Convection surface tension

A comprehensive water transport model was developed to account for effect of liquid water on the performance of the cell. This involved solution of an additional transport equation for liquid water saturation. Effects of convection, surface tension, electro-osmotic drag, gravity and surface tension are taken into account in this model. 

Pojman discusses thermal frontal polymerization in Chapter 4. He focuses on thermal frontal polymerization in which a locahzed reaction zone propagates through the coupling of thermal diffusion and the Arrhenius dependence of the kinetics of an exothermic polymerization. Frontal polymerization is close to commercial apphcation for cure-on-demand appHcations and is also showing value as a way to make some materials that are superior to those prepared by traditional methods. It also manifests many types of instabihties, including buoyancy-driven convection, surface-tension-driven convection, and spin modes. 

Steam-liquid flow. Two-phase flow maps and heat transfer prediction methods which exist for vaporization in macro-channels and are inapplicable in micro-channels. Due to the predominance of surface tension over the gravity forces, the orientation of micro-channel has a negligible influence on the flow pattern. The models of convection boiling should correlate the frequencies, length and velocities of the bubbles and the coalescence processes, which control the flow pattern transitions, with the heat flux and the mass flux. The vapor bubble size distribution must be taken into account. 

Bubble size at departure. At departure from a heated surface, the bubble size may theoretically be obtained from a dynamic force balance on the bubble. This should include allowance for surface forces, buoyancy, liquid inertia due to bubble growth, viscous forces, and forces due to the liquid convection around the bubble. For a horizontally heated surface, the maximum static bubble size can be determined analytically as a function of contact angle, surface tension, and... 

At low Rayleigh numbers, Wragg (W6) found a smaller Ra dependence, resembling more the dependence in laminar free convection. In this range of Ra numbers, a cellular flow pattern is believed to exist, analogous to that of thermal and surface tension-driven cellular convection (Benard cells F3). In the range where the convection is turbulent, the Ra1/3 dependence has been confirmed over seven powers of Ra by Ravoo (R9), who used a centrifuge to vary the body force at constant bulk composition. 

If the supply of surfactant to and from the interface is very fast compared to surface convection, then adsorption equilibrium is attained along the entire bubble. In this case the bubble achieves a constant surface tension, and the formal results of Bretherton apply, only now for a bubble with an equilibrium surface excess concentration of surfactant. The net mass-transfer rate of surfactant to the interface is controlled by the slower of the adsorption-desorption kinetics and the diffusion of surfactant from the bulk solution. The characteris-... 

A current maximum of the first kind has the form of a sharp, straight line which starts to form just before the main polarographic wave (curve a in Figure 6.32). Such a maximum can be considerably larger than the wave itself, although it will usually drop suddenly back to the normal wave. Maxima of the first kind are caused by convective effects, as electrolyte flows past the surface of the mercury drop, resulting from surface tension differences at various points on the surface of the drop. 

Opposing surface tension force is the pinning force. Essentially, pinning forces promoted by surface features tend to fix the contact line of the droplet and drive the DNA toward the contact line (solvent perimeter). Solutes such as salts and probes spread to the perimeter by convection as the droplet evaporates (Figure 4.36). Uneven evaporation leads to differences in spot uniformity. 

The factors inducing anisotropy into the ambient phase flows in solution, such as laminar or turbulent flow, convection induced by temperature difference, concentration difference, or difference in surface tension. 

As was stressed by Professor Ubbelohde, in the process of cell recognition not only the lateral diffusion of the binding sites has to be considered, but also the mechanical effects resulting from the local change of surface tension, inducing convection at the cell surface. It is well known, in the cell-to-cell contact inhibition of motion, in tissue culture, that a cell approaches another cell by touching it by means of microvilli and that this process can be affected when adding surfactants to the culture. Now the point is, What is the relative importance of both diffusion and convection Well, in binary surface films, it was observed that the transport process induced by two-dimensional convection is much more rapid than the two-dimensional diffusion. 

Maxima may be removed by the addition of small amounts of certain surface-active substances, e.g. Triton-X-100 and gelatin (see Sect. 3.3.3), whose action is ascribed to their effect on the mercury surface tension. When addition of such substances is not possible, the placement of a shroud around the capillary tip has been suggested to minimise convection effects [65]. An alternative is to arrange for short drop times by mechanical means. 

Convection in Melt Growth. Convection in the melt is pervasive in all terrestrial melt growth systems. Sources for flows include buoyancy-driven convection caused by the solute and temperature dependence of the density surface tension gradients along melt-fluid menisci forced convection introduced by the motion of solid surfaces, such as crucible and crystal rotation in the CZ and FZ systems and the motion of the melt induced by the solidification of material. These flows are important causes of the convection of heat and species and can have a dominant influence on the temperature field in the system and on solute incorporation into the crystal. Moreover, flow transitions from steady laminar, to time-periodic, chaotic, and turbulent motions cause temporal nonuniformities at the growth interface. These fluctuations in temperature and concentration can cause the melt-crystal interface to melt and resolidify and can lead to solute striations (25) and to the formation of microdefects, which will be described later. 

Numerical simulations that combine the details of the thermal-capillary models described previously with the calculation of convection in the melt should be able to predict heat transfer in the CZ system. Sackinger et al. (175) have added the calculation of steady-state, axisymmetric convection in the melt to the thermal-capillary model for quasi steady-state growth of a long cylindrical crystal. The calculations include melt motion driven by buoyancy, surface tension, and crucible and crystal rotation. Figure 24 shows sample calculations for growth of a 3-in. (7.6-cm)-diameter silicon crystal as a function of the depth of the melt in the crucible. 

The surface tension at the surface increases during evaporation, thus giving rise to the onset of Marangoni convection. 

Free or natural convection occurs when fluid motion is generated predominantly by body forces caused by density variations, under the earth s gravitational field. In the absence of the gravitational field, body forces may be caused by surface tension. The subject material here is focussed on heat transfer with motion produced by buoyancy forces. 

When a fluid moves under natural convection Because of body forces caused by density variations This phenomenon results from the earth s field of gravitation Body forces may also be caused by surface tension. 

The surface tension unit length. Consider a convective heat transfer situation in which surface tension is important Show that the additional quantity pU2Ha, termed the Weber number, We, is required to determine the Nusselt number. 

Marangoni streaming — A -> surface tension gradient (due to local temperature or composition variation) induces a convection effect. Marangoni effects [i, ii] occur at liquid-gas or at liquid-liquid interfaces and result in convection or streaming in the liquid adjacent to the interface. See also -> polarographic maximum. 

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