The non-Newtonian flow behavior of a culture fluid with suspended adhesive particles of microbes and polysaccharides is analyzed in this study based on a new concept. The concept assumes that the force generated by the contact between particles under shearing flow due to mixing is decreasingly transmitted through the fluid in radial directions. A viscosity equation that includes the degree of force transmisson is derived by considering the shear stress to the force. On the other hand, the shear stress dependence on the concentration of bound particles is expressed in an equation by introducing an effective shear stress that works on the contact sites of the bindings and varies the concentration. Relating the degree of force transmission to the concentration derives a non-Newtonian viscosity equation in terms of shear stress (or shear rate), in which zero-shear viscosity is correlated with both the particle concentration and molecular weight of polymers. It is confirmed that calculations based on the equation are in good agreement with experimental results previously reported for aqueous solutions of several polysaccharides.