Theoretical Analysis and Simulation Studies of the Orbiting Sphere Viscometer

We present the theoretical background of a previously introduced viscosity measurement system based on a principle similar to that of the well-known falling ball viscometer. Even though the falling ball viscometer does not allow a viscosity measurement at defined shear rates, it has been established as frequently used referenced method in the chemical industry and is still widely used today. We modified the mode of operation to permit continuous measurements by building an orbiting sphere viscometer, where a sphere mounted on a spring wire performs steady motions on a circular path. The movements are electromagnetically excited in a contactless manner such that the actuator does not have to be placed within the fluid. The readout can be performed by piezoelectric sensors (as described below) and alternatively also by means of inductive sensing. Classical rheometer principles (such as rotating cylinders or plate-cone arrangements) often involve precision drives and bearings which in our case were completely avoided. Both readout methods avoid also mechanical feedthroughs (e.g., in terms of a rotating shaft) where the inductive method additionally avoids electrical contacts in the measurement chamber. This is an important feature for process automation in the chemical industry, just as the possibility of continuous measurements, which allows uninterrupted control of the viscosity during a production process. Due to the easy scalability of the system it is applicable in a wide range of viscosities. Various operating modes are possible and allow different physical parameters to be sensed. In this paper, we describe those modes mathematically and compare them to the results of a finite element simulation. We furthermore analyze various spurious effects and studied the influences of geometrical design parameters associated with an experimental prototype.