ECEN 5341 Lecture 8 Chapter 5

1. ECEN 5341 Lecture 8 Chapter 5 Frank Barnes February 2, 2014

2. Interaction of Direct Current and ExtremelyLow-Frequency Electric Fields with BiologicalMaterials and Systems • 1. Assume we can calculate or measure the fields at the desired point in the body from Maxwell’s Equations. Numerical techniques for this are in Chapter 10 and also in a book by James Lin. • 2. In this chapter we will start with the force equation and work up from the lowest level of complexity through the chemistry to the biology.

3. Maxwell’s Equations

4. Some Physics Forces on charges These forces lead to • Ion currents, • Changes in the orientation of molecules with dipole moments. • Changes in Energy levels and transitions between them. • Induced dipole moments

5. Forces • 1. Forces from the earth’s Magnetic field on a Na+ ion moving at thermal velocity of • v= 400m/s is equal to about 2x10-2 V/m. • 2. Electrical Fields can apply forces on molecules, atoms, ion, molecules with dipole moments and can induce dipole moments.

6. Current Densities • Drift plus diffusion current densities

7. Some Conductivities and Mobilities. • 1 For blood σ= 0.65 S/m • 2. For physiological saline σ=1.45 S/m

8. Ion Movement • 1 Ion Velocity • 2. For a sphere which is large compared to molecules or Ions the mobility is given by 3. Charged particles attract dipoles there is counter ion flow

9. Ideal Dielectrics and σ=0 • Force on a dielectric particle in a dielectric fluid. • Or

10. Osmotic Pressure • 1 This the pressure arising from diffusion or the random motion of the particles • 2. The differential pressure is given by And is proportional to the gradient of the density.

11. Maximum Osmotic Force • For a spherical particle the maximum force is given when and Δr = 2r and is given by • For • with • To get a force on a dielectric particle greater than this we need.

12. Current Densities • 1. Electric current driven by diffusion • Where D is the diffusion coefficient • In meters squared /second • For a sphere in H2O

13. Ratio Diffusion to Drift Currents • 1 The ratio of the diffusion to drift current is approximately given by Where Fi is the force on the particle due to the charge and the gradient of the field on the dipole moment. The maximum value for case where ΔN and ΔF are over the same distance Where Wi is the energy acquired moving through the field. This means we need about 2mV to be significant with respect to the thermal energy 26mV

14. Other Boundary Conditions • 1. Perfectly reflecting surface so ΔN≈ 0 • 2. Slow particles are preferential absorbed. • 3. At steady state the drift current is equal to the diffusion current if there is no net flow through a membrane.

15. Forces to Consider Between Particle in an Aqueous Solution and Membranes • 1 Electrostatic • 2. Osmotic • 3. Van Der Walls • 4. Forces of Hydration

16. Electrostatic Forces or Coulomb Forces • 1 Like charges are repulsive.Opposite charges attract. • 2. Fixed charges on one side of membrane attract charges of the opposite sign to the surface that from a double layer and cancels the field at larger distances. The forces decay exponentially

17. Coulomb Forces are Short Range • 1 For Physiological Saline at O.14 M • λd= 0.83nm • 2 For like particles the forces are repulsive at short distances and attractive at longer range. • These forces are generated by thermal fluctuations and other oscillations. For single atoms these van der Waals forces fall off as 1/r7 however when integrated over the surface of thick membrane they may be much slower.

18. The Force Between two Membranes • Hydration forces are repulsive and short range

19. Effects of Externally Applied Electric Fields • 1. If we apply an external of E=1KV/m in the fluid a Na+ atom moves with drift velocity • v = 5x10-5m/s the thermal velocity is 4x102m/s • Proteins are slower. • We measured the movement of neutrophils microns /minute