Transport and Deposition of Large Aspect Ratio Prolate and Oblate Spheroidal Nanoparticles in Cross Flow

Round 1

Reviewer 1 Report

This paper is a tour de force in 

perturbation methods with asymptotic solutions merged linear systems analysis including the deployment of the Fredholm alternative theorem for the derivation of the solvability condition which is a constraint on the system spherical harmonic analysis

In terms of mathematical analysis, it is a brilliant paper demonstrating why such approximation theories have been essential in the understanding and computation of real world problems historically.  As almost an afterthought, the paper conducts a finite element numerical analysis, with a common multiphysics package, albeit the uncommon treatment of equation based modelling, to validate the analytic model.  The analytic model is import due to its ability to explore the parametric dependence functionally, rather than wholly numerically.  Additionally, the solutions are benchmarked against experiment for a limiting case.

The last time I published a matched asymptotic solution to an important reactor design problem, and validated it with a numerical solution that was a better approximation, one referee expressed satisfaction in the numerics alone.   I will not state this, as I would like to encourage the author that although these studies are a dying art, they provide a level of confidence and ability to extrapolate for design purposes that is fully rational -- you can assess the level of the neglected terms.  No one can design with multiphysics models readily -- they are useful for confirmation of the design basis and sensitivity studies / optimisation studies once a sensible design is proffered.

The paper's application to oblate and prolated spheriodal nanoparticles is relevant to the real world problems claimed.  This is a paper that I would have been proud to have written, so I can do nothing less than recommend its publication.

Author Response

Thank you for reviewing the paper. I am very glad you liked it.

In the revision of the paper I have followed suggestions from Rev2. and  introduced a new section 2 "Statement of the problem" in which the main objectives of the paper are stated and in which an explicit description of what is done in the paper is presented.

I have also used the spelling and grammar in Word to improve the english

Is that sufficient from your side?

Best regards

Hans O. Åkerstedt

Reviewer 2 Report

The present work concerns the development of a model capable of describing the rate of deposition of non-spherical particles during cross-filtering. The lack of symmetry of oblate and prolate particles leads to a dependency of their diffusion coefficients not only on their size and shape, but also on their orientation. The work is very interesting and rigorously developed, my concern regards the statement of the problem. 

The objective of the work and the configuration analyzed only becomes clear after having read the entire paper. The author should add a Statement of the problem section after the introduction, in which the objective of the work is stated clearly and the setting in which the study is carried out is described. A schematic representation of the setting would also be useful. Information on the objective and setting should also be added briefly in the abstract.

Another observation regards the results presented, for example those in Figures 4 and 5. No information is provided on the values of the parameters employed in for the numerical simulation (e.g. Pe and Re numbers). All the information required to reproduce the data should be provided.

Overall the work is interesting and worth being published after suitable revisions.

Author Response

Thank you for reviewing my paper.

I thought I have explained in detail in the introduction(after "An outline of the paper is as follows..) But maybe I am getting blind after a while and miss some important details.

So therefore in my revised paper I have followed your suggestions and introduced a new section 2."Statement of the problem" in which I clearly summarize the main objectives of the paper together with a list of whats done and where it is done in the paper.

I have also tried to revise the abstract following your suggestions.

Regarding figures 4 and figure 5.

In figure 4 which is the boundary surface of the diffusion equation equ (47) the only parameter is alpha and the value of alpha is given in the text for figure 4.

The diffusion equation (47) has only two parameters alpha and beta. Pepar/Peperp the ratio between the Peclet numbers only depends on beta. In the revised paper I have added the value of beta in figure 5.

Best regards

Hans O. Åkerstedt