1. Consider the case where a liquid is confined between two walls a distance D apart…

1. Consider the case where a liquid is confined between two walls a distance D apart with one wall located at r–D/2 and the other at x- D/2. The walls carry a surface charge density of ? and the liquid has only counter-ions to the surface charge. The Poisson-Boltzman equation (PBE) for this case is where is the electric potential that gives the electric field E- d ‘/dr, no is the nunber density of counter-ions of valency at x = 0, e = 1.602 _10-19 C is the fundamental charge, kB 1.38x 10-23 J/K is Boltzmann’s constant. Here, e-???, where ?? 8.85x 10-12 F/m and ? is the dielectric constant of the liquid (e.g. ?water-80) (a) Consider the problem where there are two walls a distance D apart with one wall located at x =-D/2 and the other at x = D/2. Show by direct substitution that the exact solution to the PBE is given by kBT ze where 2K2 = K2 = (ze)210 where K is the Debye screening length. (b) Starting from Eq1), the Poiss-Boltzman equation, expand the exponential out to linear order and neglect higher order terms, which which is valid when zev/kBT<1 You should obtain an equation of the form where A and B are constants. Show that by defining a new potential ?-?-kBT/ze that this equation can be rewritten in the form dar2 Find expressions for the constants A, B, and C. Then use this equation to find a solution for ?| and ?. What is the spatial distribution of ions as a function of x? (c) What is the Debye length for a 0.1 M NaCl solution?

Elite Writer Help
Calculate your paper price
Pages (550 words)
Approximate price: -

Why Work with Us

Top Quality and Well-Researched Papers

We always make sure that writers follow all your instructions precisely. You can choose your academic level: high school, college/university or professional, and we will assign a writer who has a respective degree.

Professional and Experienced Academic Writers

We have a team of professional writers with experience in academic and business writing. Many are native speakers and able to perform any task for which you need help.

Free Unlimited Revisions

If you think we missed something, send your order for a free revision. You have 10 days to submit the order for review after you have received the final document. You can do this yourself after logging into your personal account or by contacting our support.

Prompt Delivery and 100% Money-Back-Guarantee

All papers are always delivered on time. In case we need more time to master your paper, we may contact you regarding the deadline extension. In case you cannot provide us with more time, a 100% refund is guaranteed.

Original & Confidential

We use several writing tools checks to ensure that all documents you receive are free from plagiarism. Our editors carefully review all quotations in the text. We also promise maximum confidentiality in all of our services.

24/7 Customer Support

Our support agents are available 24 hours a day 7 days a week and committed to providing you with the best customer experience. Get in touch whenever you need any assistance.

Try it now!

Calculate the price of your order

Total price:

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Services

No need to work on your paper at night. Sleep tight, we will cover your back. We offer all kinds of writing services.


Essay Writing Service

No matter what kind of academic paper you need and how urgent you need it, you are welcome to choose your academic level and the type of your paper at an affordable price. We take care of all your paper needs and give a 24/7 customer care support system.


Admission Essays & Business Writing Help

An admission essay is an essay or other written statement by a candidate, often a potential student enrolling in a college, university, or graduate school. You can be rest assurred that through our service we will write the best admission essay for you.


Editing Support

Our academic writers and editors make the necessary changes to your paper so that it is polished. We also format your document by correctly quoting the sources and creating reference lists in the formats APA, Harvard, MLA, Chicago / Turabian.


Revision Support

If you think your paper could be improved, you can request a review. In this case, your paper will be checked by the writer or assigned to an editor. You can use this option as many times as you see fit. This is free because we want you to be completely satisfied with the service offered.