Clemson Hydro Diffusion Mass transfer in the absence of fluid motion

Clemson Hydro Important role in many processes Precipitation Calcite precipitate at pore scale Mixing Local-scale blending of fluids Mass transfer. Gas Liquid

Clemson Hydro Ore Deposits and Contaminated Sites Fracture filled with three generations of copper-bearing minerals: azurite (blue), malachite (green), chrysocolla (light blue). These minerals record changing fluid compositions and seal the pathway for fluid migration. Image; B. Dutrow C B &first=61&FORM=IDFRIR

Clemson Hydro Diffusion Sampler

Clemson Hydro Brownian Motion

Clemson Hydro Chemical potential Ideal solutions

Clemson Hydro Concept for Mass Flux Flux from high to low chemical potential Flux magnitude proportional to gradient or potential difference

Clemson Hydro Diffusion through liquid v Conceptual Stokes law: Assume (Einstein, 1905): Equate and rearrange: From previous page: Mass flux: Cussler [1997, p.116]

Clemson Hydro Mass Flux Fick’s Law D: Diffusivity[L 2 /T] Mass Transfer Law k: mass transfer coefficient [L/T] k~D/L C 1 : reference concentration [M/L 3 ] C x

Clemson Hydro Storage No Advective Flux Diffusive Flux (Fick’s Law) Source Governing Conservation of Mass Diffusion c = C S =0 (for now)

Clemson Hydro Simulation of Diffusion Governing Boundary Dirichlet, Specify Conc Neumann, Specify flux Cauchy, flux proportional to gradient

Clemson Hydro D in water Solute D aq in cm 2 /s Referenc e or source Hydrogen Nitrogen Oxygen Carbon dioxide Methane Ethane Propane Benzene Hydrogen sulfide 1622 Formic acid Acetic acid Propionic acid Butyric acid Benzoic acid Succinic acid p-Aminobenzoic acid Fluorescein 5.4_a_a Methanol 1516 Glycerol Urea Glucose Sucrose Lactose Maltose Raffinose e&source=bl&ots=7EWMwcA4xh&sig=AzbYYO7F3oydinzD2IW0SIyUpsA&hl=en&sa=X&ei=MBkkUZWhM4r S9AS04YCgCQ&ved=0CFsQ6AEwBTgK#v=onepage&q=diffusion%20constant%20table&f=false General Ions, small molecules ~ m 2 /s Water self-diffusion 2.3x10 -9 m 2 /s at 25 o C Proteins, large molecules m 2 /s m 2 /s 0.5-2x10 -9 m 2 /s Stokes-Einstein

Clemson Hydro Stokes-Einstein Lithium in Water r c : 0.076x10 -9 m T: 293K  : 0.001Pa s=0.001kg/m s Prokaryote in Water r c : 1000x10 -9 m T: 293K  : 0.001Pa s=0.001kg/m s Can microbes move by diffusion? Check with example Sizes of small things

Clemson Hydro General m 2 /s Chapman and Eskog eq. From kinetic theory Cussler [1997] D in gas ~1-10x10 -5 m 2 /s

Clemson Hydro D in solids Diffusion in calcite aggregate General ~ m 2 /s Depends on temperature, material, structure, direction Diffusivity Tensor ~ m 2 /s

Clemson Hydro Saturated Conditions Partially Saturated D in Porous Media institute/events/past-events/ porous-media/ Tortuosity Millington Quirk Buckingham Penman [Logan, 2012]

Clemson Hydro Diffusion Constant -log(D m 2 /s) gas liquid solid polymer gas liquid Porous Media Single Phase

Clemson Hydro Temp effects on D Arrhenius: Stokes-Einstein Increasing T will increase D

Clemson Hydro Scaling Sherwood number mass transfer vel./ diffusion velocity Stanton Number mass transfer vel./flow velocity Schmidt Number diffusion momentum/diffusion of mass Peclet Number flow velocity/diffusion velocity

Clemson Hydro Example: 1-D diffusion into a half-space b.c. C(0,t)=C i C(∞,t)=0 i.c. C(x,0)=0 Approximation Analyses L Many analytical solutions available

Clemson Hydro D = m 2 /s Diffusion through gas

Clemson Hydro D = m 2 /s Diffusion through liquid x coordinate (cm) How will the results change?

Clemson Hydro Diffusion into a Sphere D=10 -5 m 2 /s

Clemson Hydro Effect of boundary

Clemson Hydro Diffusion from Circle

Clemson Hydro Osmosis Arnold/VLI/Module%202/m2cellfunctionandenergetics/m2cellfunctionandenergetics6.html

Clemson Hydro Effects of osmosis on red blood cells Osmosis and cells Salted fish

Clemson Hydro Osmosis and plants Amaryllis blooming sequence

Clemson Hydro Osmosis and overpressured brine Overpressured brine in Qikou Depression, China. Du et al

Clemson Hydro Osmotic pump Continuous dispensing of drug Uniform rate Commercially available Mostly for lab testing (apparently)

Clemson Hydro Osmotic power Osmotic power plant, Norway Experimental right now Commercial plant in pilot/?searchterm=osmotic

Clemson Hydro

Estimate D from measurements of C Parameter Estimation