MODULE 2: DIFFUSION LECTURE NO DIFFUSION COEFFICIENT: MEASUREMENT AND PREDICTION

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1 NPTEL Chemical ass Transfer Oeration OULE : IFFUSION LECTURE NO. 4.4 IFFUSION COEFFICIENT: ESUREENT N PREICTION The roortionality factor of Fick s law is called diffusivity or diffusion coefficient which can be defined as the ratio of the flux to its concentration gradient and its unit is m s. It is a function of the temerature, ressure, nature and concentration of other constituents. iffusivity decreases with increase in ressure ( for moderate ranges of ressures, uto 5 atm) because number of collisions between secies is less at lower ressure. ut the diffusivity is hardly deendent on ressure in case of liquid. The diffusivity increases with increase in temerature ( T.5 ) because random thermal movement of molecules increases with increase in temerature. The diffusivity is generally higher for gases (in the range of to m s) than for liquids (in the range of 0 0 to 0-9 m s). The diffusivity value reorted for solids is higher in the range of 0 3 to 0-5 m s. iffusion is aost imossible in solids because the articles are too closely acked and strongly held together with no emty sace for articles to move through. Solids diffuse much slower than liquids because intermolecular forces in solid are stronger enough to hold the solid molecules together. Joint initiative of IITs and IISc Funded by HR Page of 5

2 NPTEL Chemical ass Transfer Oeration.4. easurement of gas-hase diffusion coefficient There are several methods of exerimental determination of gas-hase diffusion coefficient. Two methods are (a) Twin-bulb method and (b) Stefan tube method. Predictive Equations are sometimes used to determine diffusivity. These may be emirical, theoretical or semi-emirical. (a) Twin-bulb method Two large bulbs are connected by a narrow tube. The schematic reresentation is shown in Figure.6. In the beginning two bulbs are evacuated and all the three valves [V, V and V3] are ket closed. Then V is oened and bulb is filled with ure at a ressure P. fter that V3 is oened and bulb is filled with ure at the same ressure P. t steady state an a ( ) RTl an (.37) where, a is cross sectional area of the connecting tube of length l. If and are artial ressures of in two bulbs at any time, V d RT and V d RT an an (.38) (.39) From Equations (.38) and (.39) we have d( ) an RT (.40) V V d ( ) a ( ) (.4) l V V oundary conditions: t=0; ( - ) = (P-0)=P t=t, ( - ) = ( ) Joint initiative of IITs and IISc Funded by HR Page of 5

3 NPTEL Chemical ass Transfer Oeration alying the above boundary conditions, Equation (.4) is integrated to obtain the exression of as follows: ln ( P a ) l V V t (.4) t=0, =P, =0 t=t,, P V V l V3 t=0, =0, =P t=t,, P Figure.6: schematic of the twin bulb aaratus (b) Stefan tube method Stefan tube consists of a T tube made of glass, laced in a constant temerature water bath. ir um is used to suly the air, assed through the T tube as shown in Figure.7. Volatile comonent is filled in the T tube and air assed over it by the um and change in the level is observed by the sliding microscoe. Let, at any time t, artial ressure of at the Z distance from the to of the vertical tube is and that at the to it is. The diffusional flux of is given as: N P ( ) (.43) RT Z, The rate of evaoration is given by N dz P RT Z ( ), (.44) oundary conditions: t=0; Z=Z 0 Joint initiative of IITs and IISc Funded by HR Page 3 of 5

4 NPTEL Chemical ass Transfer Oeration t=t ; Z=Z Integration of Equation (.44) using the above boundary conditions gives, RT ( Z Z ), 0 (.45) P ( ) t where, artial ressure of a at liquid surface, is equal to vaor ressure at the same temerature. The artial ressure of at the to of the vertical tube, is zero due to high flow rate of. Gas + Z =0 =vaor ressure of liquid dz Volatile liquid (c)predictisve Equations: Figure.7: reresentation of the Stafan tube (I) Emirical: Fuller, Schettler and Giddings P( ) ( 7 T.75 ) 3 (.46) where, T is temerature in K, are molecular weights of and P is total ressure in bar ν, ν are atomic diffusion volume in m 3. (II) Theoretical: Chaman-Enskog Equation Joint initiative of IITs and IISc Funded by HR Page 4 of 5

5 NPTEL Chemical ass Transfer Oeration T P.5 (.47) where, σ is characteristic length arameter of binary mixture in Å, Ω is collision integral=f(ktε ) ( ) and ε = ( ε +ε ) 0.5 (.48) Joint initiative of IITs and IISc Funded by HR Page 5 of 5