Squeezing flow

Squeezing flow is interesting to fluid mechanicians because it simulates such polymer processes as compression molding and stamping. In addition, it is a simple model for the action of a lubricant film under a bearing. Because polymers are typically added to lubricant oil, a number of studies have used squeezing flow to determine whether viscoelasticity will improve load capacity of bearing. 

But the question for the rheologist is Can squeezing flow measure rheological material functions Strictly speaking, the answer is no. The flow is so complex that the squeezing force can be related to the gap change only through a constitutive equation. In fact, the flow has been used as a model to evaluate constitutive 

Schematic of squeezing flow between two pWlel plates. 

For a Newtonian fluid—neglecting gravity and inertia—we obtain Stefan s simple result (1874 Bird et al., 1987, p. 21) 

T]o = 2 Rify saniple fills plates constant sample radius (6.4.8) 

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In the past, various resin flow models have been proposed [2,15-19], Two main approaches to predicting resin flow behavior in laminates have been suggested in the literature thus far. In the first case, Kardos et al. [2], Loos and Springer [15], Williams et al. [16], and Gutowski [17] assume that a pressure gradient develops in the laminate both in the vertical and horizontal directions. These approaches describe the resin flow in the laminate in terms of Darcy s Law for flow in porous media, which requires knowledge of the fiber network permeability and resin viscosity. Fiber network permeability is a function of fiber diameter, the porosity or void ratio of the porous medium, and the shape factor of the fibers. Viscosity of the resin is essentially a function of the extent of reaction and temperature. The second major approach is that of Lindt et al. [18] who use lubrication theory approximations to calculate the components of squeezing flow created by compaction of the plies. The first approach predicts consolidation of the plies from the top (bleeder surface) down, but the second assumes a plane of symmetry at the horizontal midplane of the laminate. Experimental evidence thus far [19] seems to support the Darcy s Law approach. 

Analyze lubricated squeezing flow to determine biaxial extensional viscosity (T)R), which is calculated from biaxial stress (cB) and biaxial extensional strain rate (eB). 

Ob and Eg are determined from force-deformation curves for materials which exhibit squeezing flow behavior (e.g., peanut butter, processed cheese). 

Compression of a weakly structured food between parallel plates may achieve squeezing flow (Steffe, 1996). When lubricated parallel plates are used, the result is a form of biaxial extension. Biaxial extension may be used to measure biaxial viscosity, which is a reflection of resistance to radial stretching flow in a plane. Lubricated squeezing flow of a semi-solid... 

Figure H2.1.3 A force/deformation curve illustrating the lubricated squeezing flow of mozzarella cheese (2.3 cm length, 1.8 cm width, 1.8 cm height, 10 mm/min deformation rate), butter (2.1 cm diameter, 2.4 cm height, 5 mm/min deformation rate), and caramel (2.2 cm diameter, 1.9 cm height, 2 mm/min deformation rate) under uniaxial compression at room temperature.

Rigid specimens (e.g., apple, cheddar cheese) often exhibit a sudden decrease in force (stress) after a certain amount of deformation (maximum strain). At this point the specimen has fractured. Maximum stress and strain values may vary depending on the chosen specimen. Specimens that are weakly structured and tend to flow under lubricated compression (e.g., mozzarella cheese, marshmallow) demonstrate squeezing flow. As a result, the force (stress) continually increases as the specimen deformation (strain) increases. These materials do not fracture, but continue to stretch radially while under compression. Both rigid and soft specimens of the same material may exhibit varying characteristics depending on the deformation rate and the aspect ratio of each specimen. 

A helpful analysis of lubricated squeezing flow with... 

Another set-up that can be used to measure extensional properties without clamping problems and without generating orientation during the measurement is the lubricating squeezing flow [12], which generates an equibiaxial deformation. A schematic of this apparatus is shown in Fig. 2.50. 

Example 6.14 Squeezing Flow between Two Parallel Disks This flow characterizes compression molding it is used in certain hydrodynamic lubricating systems and in rheological testing of asphalt, rubber, and other very viscous liquids.14 We solve the flow problem for a Power Law model fluid as suggested by Scott (48) and presented by Leider and Bird (49). We assume a quasi-steady-state slow flow15 and invoke the lubrication approximation. We use a cylindrical coordinate system placed at the center and midway between the plates as shown in Fig. E6.14a. 

Fig. E6.14a Schematic representation of squeezing flow with a cylindrical coordinate system placed midway between the disks.

For fast squeezing flow we would need a constitutive equation that accounts for the stress overshoot phenomenon. 

Fig. E6.14b Dimensionless plot of squeezing flow data by Leider (50) representing 181 runs for four fluids silicone oil, 1% solution of hydroxyethyl cellulose (HEC), 0.5% solution of Separan (polyacrylamide) in glycerin, and polyisobuthylene solution. [Reprinted by permission from R J. Leider, Squeezing Flow between Parallel Disks, II, Experimental Results, Ind. Eng. Chem. Fundam., 13, 342-346 (1974).]...

P. J. Leider and R. B. Bird Squeezing Flow Between Parallel Discs I. Theoretical Analysis, Ind. Eng. Chem. Fundam., 13, 336-341 (1974). 

Squeezing Flow A disk-shaped 5-cm-diameter and 1-cm-thick molten polymer preform with in 5 x 104Ns /m2, n 0.5 at 200°C is placed between two plates. A 10 kg weight is placed on the upper plate. Calculate the preform thickness and diameter as a function of time. 

With regard to constitutive equations, White (13) notes that, in view of the short residence time of the polymer in the nip region (of the order of magnitude of seconds), it would be far more realistic to use a constitutive equation that includes viscoelastic transient effects such as stress overshoot, a situation comparable to that of squeezing flows discussed in Section 6.6. 

The extensional viscosity of semi-solid fat-based products such as butter, ice cream and some cheeses can be measured by lubricated squeezing flow rheometry (Campanella and Peleg, 2002 Gunasekaran and Ak, 2002). 

Lubricated squeezing flow rheometry (and unlubricated squeezing flow rheometry, in which friction between the sample and discs results in radial shear flow) can be used also to measure Newtonian viscosity and the flow properties of non-Newtonian liquids (Campanella and Peleg, 2002). 

Rohm (1993a) obtained agreement between values of the elongational viscosity of butter measured using creep testing and those obtained using lubricated squeezing flow rheometry, as expected from theory. 

Yiscometry (using coaxial cylinder, cone and plate and vane rotational viscometers, and controlled stress capillary viscometers) can be used for soft cheeses. Lubricated squeezing flow rheometry is particularly useful for measuring cheese meltability. 

Campanella, O.H., Peleg, M. 2002. Squeezing flow viscometry for nonelastic semisolid foods— theory and application. CRC Crit. Rev. Food Sci. Nutr. 42, 241-264. 

The purpose of this study is to develop a simple model which retains some of the features of the above complex process to predict the lay-up thickness as a function of time during the squeeze-flow lamination of circular prepreg lay-ups. The prepreg of interest is of the type commonly adopted in the board manufacturing industry. It is composed of two outer resin layers and a fabric core constructed of interlaced yarns oriented in two directions perpendicular to each other (Figure 1). The fabric core is treated as a porous slab characterized by a constant Darcy permeability coefficient (see k in Darcy s law% i.e.. Equation 2 below) which can be estimated from fabric parameters such as the yarn diameter and the pitch distances. The lay-up thickness predictions provided by this model have been found to be in reasonable agreement with experiment for the lamination of up to five epo.xy prepreg layers. 

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