Hydrodynamic resistances capillaries

For Ca < 0.1 in Figure 7 the critical capillary pressure is also independent of the initial film thickness. In this case, the hydrodynamic resistance to fluid filling or draining is small enough that the film reaches the periodic steady state in less than half a pore length. Figure 7 confirms the trend observed by Khatib, Hirasaki and Falls that P falls with increasing flow rate (5). c... 

A block-scheme of the apparatus for the study of foam films under applied pressure is shown in Fig. 2.11. The films are formed in the porous plate of the measuring cell (Fig. 2.4, variant D and E). The hydrodynamic resistance in the porous plate is sufficiently small and the maximum capillary pressure which can be applied to the film is determined by the pore material. The porous plate measuring cell (Fig. 2.4, variants D and E) permits to increase the capillary pressure up to 105 Pa, depending on the pore size and the surface tension of the solution. When the maximum pore size is 0.5 pm, the capillary pressure is 310s Pa (at cr = 70 mN/m). The cell is placed in a thermostating device, mounted on the microscopic table. 

A new inhomogeneously perfused tissue model is considered for a tissue cube with 3x3x3 capillaries. Arterial inputs and venous outputs are located at opposite comers of the tissue cube. As a simplifying condition, it is assumed that the hydrodynamic resistances of all the capillaries are equal. Furthermore, KirchofFs laws are assumed to be valid, and capillary blood flow rates and directions can be calculated theoretically. For symmetry, the analyzed tissue cube can be divided into 24 parts, where only one part, a tetrahedron, had to be considered in the final analysis (thick lines at the left-hand comer, lower part). Blood flow directions at the inputs and outputs as well as in the tetrahedron are marked by arrows. 

The microcirculation is comprised of blood vessels (arterioles, capillaries, and venules) with diameters of less than approximately 150 /xm. The importance of the microcirculation is underscored by the fact that most of the hydrodynamic resistance of the circulatory system Hes in the microvessels (especially in arterioles) and most of the exchange of nutrients and waste products occurs at the level of the smallest microvessels. The subjects of microcirculatory research are blood flow and molecular transport in microvessels, mechanical interactions and molecular exchange between these vessels and the surrounding tissue, and regulation of blood flow and pressure and molecular transport. Quantitative knowledge of microcirculatory mechanics and mass transport has been accumulated primarily in the past 30 years owing to significant innovations in methods and techniques to measure microcirculatory parameters and methods to analyze microcirculatory data. The development of these methods has required joint efforts... 

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

Let us consider the motion of the advancing meniscus in a flat capillary (Figure 3.9b and Figure 3.9c) from a state of equilibrium (Figure 3.9a). The zone of the flow in which the main hydrodynamic resistance is exerted takes in a region of the thicknesses of the layer h(x) above the surface of the substrate on the order of h. x-axis is directed along the capillary axis (Figure 3.9). 

The possible existence of an interface resistance in mass transfer has been examined by Raimondi and Toor(12) who absorbed carbon dioxide into a laminar jet of water with a flat velocity profile, using contact times down to 1 ms. They found that the rate of absorption was not more than 4 per cent less than that predicted on the assumption of instantaneous saturation of the surface layers of liquid. Thus, the effects of interfacial resistance could not have been significant. When the jet was formed at the outlet of a long capillary tube so that a parabolic velocity profile was established, absorption rates were lower than predicted because of the reduced surface velocity. The presence of surface-active agents appeared to cause an interfacial resistance, although this effect is probably attributable to a modification of the hydrodynamic pattern. 

The method of capillary Jlow measures the increase in resistance for solvent flow through a capillary (or a porous plug) due to an adsorbed polymer layer. This increase can be translated into a smaller effective capillary (or pore) radius through the Hagen-Polseuille law (1.6.4.18). The hydrodynamic radius d is supposed to be given by the difference between the "covered" and the "bare" radius. In such experiments the observed hydrodynamic thickness sometimes turns out to be flow-rate dependent. In such cases an extrapolation to zero flow rate needs to be carried out. 

Under the assumption that the capillary pressure gradient across the carrier rock-barrier rock interface is the only significant resistant force affecting hydrocarbon accumulation in a conventional hydrostatic trap, i.e. the influence of the hydrodynamic condition in the barrier rock on its sealing capacity can be considered to be negligible, the maximum height of the hydrocarbon column below the barrier rock can be given by Equation 4.22... 

The functionality of the Luggin capillary in reducing the ohmic drop contribution to the electrode potential depends also on the choice of the experimental technique. The use of four wires permits the elimination of any type of resistance outside the electrolytic ceU. The use of three wires, on the other hjind, is satisfactory only if the resistances outside the cell can be neglected, regardless of the intensity of the current flowing in the system. Moreover, a Luggin capillary should not be used when its presence may perturb the hydrodynamic conditions of the electrolytic solution. 

Adhesive penetration into wood can be categorized (i) on micrometer level as a result of the hydrodynamic flow and capillary action of the liquid resin from the outer surface into the porous and capillary structure of wood, mostly filling cell lumens, as well as fractures and surface debris caused by processing [5], and (ii) on sub-micrometer level as diffusion penetration into cell walls and micro- fissures. Hydrodynamic flow is initiated by the external compression force as a result of pressure applied to the wood surface to be bonded. The flow then continues into the interconnected network of lumens and pits, with flow moving primarily in the direction of lowest resistance [6]. The extent of utilization of an adhesive may be limited due to excessive penetration into the substrate, since this portion of the applied adhesive is lost within porous substrate structures for the adhesion effect. 

Physically, the resin movement is promoted by pressure gradient and capillary action and is resisted by viscous forces. In this context, it is useful to separate the pressure in the hydrodynamic part (corresponding to the externally applied contribution) and the capillary part [20]. Gravitational force... 

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... 

---