Chapter 17: Hydrodynamic Interactions

Question 1

Hydrodynamic Interactions

Answer 1

relates to diffusive transport of particle in solvent

Question 2

Kinematic Velocity

Answer 2

relates information on how fast particle/signal moves through system

• η ≡ sheer viscosity

Question 3

Retardation Time

Answer 3

how fast infirmation flows

Question 4

Schmidt Number

Answer 4

relates inforation about mass transfer

• D ≡ diffusion constant
• S_c ϵ {10², 10³}^{molecular_fluid}, {10⁶}_colloid

Question 5

Retardation Effects

Answer 5

can neglect retardation effects

• HI in equilibrium with surroundings

Question 6

Navier-Stokes Equation

Answer 6

describes motion of viscous fluid

Question 7

Reynolds Number

Answer 7

ratio of inertial and viscous forces

• R_e << 1 → laminar flow
• R_e >> 1 → turbulent flow

Question 8

Navier-Stokes Simplifying Assumptions

Answer 8

• R_e << 1 → laminar flow
• small particles
• equilibrium
  
  • can neglect momentum and intertia of particles when in equilibrium with colvent

Question 9

HI Methods

Answer 9

• there exist continuum and (coarse-grained) “particle” methods
  
  • “particle” has only translational degree of freedom
  • level of coarse-graining depends on what one wants to capture and determines attainable length and time scales

Question 10

Stokesian Dynamics

Answer 10

conservative force-free particles

• only hydrodynamic forces

Question 11

HI (Microscopic Description)

Answer 11

• collection of particles with r_i, v_i according to potential
• very expensive

Question 12

HI (Macroscopic Descroption)

Answer 12

• define elemental fluid volume dV
• solve mass flux integrals

Question 13

HI (Mesoscopic Description)

Answer 13

• use mass distribution of fluid F (r,v, t )
• statistical description
  
  • can extract observables