Contrarily to this, according to the ultrasonic fusion bonding, as illustrated in FIG. 6, when the used microporous filtration membrane is peeled off from the plate, a deformed protrusion is left on the peeled-off position, which necessitates to reshape this protrusion to enable the ultrasonic fusion bonding for reuse . This is not preferable from view point of the cost for reuse, and is still not preferable from the view point of the waste treatment and cost even in a case where the membrane element is discarded and replaced with a new one. Contrarily to this, when ultrasonic wave is employed, a rectangular horn cannot be used and therefore the respective sides must be fusion bonded independently of each other through several actions.

% recovery is defined as the ratio of permeate flow to feed flow rate. Parameters such as operating temperature, source of feed, composition of feed, feed concentration, and pH can have an effect on the overall % system recovery and % recovery of individual element. In all cases though, % system recovery is often set to maximize permeate flow while preventing precipitation of super-saturated salts within the membrane system. The placement of shims on the adapter within the vessel minimizes movement of the individual membrane elements is called “shimming”.

The transverse forces are applied at three nodes as illustrated in Figure 4. where is the interpolation matrix of the assumed element strain field and are the generalized strain parameters. QCQ4-2 has the same element topology and nodal displacement degrees of freedom as those of QCQ4-1 which is illustrated in Figure 2. The element local coordinates are also established in the same manner as QCQ4-1.

There are no independent internal parameters and numerical integration involved in the evaluation of the strain parameters in these four-node quadrilateral membrane elements, and their element stiffness matrices are computed explicitly in Cartesian coordinates. Consequently, the formulation of these four-node quadrilateral membrane elements is extremely simple, and the resulting elements are very computationally efficient. These two quasi-conforming quadrilateral membrane elements pass the patch test and are free from shear locking and insensitive to the element distortion in the range of practical application.

The mesh 2 × 10 is the mesh with two layers of elements along the beam thickness, and the stresses given by 2 × 10 mesh are at the same location as illustrated in Figure 5. The results of Q8 in Table 3 were computed using the popular CAE code ANSYS by the authors. It was shown by Shi and Voyiadjis as well as Wang and Shi that the analytical solution of the shear flexible cantilevered beam given in the text book of elasticity is not the exact solution. The numerical results of the fine mesh given by ANSYS-Q8 confirm the point given in . The objective of this paper is to develop a more accurate four-node quadrilateral quasi-conforming membrane element with two degrees of freedom per node by explicitly taking account of the Poisson effect in the assumed element strain field.

Suspended solids and precipitated metals can also end up on any membrane in the system. Therefore, if suspended solids such as limestone particles are found in a tail element, they can be confused for scale if a lead element is not also autopsied. The last membrane in the system receives water that has been concentrated and is the most likely to scale. A membrane autopsy includes over 20 specific tests on membranes.