[OmniReader]

Problem:

Consider a capillary tube with radius [itex]r[/itex] much larger than the Debye-Huckel screening length [itex]\lambda[/itex] containing monovalent dissociated salt ions of concentration c₀ = (c⁺)₀ = (c^-)₀ and resistivity [itex]\rho[/itex]. The capillary has length [itex]l[/itex] and connects two semi-infinite reservoirs.

(I.) Calculate the total resistance of the capillary taking into account the access resistance given by [itex]\frac{\rho}{4r}[/itex].
(II.) Derive the total resistance for a conical capillary with different radii at both its ends [itex]r_1[/itex] and [itex]r_2[/itex], where [itex]r_1>r_2[/itex]. Sketch the electric field and potential for the cylindrical case.

Assume that the surface of the cylindrical capillary is charged and has a fixed surface potential ζ < 0.

Under the assumption that r is much greater than λ, show that the fluid velocity [itex]v[/itex] of the electro-osmotic flow in the centre of the capillary can be written as

[tex]v= -\frac{\epsilon_0 \cdot \epsilon_r \cdot E \cdot \zeta}{\theta}[/tex]

where θ is the fluid viscosity and E the applied electric field along the capillary. Sketch the velocity as a function of r.

Comments:

I am not really sure how to approach this problem or even what field to look into for the theory. It is an exam problem this year. How is the resistance of a capillary modelled?

I am familiar enough with basic physical chemistry concepts like surface potential.

What sources should I see, for biochemical theory on this level?

[mjc123]

How is the resistance of a capillary modelled?

How is any resistor modelled? What is the resistance of a resistor of length l, cross-sectional area A and resistivity ρ?
For the conical case, use Ohm's law in the form i = 1/ρ*dV/dx, where i is the current density (in A/m²). How does i vary with x?
This is not biochemical theory. I would look for a text on capillary electrophoresis.