This is not a trivial question. I upvoted it. I would be happy to be involved in the discussion, but first you need to clarify what is a solvent? I presume that you mean aqueous solutions. 

Thanks, Michael. For a long time I'm wondering what reaction rate constants should be assigned for the equilibrium H+ + HO- = H2O? This question might be worthy to discuss separately.  

I gave a "long" answer for another, similar question with a plenty of references :

https://www.researchgate.net/post/what_reaction_rate_constants_should_be_assigned_for_the_equilibrium_H_HO-H2O

By doing experiment you wil have values with time 

I will attach the helpful  file as soon as possible 

Basically I am trying to run some simulations that involve the neutralization of HCl and NaOH in biological tissues. Alternatively, one can view it simply as injecting HCl (or NaOH) into a beaker filled with NaOH (or HCl). Before I can run those simulations, I need to know the rate constant involve in this neutralization process. I thought that such reactions are common and was hoping it to be available in some Chemistry Handbook but apparently not. Hence, I am wondering whether it would be easy to carry out experiments to quantify the rate constant.

This brings me to another question. Is the rate constant always the same for neutralization of HCl and NaOH? In other words, the reaction rate may change depending on the concentration and temperature, but will the rate constant also change? Given that it is called a rate constant, is it fair to say that rate constants are indeed constants?

As Michael recommended, read Manfred Eigen's Nobel lecture of 1967. After your post I asked the similar question; https://www.researchgate.net/post/w...signed_for_the_equilibrium_H_HO-H2O

In your case "injecting HCl (or NaOH) into a beaker filled with NaOH (or HCl)" the answer is pretty simple. The rate of neutralization will be controlled by a mass transfer (stirring). 

" Is the rate constant always the same for neutralization of HCl and NaOH? " this question does not make any sense. HCl and NaOH do not exist in solutions, they are  completely dissociated. Therefore, I reformulated your question and asked about the rate constant for the reaction H+ with HO-. 

Thank you Yurii. I am not a physical chemist, hence my understanding of this is very limited. Let me expand my question a little bit more. I am trying to model the reaction as a second order reaction given by: R = k[H+][OH-], where k is the rate constant and [i] are the concentration of H+ and OH-.

To run my simulations, I need to know what k is for neutralization of H+ and OH-. Is this rate constant a published data? I understand k can increase with temperature (Arrhenius dependence). My concern is where I can get the value of k, or in the case of temperature dependence, the parameters to describe the Arrhenius equation. If I have to run experiments, how complicated is it? If not, are there published values for k?

Thank you.

Is it possible to simplify the reaction to a first-order reaction? In a neutralization reaction either base or acid is in excel compared to the other component and can be regarded as close to constant? 

Dear E.H.Ooi and Henrik. Welcome to the ultrafast reactions.Sorry, I don't have a simple answer. Therefore:

Yurii V Geletii asked a question in Equilibrium:

"What reaction rate constants should be assigned for the equilibrium H+ + HO- = H2O? If you build a kinetic model of some process involving acid base equilibria, you have to assign formal reaction rate constants for this equilibrium. What is your opinion?"

You will find some answers in:

https://www.nobelprize.org/nobel_prizes/chemistry/laureates/1967/eigen-lecture.pdf