Capillary tube model

The method that has received the most attention belongs to the first category. Specifically, the particular model is the capillary tube model for porous medium and the power law model for the emulsion (J6). The shear-stress (t) rate relationship for a power law fluid is given by... 

A capillary tube model can be used to estimate the permeability of the medium before fines deposition or release has occurred. The Car-man-Kozeny equation uses the diameter of the substrate particles, dg, and the tortuosity of the medium, r, to evaluate the effective permeability of the porous medium. 

Electrokinetic effects in porous media have been investigated by using either capillary tube models or, as mentioned before, concentrated suspensions or unconsolidated packings of particles. 

The most popular approach is the pipe flow analogy model, also called the capillary tube model or channel model, which approximates the flow through the packed bed by the flow through a bundle of straight capillaries of equal size. Further refinement produced the constricted tube model. In this model, an assembly of tortuous channels of varying cross sections simulates the varying dimensions and curvatures of pores in the packed bed. The major contributions following this approach include Blake (1922), Kozeny (1927),... 

The analysis of the resultant data is based on the model that the pores in the nonwoven fabric are a series of parallel nonintersecting cylindrical capillaries of random diameters (or capillary tube model)." The variables of pore stractures in nonwoven fabrics obtained in porosimetry include the total pore volume (or porosity), the pore size, pore size distribution, and the pore connectivity. 

In the following section, the capillary tube model will be discussed more in detail. This simple model ... 

The simple capillary tube model assumes a constant radius of the pore channel. Miiller-Huber (2013) expanded this model by introducing a variable pore radius, simulating pore throats (rj as the minimum and pore body (rb) as the maximum (Fig. 2.28a). The radius is described by an exponential function... 

FIGURE 2.32 Capillary tube model for dispersed shaly sand. Clay reduces pore radius from r to r-d. Schon and Georgi (2003). 

SINGLE CAPILLARY TUBE MODEL Averjanov(ref.4) Irmay(ref.5)... 

One of the earliest models is illustrated in Figure 13.3, which clearly shows the principles used in later improvements. The LC effluent was pumped along a length of silica capillary tubing inside... 

If it is known that a particular form of relation, such as the power-law model, is applicable, it is not necessary to maintain a constant shear rate. Thus, for instance, a capillary tube viscometer can be used for determination of the values of the two parameters in the model. In this case it is usually possible to allow for the effects of wall-slip by making measurements with tubes covering a range of bores and extrapolating the results to a tube of infinite diameter. Details of the method are given by Farooqi and Richardson. 21 ... 

In a series of experiments on the flow of flocculated kaolin suspensions in laboratory and industrial scale pipelines(26-27-2Sl, measurements of pressure drop were made as a function of flowrate. Results were obtained using a laboratory capillary-tube viscometer, and pipelines of 42 mm and 205 mm diameter arranged in a recirculating loop. The rheology of all of the suspensions was described by the power-law model with a power law index less than unity, that is they were all shear-thinning. The behaviour in the laminar region can be described by the equation ... 

In this section we present the system of quasi-one-dimensional equations, describing the unsteady flow in the heated capillary tube. They are valid for flows with weakly curved meniscus when the ratio of its depth to curvature radius is sufficiently small. The detailed description of a quasi-one-dimensional model of capillary flow with distinct meniscus, as well as the estimation conditions of its application for calculation of thermohydrodynamic characteristics of two-phase flow in a heated capillary are presented in the works by Peles et al. (2000,2001) and Yarin et al. (2002). In this model the set of equations including the mass, momentum and energy balances is ... 

Interfacial Tension (IFT) Measurements. All IFT measurements were done using a University of Texas Model 300 Spinning Drop Interfacial Tensiometer. The basic principle is to introduce a drop (about 2 p ) of an oil sample into a glass capillary tube (1.5 mm I.D., 78 mm long) filled with the aqueous medium. The tube is then spun about its main axis. The oil drop will elongate to a length determined by the IFT value of the system. Details of the theory and application can be found elsewhere (15.16). According to the equipment manufacturer, the formula used to calculate IFT value is ... 

Details of the SEC/Viscometer detector system have been described previously.(16) The key component of the viscometer detector is a differential pressure transducer (CELESCO Model P-7D, Canoga Park, CA) with a jf25 psi pressure range. The transducer monitors the pressure drop across a section of stainless steel capillary tubing (length 2 ft., I.D. = 0.007 in.). Pump pressure fluctuations... 

We use 100 pi glass capillary tubes (VWR international 53432-921) pulled by a horizontal micropipette puller (Sutter Instrument Co. Model P-97) for suctioning of adipose tissue. Suction strength is controlled by tip size which is typically 10-20 pm. 

In bringing the models to a non-dimensional form, the presence of dominant Peclet and Damkohler numbers in reactive flows is observed. The problems of interest arise in complex geometries-like porous media or systems of capillary tubes. 

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