Friction liquid flow

Filter aids should have low specific surface, since hydraulic resistance results from frictional losses incurred as liquid flows past particle surfaces. Specific surface is inversely proportional to particle size. The rate of particle dispersity and the subsequent difference in specific surface determines the deviations in filter aid quality from one material to another. For example, most of the diatomite species have approximately the same porosity however, the coarser materials experience a smaller hydraulic resistance and have much less specific surface than the finer particle sizes. 

When liquid flows along a solid surface (see Fig. 4.2) a shearing stress is set up (friction power/surface), which is expressed by... 

An alternative approach to the representation of results for solid-liquid flow is to use the two-layer model which will be described in the following section. It will be seen that the coefficient of friction between the particles and the wall of the pipe is an important parameter in the model. It is suggested that its complete absence in equation 5.24 may be an important reason for the extent of the scatter. Unfortunately, it is a quantity which has been measured in only a very few investigations. It is interesting to note that the form of equation 5.19 was obtained by NEWITT et alP2) using a force balance similar to that... 

In the usual case h and hf are falling in the direction of flow and Ah and Ahf are therefore negative. Values of frictional pressure drop, — APtpf may conveniently be correlated in terms of the pressure drop —APL for liquid flowing alone at the same volumetric rate. Experimental results obtained for plug flow in a 25 mm. diameter pipe are given as follows by Richardson and Higson(6) ... 

The frictional pressure drop for liquid flows through micro-channels with diameter ranging from 15 to 150 pm was explored by Judy et al. (2002). Micro-channels fabricated from fused silica and stainless steel were used in these experiments. The measurements were performed with a wide variety of micro-channel diameters, lengths, and types of working fluid (distilled water, methanol, isopropanol), and showed that there were no deviations between the predictions of conventional theory and the experiment. Sharp and Adrian (2004) studied the fluid flow through micro-channels with the diameter ranging from 50 to 247 pm and Reynolds number from 20 to 2,300. Their measurements agree fairly well with theoretical data. 

Brutin D, Tadiist L (2003) Experimental friction factor of a liquid flow in micro-tubes. Phys Fluids 15 653-661... 

Judy J, Maynes D, Webb BW (2002) Characterization of frictional pressure drop for liquid flows through micro-channels. Int J Heat Mass Transfer 45 3477-3489 Kandlikar SG, Joshi S, Tian S (2003) Effect of surface roughness on heat transfer and fluid flow characteristics at low Reynolds numbers in small diameter tubes. Heat Transfer Eng 24 4-16 Koo J, Kleinstreuer C (2004) Viscous dissipation effects in microtubes and microchannels. Int J Heat Mass Transfer 47 3159-3169... 

The Lockhart-Martinelli model can correlate the data obtained from pressure drop measurements in gas-liquid flow in channels with hydraulic diameter of 0.100-1.67 mm. The friction multiplier is 0l = 1 + C/X - -1 /X. ... 

In Table 6.7, C is the Martinelli-Chisholm constant, / is the friction factor, /f is the friction factor based on local liquid flow rate, / is the friction factor based on total flow rate as a liquid, G is the mass velocity in the micro-channel, L is the length of micro-channel, P is the pressure, AP is the pressure drop, Ptp,a is the acceleration component of two-phase pressure drop, APtp f is the frictional component of two-phase pressure drop, v is the specific volume, JCe is the thermodynamic equilibrium quality, Xvt is the Martinelli parameter based on laminar liquid-turbulent vapor flow, Xvv is the Martinelli parameter based on laminar liquid-laminar vapor flow, a is the void fraction, ji is the viscosity, p is the density, is the two-phase frictional... 

Apart from obvious features such as laminarity, there are speculations that flows in micro channels exhibit a behavior deviating from predictions of macroscopic continuum theory. In the case of gas flows, these deviations, manifesting themselves as, e.g., velocity slip at solid surfaces, are comparatively well understood (for an overview, see [130]). However, for liquid flows on a length scale above 1 pm, there is no clear theoretical foundation for deviations from continuum behavior. Nevertheless, various unexpected phenomena such as friction factors deviating from the continuum prediction [131-133] have been reported. A more detailed discussion of this still unsettled matter is given in Section 2.2. At any rate, one has to be careful here since it may be that measurements in small systems lack precision, essentially because of the incompatibility of analysis in a confined space and with large measuring equipment... 

