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The stress tensor of dilute active colloidal suspensions

The stress tensor is calculated for dilute active suspensions composed of colloidal Janus particles propelled by self-diffusiophoresis and powered by a chemical reaction. The Janus particles are assumed to be spherical and made of catalytic and non-catalytic hemispheres. The chemical reaction taking place on the catalytic part of each Janus particle generates local molecular concentration gradients at the surface of the particle and, thus, an interfacial velocity slippage between the fluid and the solid particle, which is the propulsion mechanism of self-diffusiophoresis. In the dilute-system limit, the contributions of the suspended particles to the stress tensor are calculated by solving the chemohydrodynamic equations for the fluid velocity and the molecular concentrations around every Janus particle considered as isolated and far apart from each other. The results are the following. First, the well-known Einstein formula for the effective shear viscosity of colloidal suspensions is recovered, including the effect of a possible Navier slip length. Next, two further contributions are obtained, which depend on the molecular concentrations of the fuel and product species of the chemical reaction and on the orientation of the Janus particles. The second contribution is caused by simple diffusiophoresis, which already exists in passive suspensions with global concentration gradients and no reaction. The third contribution is due to the self-diffusiophoresis generated by the chemical reaction, which arises in active suspensions. The calculation gives quantitative predictions, which depend on the constitutive properties of the fluid and the fluid-solid interfaces, as well as on the geometry of the Janus particles.