Hydrodynamics meniscus

The quasi-one-dimensional model used in the previous sections for analysis of various characteristics of fiow in a heated capillary assumes a uniform distribution of the hydrodynamical and thermal parameters in the cross-section of micro-channel. In the frame of this model, the general characteristics of the fiow with a distinct interface, such as position of the meniscus, rate evaporation and mean velocities of the liquid and its vapor, etc., can be determined for given drag and intensity of heat transfer between working fluid and wall, as well as vapor and wall. In accordance with that, the governing system of equations has to include not only the mass, momentum and energy equations but also some additional correlations that determine... 

The continuous formation of drops, however, can lead to substantial errors in obtained adsorption kinetic data. For short drop formation times, hydrodynamic effects have to be taken into account. At large flow rates, the measured drop volume at the moment of detachment must be corrected. This is because a finite time is required for the drop meniscus to be disrupted and the drop to detach. Even though the volume has already reached its critical value, fluid may still flow from the reservoir into the drop. The volume of the drop is thus larger than its measured value, which leads to larger calculated interfacial tension values. The shorter the drop formation time is, the larger the error w i 11 be. K1 oubek et al. (1976) were the first to quantify this effect by introducing a corrected critical drop volume, Vc ... 

Meniscus Shape. Figure 6 shows a schematic representation of the inner portion of a CZ furnace fonned by the melt, crystal, and crucible. The crystal is attached to the melt by the melt-ambient meniscus denoted by dDm, If the traction caused by hydrodynamic forces is neglected (a good... 

There are two limitations for inereasing of heat transfer intensity hydrodynamic ability of porous coating to transport the liquid and finite number of potential centres of vaporization (micropores). On reaching the certain quantity of heat flux a heat transfer surface (meniscus) above liquid-level doesn t supplied a sufficient amount of liquid, a dry spot appears and then dry spots are spreading to all the surface. At some liquid-levels and heat fluxes heat transfer intensity for the opened tube surface of the evaporation is higher than for the tube immersed in the pool. 

Interfacial Electrokinetic Flow, Fig. 1 Liquid meniscus issuing from a 100 (xm capillary in DC electrospraying showing its conical shape and a thin jet that emanates from the meniscus tip. The Jet subsequently breaks up due to hydrodynamic or Coulombic instabilities to generate very small aerosol drops... 

The role of the Maxwell pressure residting from a normal gas phase interfacial electric field that scales as /R in elongating the Uquid meniscus into a cylindrical microjet stracture can also be verified through a dynamic simulation in which the equations governing the coupled interactions between the hydrodynamics (Eqs. 1-3) and electrodynamics (Eq. 9) are solved simultaneously for a constant potential liquid meniscus in the longwave limit in axisymmetric polar coordinates (r,0,z), subject to the boundary conditions... 

In contrast, if the surfactant film has a low surface shear viscosity, another type of hydrodynamic instabihty may develop in which the film shape becomes asymmetric and the hquid in the dimple rapidly escapes into the meniscus, leaving a film that is relatively flat. It is imder these circumstances that the uniform film models described above provide a first approximation of the subsequent drainage. Because the dimple disappears quickly, overall drainage time is much faster when asymmetric drainage occurs, as shown by Figure 7.8 for films made with sodiiun dodecyl sulfate (SDS)/dodecanol mixtures. 

Fig. 1.21. Graph of speed as a function of dynamical contact angle according to the theory of hydrodynamics. For V < Vm, there exists an angle d, and hence a dynamical meniscus. For V > Vm, hydrodynamic instability occurs a liquid film is drawn along behind. Vd is the dewetting speed of this film, discussed later...

Chesters et al. [46 have addressed the transport of low concentrations of surfactant in a theoretical framework. A hydrodynamic model of steady wetting was extended to include the effect of a nonionic surfactant. This model indicated that under certain conditions surfactant may concentrate at the contact line between a surface and a meniscus to significantly reduce the contact angle. 

Hydrodynamic resistance of the capillary with attached meniscus.494... 

Different hydrodynamic effects in the bulk phases contribute to the measured signal. The most important of them are inertia, viscosity and bulk compressibility of the mediums moving together with the meniscus [3, 11, 13, 14, 24],... 

The resistance of a capillary with an attached meniscus RpO ) can be determined via the corresponding hydrodynamic problem which relates the volume flow through the capillary with the pressure in the fluid phases at its two ends. The pressure drop between the phases A and B includes the pressure drop over the capillary and over the meniscus. Under dynamic conditions the pressure drop at the meniscus can be obtained from the viscous stress balance at the interface [3, 11]. The contribution of added liquid mass moving with the meniscus [11,26] has also to be included. The Fourier images of the pressure drop can be expressed by [26]... 

Ih - 3c where aC is the capillary radius and v = rjB/pB is the kinematic viscosity of gas or liquid in the capillary. When the characteristic time of the pressure variation is smaller than th then the mobility of the flow inside the capillary should be taken into account. In this case the velocity distribution over the capillary cross-section is not parabolic and the resistance of the capillary is not described by the Poiseuille law [25-28]. Hydrodynamic relaxation influences the volume flow through the capillary and as a consequence the meniscus volume variation. If phase B is a gas and the capillary is long enough then the gas compressibility can also influence the flow through the capillary. Because of compressibility the flow through the entrance of the capillary can differ from that through the opposite end. The pressure and velocity distributions along the capillary can be described in terms of the direct waves and those reflected from the meniscus [26]. The volume flow at the capillary outlet (i.e. the inflow to the bubble or drop) can be obtained as... 

Hydrodynamics and computer simulation of crystal growth In the crystal pulling growth technique, two types of convection have to be taken into consideration, namely natural and forced convections (Dupret and Van Den Bogaert 1994). The behavior of the meniscus is also important for the control of the diameter and... 

The counter-ion accumulation at the tip then creates a Coulombic repulsion force which causes the tip to disintegrate into a thin jet that emanates from meniscus when the surface tension force holding the drop together is exceeded, as shown in Fig. 1. This jet subsequently breaks up due to hydrodynamic or Coulombic instabilities to form a spray of small liquid drops. As the accumulated charge at the tip is transferred from the meniscus tip to the jet and subsequently to the drops, each individual drop carries a net charge. Since the size of the ejected drop shrinks during its flight due to evaporation, the repulsive force builds... 

Experiments in thick channels - have established that hydrodynamic flows are generally slower than one would expect from theory. Current analytical models of the superhydrophobic effective slip are based on the idealized model of a heterogeneous surface with patches of boundary conditions and mostly neglect a number of dissipation mechanisms in the gas phase and at the interface. The effects associated with different aspects of the gas flow and meniscus curvature must be included in the models. Regardless of recent semianalytical and numerical analyses,the goal should remain to find simple analytical formulas, with as few adjustable parameters as possible, to fit experimental data. 

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