In the canonical use of the Arrhenius law (i.e. kinetics), the activation energy is related to the height of the reaction barrier and the pre-exponential factor is related to the probability of successful collisions between the molecules. But when I fit viscosity data using an Arrhenius-like model, what are the meanings of these two parameters?
See Tyrrell and Harris, Diffusion in Liquids chapter 6. Available, at a cost, from Elsevier.
http://dx.doi.org/10.1016/B978-0-408-17591-3.50001-0
For transport properties in liquids, Ea is too low to match the assumptions of the Eyring theory - really the process is not one of activation as in chemical kinetics. Few systems actually fit the "Arrhenius" or Andrade eq. except some hydrocarbons and simple molten salts - the so-called "strong" liquids.(Angell). Most have a stronger T dependence - the "fragile" liquids in Angell's theories.
Hi Alessandro.
It depends on the rheological model. If the liquid is Newtonian, then viscosity is actually modeled as momentum diffusion in a direction perpendicular to the flow direction. In that example, the term that would be analogous to the diffusion coefficient in mass diffusion would be the kinematic viscosity (which has units of length^2/time).
An example would be liquid flow between two stationary parallel flat plates, in which the flow is parallel to the plate surfaces. Because of a no-slip boundary at the plate-liquid interface, the liquid velocity at the interface is zero, but it increases in magnitude as the distance from the plate increases. (For two plates, it will reach a maximum in the middle, then decline closer to the other plate.) The change in velocity with distance from the plate is the velocity gradient. The diffusion model comes in because molecules closer to one plate migrate by diffusion. While the molecular migration is in all directions, the migration perpendicular to the flow direction cause a mixing of slower molecules with faster molecules (moving away from the plate) and of faster molecules with slower ones (for those that move closer to the plate). This causes a diffusion of momentum, which is the basis for the relationship between stress and strain in Newtonian flow. Since diffusion is an activation process that typically follows an Arrhenius behavior, the result is that the viscosity also follows this model.
Because the molecular basis for resistance to flow is different for polymer flow and other non-Newtonian materials, the models are different and the Arrhenius analogy typically does not hold.
Hope this is of some interest. Good luck!
Interesting question evoked in similar ones before, hope you find any plus!
https://www.researchgate.net/post/What_is_the_effect_of_the_types_of_interactions_between_molecules_in_solution_on_the_viscosity_Arrhenius_activation_energy_in_binary_mixtures
https://www.researchgate.net/post/Is_the_viscosity_Arrhenius_behavior_an_ideal_phenomenon2
https://www.researchgate.net/post/What_difference_between_dynamic_and_kinematic_viscosity
https://www.researchgate.net/post/How_many_equations_do_we_use_to_correlate_the_viscosity_of_binary_mixtures_in_a_single_publication
Moreover, there are some hidden properties and implicit in the viscosity-temperature dependence at liquid state, like prediction of normal boiling temperature, prediction of viscosity of the studied system at its vapor phase at the studied pressure of treated liquid, etc.
https://www.researchgate.net/publication/333607111_Validation_of_Messaadi_equation_on_viscosity-temperature_dependence_for_some_ternary_liquid_mixtures_by_statistical_correlation_analysis?_sg=h7JLBtcmhuCb7y6hYzsj5c2uUsRc1gE5HGw2NXGNyzqbovEKM0TXxU5k8LcrWUKkvRGLgP1BJZ7_4-RkyWs23TiK2t3LdR9nDGNZGv4g.teLW_5TpYT6Kc-kxNGWJwLjPgMFPmfC_GCldH_W1EokiQTAFuM8MCPr2iGj0KD0_OLcKdVqHRUzcA7YeTSOXwA
https://www.researchgate.net/publication/326610394_On_the_Homographic_Dependence_of_Activation_Energy_and_Viscosity_Arrhenius'_Temperature_for_Some_Pure_Fluids
https://www.researchgate.net/publication/326610394_On_the_Homographic_Dependence_of_Activation_Energy_and_Viscosity_Arrhenius'_Temperature_for_Some_Pure_Fluids
We have not yet investigated on ionic liquids, the pre-exponential factor maybe is very close the viscosity of the corresponding vapor of the corresponding ionic liquid at the normal boiling temperature if the study is performed at atmospheric pressure, I'm almost sure!!
We have not yet investigated on ionic liquids, the viscosity activation energy maybe is close to the energy of transition state of molecules between to adjacent liquid layers (layer n to n+1 or to n-1) if we adopt the shear movement of these molecules as quasi-Newtonian fluids?
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