The effect of volume fraction ϕ on the xy- and yx-components of the apparent viscosity of a suspension of bottom-heavy squirmers, under the conditions of weak shear flow and strong bottom heaviness, with β = 5. For details, see Ishikawa & Pedley (2007a). A simple shear flow is applied in the xy-plane, and the gravitational directions are taken in the −x- or −y-directions, i.e. vertical or horizontal shears. The broken line indicates the values obtained from the analytical equation of Batchelor (1977) for a suspension of Brownian spheres. Vertical: filled circle, ηxy; open circle, ηyx. Horizontal: filled triangle, ηxy; open triangle, ηyx. Dashed line, 1+2.5ϕ+5ϕ2.