Question 1

What is Fick's law?

Accepted Answer

Fick's law describes the diffusion of particles from regions of high concentration to regions of low concentration. The first law states that the diffusion flux (J) is proportional to the negative concentration gradient: J = -D × (dC/dx), where D is the diffusion coefficient, dC/dx is the concentration gradient, and the negative sign indicates flux opposite to the gradient direction. This fundamental law governs molecular transport in gases, liquids, and solids.

Question 2

What is the formula for Fick's law?

Accepted Answer

Fick's first law is J = -D × (dC/dx), where J is the diffusion flux [mol/(m²⋅s)], D is the diffusion coefficient [m²/s], and dC/dx is the concentration gradient [mol/m⁴]. For mass transfer rate: ṁ = J × A = -D × A × (dC/dx), where A is the cross-sectional area [m²]. The concentration gradient can be calculated as dC/dx = -J / D. Fick's second law describes how concentration changes with time: ∂C/∂t = D × (∂²C/∂x²).

Question 3

How do you calculate diffusion coefficient?

Accepted Answer

The diffusion coefficient (D) depends on temperature, pressure, and molecular properties. For gases: D ∝ T^1.5/P (temperature and pressure dependence). For liquids: D ∝ T/μ (temperature and viscosity dependence). For solids: D = D₀ × exp(-Eₐ/RT) (Arrhenius equation). Common values: gases ~10⁻⁵ m²/s, liquids ~10⁻⁹ m²/s, solids ~10⁻¹⁵ m²/s. The Stokes-Einstein equation relates D to molecular size: D = kT/(6πηr), where k is Boltzmann's constant, T is temperature, η is viscosity, and r is molecular radius.

Question 4

What are the key properties of Fick's law?

Accepted Answer

Key properties include: 1) Linear relationship between flux and concentration gradient, 2) Flux is opposite to concentration gradient direction, 3) Diffusion coefficient is temperature and pressure dependent, 4) Mass conservation - no net creation or destruction of particles, 5) Steady-state assumption for first law, 6) Valid for dilute solutions and ideal conditions, 7) Applies to molecular, thermal, and momentum diffusion, 8) Foundation for more complex transport phenomena like convection-diffusion.

Question 5

What are real-world applications of Fick's law?

Accepted Answer

Common applications include: 1) Drug delivery - controlled release from pharmaceutical devices, 2) Membrane separation - reverse osmosis, dialysis, gas separation, 3) Food processing - drying, curing, flavor migration, 4) Environmental engineering - pollutant transport in soil and water, 5) Materials science - alloy formation, heat treatment, 6) Biological systems - nutrient transport across cell membranes, 7) Chemical engineering - reactor design, catalyst deactivation, 8) Semiconductor manufacturing - dopant diffusion in silicon wafers.

Question 6

How do you interpret Fick's law results?

Accepted Answer

Interpretation depends on the calculation type: J (flux) tells you the rate of mass transfer per unit area. ṁ (mass transfer rate) shows the total mass transfer rate across the entire area. dC/dx (concentration gradient) indicates how rapidly concentration changes with distance. Negative flux means diffusion from high to low concentration. Higher diffusion coefficient means faster diffusion. Steeper concentration gradient results in higher flux. The law assumes steady-state conditions and no convection.

Question 7

What's the difference between Fick's first and second law?

Accepted Answer

Fick's first law describes steady-state diffusion: J = -D × (dC/dx), relating flux to concentration gradient. Fick's second law describes transient diffusion: ∂C/∂t = D × (∂²C/∂x²), showing how concentration changes with time. First law assumes constant flux over time, second law accounts for accumulation/depletion. First law is used for steady-state problems, second law for time-dependent problems. Both laws are related through the continuity equation: ∂C/∂t = -∂J/∂x.

Question 8

How do you use Fick's law for problem solving?

Accepted Answer

Problem-solving steps include: 1) Identify the system and determine if steady-state or transient, 2) Choose appropriate law (first for steady-state, second for transient), 3) Determine boundary and initial conditions, 4) Calculate or look up diffusion coefficient, 5) Apply the law with proper units, 6) Consider temperature and pressure effects, 7) Check for convection effects, 8) Validate results against physical constraints. For complex geometries, use numerical methods or finite difference techniques.

Question 9

What are common mistakes when using Fick's law?

Accepted Answer

Common mistakes include: 1) Forgetting the negative sign in the flux equation, 2) Using wrong units for diffusion coefficient or concentration gradient, 3) Not considering temperature and pressure effects on D, 4) Assuming steady-state when transient conditions exist, 5) Ignoring convection effects in moving fluids, 6) Using Fick's law for non-dilute solutions without activity corrections, 7) Not accounting for boundary layer effects, 8) Confusing mass flux with molar flux units.

Question 10

How do you calculate Fick's law with multiple components?

Accepted Answer

For multicomponent systems, use the Maxwell-Stefan equations or extended Fick's law: Jᵢ = -Dᵢᵢ × (dCᵢ/dx) - Σ(Dᵢⱼ × dCⱼ/dx), where Dᵢᵢ is self-diffusion coefficient and Dᵢⱼ are cross-diffusion coefficients. For binary systems: J₁ = -D₁₂ × (dC₁/dx) and J₂ = -D₂₁ × (dC₂/dx), where D₁₂ = D₂₁. Use the Darken equation for interdiffusion: D̃ = x₂D₁ + x₁D₂, where xᵢ are mole fractions. Consider coupling effects between different species and use appropriate boundary conditions for each component.

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