You have a setups where you can use a stirring unit wih an intergrated measurement system, but this fits to small Miniplant reactors and it is difficult to integrate to an existing system. I talked to my PLT-Technician to read the power consumption of the motor, the difficulty is just, that the changes you obtain in viscosity are smaller than the average threshhold of the power consumption, so you will not receive reliable data.
I think real inline process viscoimeters are quit expensive and not available for most researchers, so I would propose that you take sampes and to a semi-continous external measurement on your standard viscosimeter.
If your volume is to less, you can think about integrating one of the classic glas capillatry-viscosymeter like the Ubbelohde into your system, you can sterilze it together with the whole unit and you might take semi-continuos steril samples
http://en.wikipedia.org/wiki/Ubbelohde_viscometer
you can connect it with silicon tubes to your reactor, they are sold in specific viscosity ranges, so you need to fix your rane of desire and try to find a fitting viscosometer.
The bioreactor agitator may possibly be adapted to provide real-time torque measurements, which could be correlated with off-line viscosity data obtained trough laboratory essays. A small level of sinusoidal disturbance of the agitation speed can help to obtain on-line viscosity estimates through the recursive least squares algorithm with forgetting factor. For a study based at a related estimation strategy, applied for the energetic optimization and adaptive control of aerobic fermenters, you can check: C.M.G.A. Queirós, "Controlo do Oxigénio Dissolvido em Fermentadores para Minimização de Energia Consumida", MSc Thesis, Instituto Superior Técnico, Universidade Técnica de Lisboa, 1997 (in Portuguese);
Thesis Controlo do Oxigénio Dissolvido em Fermentadores para Minimi...
I don´t know of any direct measurements that you could do easily. If you need a precise measurement, then you may have to develop a probe; but for a quick setup I have two suggestions:
1) Talk to you colleagues on the Physics or Electrical engineering department; they may lend you an ammeter, or you can buy a cheap power meter. The power consumed will correlate with the viscosity - of course, you will need to calibrate your system. Airflow intensity will probably interfere with the reading.
2) If your culture is bacterial, i.e. relatively homogeneous, you may recicle the broth using a peristaltic pump. In the return line, you can put a constrainded glass tube (e.g. a pipette tip) and verify if the liquid level correlates with the viscosity. Again, you will need to calibrate the system.
You may possibly find of some interest a discussion on the meaning of 'online' (or 'on-line') experimentation, earlier presented at this forum: https://www.researchgate.net/post/What_the_meaning_of_online_experimentation
Depending on what does the bioreactor fluid mixture contains: (i) If it a clear liquid/solution one can use a glass capillary viscometer, which can be fabricated and standardized in laboratory. These viscometers can be used to measure the viscosity of the reactor solution with the desired frequency depending on the variation of reactor fluid characteristics.
(ii) If it a suspension containing solid particles one may use rotational viscometer keeping in mind nature of suspension stable, settling type etc.