product of the mean free path and the root mean square velocity of the molecules, and that the expressions for the transfer of momentum, heat, and mass are of the same form. 

For reasons of simplicity, the Thiele modulus will be defined and calculated for a catalyst plate with pore access at both ends of the plate and not at the bottom or top. Note that for most cases in real-life applications the assumptions have to be modified using polar coordinates for the calculations. The Thiele modulus q> is therefore defined as the product of the length of the catalyst pore, /, and the square root of the quotient of the constant of the speed of the reaction, k. divided by the effective diffusion coefficient DeS ... 

Because urease activities are much greater in the soil than in the floodwater, the NH4+ is largely formed in the soil as the urea moves downward by mass flow and diffusion. The NH4+, H+ and other reactants will also move between the floodwater and soil-both upward and downward-with NH3 being lost from the floodwater by volatilization. The recovery of N in the crop therefore depends on the rate of movement of urea and its reaction products through the soil and on the rate at which the roots remove N from the downward moving pool. 

The pore volume j)er unit mass, Vg, (a measure of the catalyst pellet porosity) is also a parameter which is important and is implicitly contained in eqn. (14). Since the product of the particle density, Pp, and specific pore volume, V, represents the porosity, then Pp is inversely proportional to Fg. Therefore, when the rate is controlled by bulk diffusion, it is proportional not simply to the square root of the specific surface area, but to the product of Sg and Vg. If Knudsen diffusion controls the reaction rate, then the overall rate is directly proportional to Vg, since the effective Knudsen diffusivity is proportional to the ratio of the porosity and the particle density. 

Equation 13 reduces to the Rayeigh equation (3) when the ratio of the gas-phase diffusivities, , is unity. Since gas-phase diffusivity is inversely proportional to the square root of the reduced mass, in the case of fission product-sodium systems where sodium has the smallest molecular weight, the above diffusivity ratio is less than unity. Therefore, the Rayleigh equation, which was derived on the basis of equilibrium vaporization, in fact represents an upper limit for the fractional fission-... 

The gaseous diffusion method of isotope separation is based upon the difference in the rate of diffusion of gases that differ in density. Since the rate of diffusion of a gas is inversely proportionate to the square root of its density, die lighter of two gases will diffuse more rapidly than the heavier. Therefore, die result of a partial diffusion process will be an enrichment of the partial product in die lighter component. 

If the sensory hair is suddenly immersed in a homogeneous air sample that contains the two chemicals, the ratio of the rates at which the hair takes up the two compounds will be directly proportional to the product of their molecular concentrations and the square root of the ratio of the diffusion coefficients (approximating using the first term in equation 21.16). That is, if ethanol and hexadecanol had similar diffusion coefficients, the 3 1 ratio in their molecular concentration would be reflected in an expected 3 1 ratio in interception by the hair. The diffusion coefficients actually differ by a factor of 5.3, and therefore the odorant with the smaller diffusion coefficient (ethanol, in this case), will be taken up at a rate of approximately 2.3 times what would be expected on the basis of their molecular concentrations. Thus, the 3 1 ethanol hexadecanol ratio would be expected to result in an interception ratio of 6.9 1. This boundary condition corresponds approximately to the case of a filiform antenna suddenly immersed in a cloud of odorant in still air. 

In our current example, the osmotic pressure of the phloem solution decreases from 1.7 MPa in the leaf to 0.7 MPa in the root (Fig. 9-18). Such a large decrease in n is consistent with the phloem s function of delivering photosynthetic products to different parts of a plant. Moreover, our calculations indicate that flow is in the direction of decreasing concentration but that diffusion is not the mechanism. (Although the total concentration decreases in the direction of flow, the c - of every solute does not necessarily do so.) Finally, we note the importance of removing solutes from the phloem solution at a sink, either by active transport or by diffusion into the cells near the conducting cells of the phloem. 

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