Mathematical Modeling of Recursive Drug Delivery with Diffusion, Equilibrium, and Convection Coupling

Round 1

Reviewer 1 Report

This is an interesting paper on the analytical solution of a model for drug delivery, including recursive delivery. There is quite some interest in predictive models for the release of drugs from a carrier matrix, and the current paper seems a valuable contribution. I have just a few comments:

* Experimental data should have error bars to indicate uncertainty. Please can this be added?

* While the authors have considered an analytical solution approach, it is unclear when numerical methods would be required. Please add in the conclusion or introduction a discussion on modifications to the model that would need numerical methods.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

I think this manuscript contains enough interesting material to be published. It is mostly well written, I just try to further increase its quality with my comments.

1. There are many methods, either analytical or numerical, to solve this diffusion (+convection) problem. Could the authors mention a few in the introduction? I encourage the authors to perform some numerical simulations as well in the future.

2. In point 7. they write that they assume perfect sink conditions. does it mean that the concentration in the liquid C_l is considered uniform, i.e. the time-scale of mass transport in the liquid is much faster than in the solid? Because this is also assumed.

3. In Eq. (2) they should write that C_ini is a number between 0 and 1, and does not depend on the space variable.

4. The first sentence of the Discussion (line 211) is redundant and could be removed since it belongs to the introduction.

5. "very large value for the Sherwood number" How large actually?

Language usage problems:
- Line 44: "In this regarding"
- Line 54: "The main goal of the following model is to understanding" either to understand or the understanding.
- Line 178: some reordering of the words is suggested, e.g. "The total fraction of solute mass inside the solid matrix with respect to
the initial solute mass at each instant is".
- "Study case" should be replaced by "Case study".
- "a response that non necessarily is proportional to" -> "a response that is not necessarily proportional to"
- The sentence in Line 245 is strange. E.g. role instead of roll, etc. 
- "a unidirectional recursive diffusion process in the Fick’s second law". I think "which follows Fick’s second law" or something like this.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf