Laminae

Laminae of clay and clay drapes act as vertical or horizontal baffles or barriers to fluid flow and pressure communication. Dispersed days occupy pore space-which in a clean sand would be available for hydrocarbons. They may also obstruct pore throats, thus impeding fluid flow. Reservoir evaluation, is often complicated by the presence of clays. This is particularly true for the estimation of hydrocarbon saturation. 

Bioturbation, due to the burrowing action of organisms, may connect sand layers otherwise separated by clay laminae, thus enhancing vertical permeability. On the other hand, bioturbation may homogenise a layered reservoir resulting in an unproducible sandy shale. 

The foregoing discussion leads to the question of whether actual foams do, in fact, satisfy the conditions of zero resultant force on each side, border, and comer without developing local variations in pressure in the liquid interiors of the laminas. Such pressure variations would affect the nature of foam drainage (see below) and might also have the consequence that films within a foam structure would, on draining, more quickly reach a point of instability than do isolated plane films. 

Laminates aie materials made up of plies or laminae stacked up like a deck of cards and bonded together. Plywood is a common example of a laminate. It is made up of thin pHes of wood veneer bonded together with various glues. Laminates ate a form of composite material, ie, they ate constmcted from a continuous matrix and a reinforcing material (1) (see also Reinforced plastics). 

By comparison, high performance composite laminates ate not only ctossphed like plywood, but actually have laminae stacked at very specific angles to one another to achieve optimal uniform properties in the x—y plane (2). 

Mica splittings are processed from lower quaUty blocks and from sheets too thin for blocks and unsatisfactory for producing film. The splittings are packed for sale in three ways book form, which are laminae spHt to the desired thickness from the same book of mica, then dusted with mica dust, and restacked in book form pan packed, in which splitting layers are placed evenly in a pan, and each layer separated by a thin sheet of paper then pressed together and loose packed, in which splittings are si2ed with screens then padded loosely in a wooden box for shipment. 

Three tachykinin GPCRs, NK, NK, and NK, have been identified and cloned. AH are coupled to phosphatidjhnositol hydrolysis. The NK receptor is selective for substance P (SP) and is relatively abundant in the brain, spinal cord, and peripheral tissues. The NK receptor is selective for NKA and is present in the gastrointestinal tract, urinary bladder, and adrenal gland but is low or absent in the CNS. The NIC receptor is selective for NKB and is present in low amounts in the gastrointestinal tract and urinary bladder, but is abundant in some areas of the CNS, ie, the spinal dorsal bom, soUtary nucleus, and laminae IV and V of the cortex with moderate amounts in the interpeduncular nucleus. Mismatches in the distribution of the tachykinins and tachykinin receptors suggest the possibility of additional tachykinin receptor subtypes. 

The characteristic features of a cord—mbber composite have produced the netting theory (67—70), the cord—iaextensible theory (71—80), the classical lamination theory, and the three-dimensional theory (67,81—83). From stmctural considerations, the fundamental element of cord—mbber composite is unidirectionaHy reinforced cord—mbber lamina as shown in Figure 5. From the principles of micromechanics and orthotropic elasticity laws, engineering constants of tire T cord composites in terms of constitutive material properties have been expressed (72—79,84). The most commonly used Halpin-Tsai equations (75,76) for cord—mbber single-ply lamina L, are expressed in equation 5 ... 

Fig. 5. Calendered unidirectionaHy reinforced single-ply cord—mbber lamina where 9 is the helix angle, E is lamina, and Tis tire.

Liquid fuel is injected through a pressure-atomizing or an air-blast nozzle. This spray is sheared by air streams into laminae and droplets that vaporize and bum. Because the atomization process is so important for subsequent mixing and burning, fuel-injector design is as critical as fuel properties. Figure 5 is a schematic of the processes occurring in a typical combustor. 

Fig. 1. A unidirectional lamina. The material axes are labeled 1 for the fiber direction and 2 for the direction transverse to the fibers.

The stiffness of of a unidirectional lamina in the fiber direction is also given approximately by the rule of mixtures ... 

Thus the addition of the stiff carbon fibers has a very great effect in stiffening the epoxy matrix. Eor the commonly used fiber volume fraction of 0.6 the unidirectional carbon—epoxy lamina has a predicted extensional stiffness E = 145 GPa (2.1 x 10 psi)-... 

The relationship between fiber and matrix moduH and fiber volume fraction for a unidirectional lamina loaded in the direction transverse to the fibers is not simple. A lower bound (1) is given by the expression of the series spring model. 

