A concentrated, vertical monolayer of identical spherical squirmers, which may be bottom heavy, and which are subjected to a linear shear flow, is modelled computationally by two different methods: Stokesian dynamics, and a lubrication-theory-based method. Inertia is negligible. The aim is to compute the effective shear viscosity and, where possible, the normal stress differences as functions of the areal fraction of spheres, the squirming parameter (proportional to the ratio of a squirmer's active stresslet to its swimming speed), the ratio of swimming speed to a typical speed of the shear flow, the bottom-heaviness parameter, the angle that the shear flow makes with the horizontal and two parameters that define the repulsive force that is required computationally to prevent the squirmers from overlapping when their distance apart is less than a critical value. The Stokesian dynamics method allows the rheological quantities to be computed for values of up to; the lubrication-theory method can be used for 0.5]]>. For non-bottom-heavy squirmers, which are unaffected by gravity, the effective shear viscosity is found to increase more rapidly with than for inert spheres, whether the squirmers are pullers (0]]>) or pushers (<![CDATA[\beta); it also varies with, although not by very much. However, for bottom-heavy squirmers the behaviour for pullers and pushers as and are varied is very different, since the viscosity can fall even below that of the suspending fluid for pushers at high. The normal stress differences, which are small for inert spheres, can become very large for bottom-heavy squirmers, increasing with, and varying dramatically as the orientation of the flow is varied from 0 to. A major finding is that, despite very different assumptions, the two methods of computation give overlapping results for viscosity as a function of in the range <![CDATA[0.5 < \phi. This suggests that lubrication theory, based on near-field interactions alone, contains most of the relevant physics, and that taking account of interactions with more distant particles than the nearest is not essential to describe the dominant physics.
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