Suspensions of swimming microorganisms play important roles in biology, medicine, and engineering. To predict and control the flow field of such suspensions, an understanding of their rheological properties is required. In this background, the suspension rheology of various types of microorganisms has been investigated intensively. Research has shown that some microorganisms, such as ciliates, deform when a strong force is exerted on their bodies. However, the effect of cell deformability on suspension rheology has not yet been clarified. In this study, we used a deformable torque swimmer, as a model ciliate, to investigate the rheological properties of a dilute suspension under shear flow. Our results show that the model swimmer tends to gradually change its orientation toward the shear plane or vorticity axis. Regardless of the swimming mode, the apparent shear viscosity shows shear-thinning properties, with the first normal stress difference being positive in sign. The second normal stress difference can be positive or negative, depending on the swimming mode, the deformability, and the shear rate. The mechanism to show such rheological properties can be understood based on the deformed shape and direction of the swimmer's stresslet. These findings are important for understanding the suspension rheology of natural microorganisms and artificial deformable swimmers, which is essential to predict and control the flow of these suspensions.
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