There are several methods that measure the density, diffusion coefficient and velocity of fluorescently labeled macromolecules in cells, but I can't find a way for microfluidics systems.
I think Dr Mehdi Hedayati may could help you in this case. He is the head of biochemistry laboratory at Research Institute for Endocrine Sciences, Shahid Beheshti University of Medical Sciences. He is a knowledgeable scientist in the field of biochemistry. You can find him in ResearchGate. No hesitate to contact me if I could help you more.
if the concentration of ur protein /macromolecule is large enough, then you can use gradient field NMR, there is an experiment called DOSY, if u have a Bruker NMR equipped with a gradeint probe it's done easily, a probe with z-gradient is more than enough. however, if the concentration is very low, or the structure is very complicated to code/decode certain peaks u can go to DLS, but I've never used it for macromolecules before and it is not sensitive to ur molecules (it measure whatever particles u have in fluid and for complex samples u can't differentiate between them)
A common way to measure diffusion coefficient of macromolecules using microfluidics systems is: label your macromolecule with a fluorescent probe. In this context, proteins can be labeled with FITC, which is fluorescent in green.
Then you can use your microfluidic system to generate a gradient and study by fluorescence microscopy how your molecule diffuses. Normally, you can generate a gradient using parallel flow of one control liquid and other liquid containing your fluorescent macromolecule. Using hydrogels you can also determine the diffusion coefficient, but in this case it would be the diffusion coefficient in the hydrogel.
In this paper they calculate the diffusion coefficient for two chemokines within a collagen hydrogel using microfluidics systems.
An alternative to Jose's suggestion is calculating the diffusion coefficient using particle tracking methods. The paper below describes a tracking method applicable to nanoparticles:
Marki etal 2014. Biomech Model Mechanobiol, doi 10.1007/s10237-013-0499-7
The problem is I want to design the length of my channels in the microfluidic based on the diffusion coefficient of the proteins .... So I was wondering whether there is other way (instead of calculating the variable in a microfluidic) to calculated these variables before developing the test
I think you want to design a Micromixer. In that case, you can use the diffusion coefficient of 10^-6 cm^2 s^-1 (typical value of protein in aqueous solution).
You could perform single molecule mobility observations using particle tracking procedures, or perform Fluorescence Correlation Spectroscopy analysis; bot things you can do in situ, and account for microchannel wall-protein interactions, microchannel confinement on lateral mobility.