Bulk convection

Both pH and the availability of nutrient ions in soil play important roles in rhizo-sphere dynamics and are often dependent on one another. Nutrient ions move in soil toward plant roots either by mass flow with the soil water or by diffusion. Mass flow is the result of bulk convective movements of the soil solution toward roots, whereas diffusion occurs in response to a concentration gradient for a particular ion, which results from its absorption by the root and depletion from the... 

In view of the highly unusual nature of these results and the lack of a routine method for transport measurements unambiguously establishing that rapid transport was indeed a real manifestation of the system, our studies on rapid polymer transport remained unreported in detail. However, in a recent article 46> we have demonstrated that rapid polymer transport actually occurs in these systems due to the formation of ordered macroscopic structures which move rapidly. This rapid transport has been shown to be not the result of bulk convection since normal diffusional kinetics was observed for solvent markers such as [l4C]sorbitol. The striking feature of this new type of transport process is that it is accompanied by ordered structured flows in the... 

One-Dimensional, Diffusion-Controlled Crystal Growth. Neglecting bulk convection leads to an idealized picture of diffusion-controlled solute transport of a dilute binary alloy with the solute composition c0 far from an almost flat melt-crystal interface located at z = 0 (I, 21). 

Solute segregation with bulk convection is given rigorously by solving the two-dimensional solute balance equation [for a two-dimensional velocity... 

Although the balance equations are linear, in the absence of bulk convection, the unknown shape of the melt-crystal interface and the dependence of the melting temperature on the energy and curvature of the surface make the model for microscopic interface shape rich in nonlinear structure. For a particular value of the spatial wavelength, a family of cellular interfaces evolves from the critical growth rate VC(X) when the velocity is increased. 

The mass transfer coefficient, K, is defined as the ratio of the mass transport controlled reaction rate to the concentration driving force. The concentration driving force will depend on both turbulent and bulk convection. Bulk convection depends on molecular diffusivity, while the turbulent component depends on eddy diffusivity (4). The mass transfer coefficient considers the combination of the two transport mechanisms, empirically. 

In this case, the interfacial gradients of surfactant occur because of interfacial gradients in the bulk concentration driven by bulk convection rather than interfacial convection. Although generally requiring numerical analysis, an analytic approximation can be obtained in the limit k

interface concentration is small. Again, we shall consider this case shortly. 

For the case of a binary electrolyte (i.e., a single salt that dissociates in solution into one cation and one anion species), we can rewrite the molar flux equations for positive and negative ions in terms of a salt concentration gradient diffusion term, a migration term explicit in the current density (as opposed to the VO driving force term in Equation (26.54)), and a bulk convection term ... 

Figure 5 also shows the Peclet number based on the flame standoff distance, Pe = Xgfh, which can be interpreted as the ratio of the bulk convective velocity to diffusion velocity Pe = ul DIXg) = ul ag IXg)). In the intermediate pressure... 

In more complicated models both equations have to be generalised by coupling surface and bulk convective diffusion and hydrodynamics. The situation is finely balanced since the motion of the surface has an effect on the formation of the dynamic adsorption layer, and vice versa. Adsorption increases in the direction of the liquid motion while the surface tension decreases. This results in the appearance of forces directed against the flow and retards the surface motion. Thus, the dynamic layer theory should be based on the common solution of the diffusion equation, which takes into account the effect of surface motion on adsorption-desorption processes and of hydrodynamics equations combined with the effect of adsorption layers on the liquid interfacial motion (Levich 1962). 

The interpretation of the output signal as being purely resistive is complicated by the effect of charge transport through bulk convection of particles and by a transient capacitance effect due to the variation in the... 

The fluxes p,u and c,u" simply represent the bulk convective fluxes. In examining systems containing reacting chemical species it is generally useful to use molar fluxes. 

To take into account the role of surface-active species the transport equations in the bulk and at surfaces for each of them (i = 1,2,...,AO are studied (Dukhin et al. 1995, Danov et al. 1999). In the bulk the change of concentration, C/, is compensated by the bulk diffusion flux, j bulk convective flux, C/V, and rate of production due to chemical reactions, (see Fig. 1). The bulk diffusion flux includes the flux driven by external forces (e.g. electro-diffusion), the molecular diffusive and thermodiffusion fluxes. The rate of production, r/,... 

Alvarez NJ, Vogias DR, Walker LM, Anna SL Using bulk convection in a microtensiometer to approach kinetic-hmited surfactant dynamics at fluid—fluid interfaces, J Colloid Interface Sd 372 183-191, 2012. 

Distributive or simple mixing is induced by plug or bulk convection. Bulk convection can be random or ordered. Ordered bulk convection rearranges constant volumina in a well defined way, and the progress of mixing action can be predicted mathematically. In random bulk convection, chunks of material are randomly redistributed, and modeling the mixing action is for most cases not possible. 

In slurry systems, of course, the mass transfer is enhanced by convective currents originating from bulk convection and turbulence In the first approach main emphasis is put on bulk convection and mass transfer related to the particle (terminal) slip velocity v,p e.g. via the modified Frbssling equation ... 

Chung and Lange [26] studied convective diffusion and dispersion in steel melts and the relative contributions of bulk convection and eddy diffusion to the Peclet number. It was found that for Peclet numbers less than five the mixing time was determined by turbulent diffusion, while for increasing Peclet number, the contribution of the bulk convection to mixing increased due to the decrease in the effective diffusion distance. 

The model deseribed is now sufficient to enable an initial model of the eombustion proeess, ineluding as it does terms for heat eonduction through the bulk, convection and radiation exchanges at the surface, degradation and combustion occurring both at the surfaee and within the slab bulk, and finally, volatile mass and enthalpy transport from within the bulk to the surface of the laminate and into the headspace. However, to use this model effeetively, two erueial elements must be adequately addressed ... 

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