Poisson s ratio, is the negative of the ratio of the strain transverse to the fiber direction, 8, and the strain ia the fiber direction, S, when the lamina is loaded ia the fiber direction and can also be expressed ia terms of the properties of the constituents through the rule of mixtures. 

The tensile strength of a unidirectional lamina loaded ia the fiber direction can be estimated from the properties of the fiber and matrix for a special set of circumstances. If all of the fibers have the same tensile strength and the composite is linear elastic until failure of the fibers, then the strength of the composite is given by... 

The stress—strain relationship is used in conjunction with the rules for determining the stress and strain components with respect to some angle 9 relative to the fiber direction to obtain the stress—strain relationship for a lamina loaded under plane strain conditions where the fibers are at an angle 9 to the loading axis. When the material axes and loading axes are not coincident, then coupling between shear and extension occurs and... 

The strength of laminates is usually predicted from a combination of laminated plate theory and a failure criterion for the individual larnina. A general treatment of composite failure criteria is beyond the scope of the present discussion. Broadly, however, composite failure criteria are of two types noninteractive, such as maximum stress or maximum strain, in which the lamina is taken to fail when a critical value of stress or strain is reached parallel or transverse to the fibers in tension, compression, or shear or interactive, such as the Tsai-Hill or Tsai-Wu (1,7) type, in which failure is taken to be when some combination of stresses occurs. Generally, the ply materials do not have the same strengths in tension and compression, so that five-ply strengths must be deterrnined ... 

These values are determined by experiment. It is, however, by no means a trivial task to measure the lamina compressive and shear strengths (52,53). Also the failure of the first ply of a laminate does not necessarily coincide with the maximum load that the laminate can sustain. In many practical composite laminates first-ply failure may be accompanied by a very small reduction in the laminate stiffness. Local ply-level failures can reduce the stress-raising effects of notches and enhance fatigue performance (54). 

Gravitational force favors the separation of gas from liquid in a disperse system, causing the bubbles to rise to the hquid surface and the liquid contained in the bubble walls to drain downward to the main body of the liquid. Interfacial tension favors the coalescence and ultimate disappearance of bubbles indeed, it is the cause of bubble destruction upon the rupture of the laminae. 

Even if the interfacial tension is measured accurately, there may be doubt about its applicability to the surface of bubbles being rapidly formed in a solution of a surface-active agent, for the bubble surface may not have time to become equihbrated with the solution. Coppock and Meiklejohn [Trans. Instn. Chem. Engrs., 29, 75 (1951)] reported that bubbles formed in the single-bubble regime at an orifice in a solution of a commercial detergent had a diameter larger than that calculated in terms of the measured surface tension of the solution [Eq. (14-206)]. The disparity is probably a reflection of unequihbrated bubble laminae. 

The previous section illustrated how to obtain the elastic properties of a unidirectional lamina. In practice considerably more information may be required about the behavioural characteristics of a single lamina. To obtain details of the stresses and strains at various orientations in a single ply the following type of analysis is required. 

Consider the situation of a thin unidirectional lamina under a state of plane stress as shown in Fig. 3.9. The properties of the lamina are anisotropic so it will have modulus values of E and Ei in the fibre and transverse directions, respectively. The values of these parameters may be determined as illustrated above. 

Fig. 3.9 Single thin lamina under plane stress...

Now, in order to determine the stiffness in the global (jc, y) directions for a lamina in which the fibres are aligned at an angle 6 to the global x direction, it is necessary to go through the following three steps ... 

Thus one may use the above expressions to calculate the stiffness of a unidirectional lamina when it is loaded at any angle 6 to the fibre direction. If computer facilities are available for the matrix manipulation then it is not necessary to work out the individual terms as above - the required information can be determined directly from the matrices. For example, as indicated above... 

Solution The lamina properties in the local (1-2) directions are calculated as follows ... 

The behaviour of the lamina when subjected to loading at 6 degrees off the fibre axis is determined using matrix manipulation as follows ... 

Alternatively the lamina properties can be calculated from the equations given above. 

The previous analysis has shown that the properties of unidirectional fibre composites are highly anisotropic. To alleviate this problem, it is common to build up laminates consisting of stacks of unidirectional lamina arranged at different orientations. Clearly many permutations are possible in terms of the numbers of layers (or plies) and the relative orientation of the fibres in each... 

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