The velocity of liquid flow around suspended solid particles is reduced by frictional resistance and results in a region characterized by a velocity gradient between the surface of the solid particle and the bulk fluid. This region is termed the hydrodynamic boundary layer and the stagnant layer within it that is diffusion-controlled is often known as the effective diffusion boundary layer. The thickness of this stagnant layer has been suggested to be about 10 times smaller than the thickness of the hydrodynamic boundary layer [13]. 

Fig. 15 shows the detailed structure of the droplet from a viewing angle of 60°. Experimental images show that a hole is formed in the center of the droplet for a short time period (3.4 4.8 ms) and the center of the liquid droplet is a dry circular area. The simulation also shows this hole structure although a minor variation exists over the experimental images. As the temperature of the surface is above the Leidenfrost temperature of the liquid, the vapor layer between the droplet and the surface diminishes the liquid-solid contact and thus yields a low surface-friction effect on the outwardly spreading liquid flow. When the droplet periphery starts to retreat due to the surface-tension effect, the liquid in the droplet center still flows outward driven by the inertia, which leads to the formation of the hole structure. 

Figure 4-6 Liquid flowing through a pipe. The frictional flow losses between the fluid and the pipe wall result in a pressure drop across the pipe length. Kinetic energy changes are frequently negligible.

The suction head hs decreases and the discharge head hd increases with increasing liquid flow rate because of the increasing value of the friction head loss terms hfs and hfd. Thus the total head Ah which the pump is required to impart to the flowing liquid increases with the liquid pumping rate. 

If the approximation is made that the friction factor for the two-phase flow / is equal to that for the hypothetical liquid flow fLO, a very simple relationship is obtained between the frictional pressure gradients for the two flows ... 

The pressure gradient for the wholly liquid flow can be calculated from equation 7.68, in which the friction factor is evaluated for the Reynolds number given by... 

Use of the correlation is very simple. First the frictional pressure gradients are calculated for only the liquid flowing in the pipe, and for only the gas ... 

When a change of phase occurs, as in boiling, it is necessary to use the wholly liquid reference flow (an only liquid basis would change as the liquid flow rate decreases during boiling). At low pressures, the results of the Lockhart-Martinelli correlation can be used for the frictional component of the pressure gradient but it is necessary to convert the only liquid basis used in the earlier correlation to the wholly liquid basis. It is assumed that the frictional pressure gradients for the two reference flows are related by the expression... 

For separation of colloidal particles and for breaking down emulsions, the ultra-centrifuge is used. This operates at speeds up to 30 rpm (1600 Hz) and produces a force of 100,000 times the force of gravity for a continuous liquid flow machine, and as high as 500,000 times for gas phase separation, although these machines are very small. The bowl is usually driven by means of a small air turbine. The ultra-centrifuge is often run either at low pressures or in an atmosphere of hydrogen in order to reduce frictional losses, and a fivefold increase in the maximum speed can be attained by this means. 

For a given F, the height of hquid in the tank at steadystate would also be some constant h. The value of k would be that height that provides enough liy drau-lic pressure head at the inlet of the pipe to overcome the frictional losses of liquid flowing down the pipe. The higher the flow rate F, the higher h will be. 

When two-phase flow is compared to the single-phase case for the same flow rate of an individual phase, it is an experimental fact that the frictional pressure drop will always be higher for two-phase flow. This higher pressure drop may be caused by the increased velocity of the phases due to the reduction in cross-sectional area available for flow, and also to interactions occurring at the extended gas-liquid interface which exists in most of the possible flow patterns. It is equally true that the heat flux will always be higher for two-phase flow than for the same situation in single-phase flow with the same liquid flow rate. On the other hand, mass transfer will depend upon both the extent of the gas-liquid interface and the relative velocity between the two flowing phases. 

The Bernoulli equation can now be written for the liquid in channel flow in the bottom part of the tube, and for the liquid in slug flow in the upper part. The acceleration terms are then neglected, and the friction factors for each type of liquid flow found from the Blasius equation and from true Reynolds numbers. The resulting equations cannot be readily evaluated because of the two hydraulic-radius terms involved in the two types of flow, and an unknown fraction defining the relative mass of liquid in each part of the tube. 

---