The transport of solute molecules in the region 0 < x < L is characterized by...

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The transport of solute molecules in the region 0 < x < L is characterized by a diffusivity D (assume no convective mass transport); the region is bounded by two walls (at x = 0 and x = L). Initially, the solute molecules are uniformly distributed at a concentration w=wo (see sketch). 00 w (x, t) = [ an 11=1 W Show all steps. (b) Give an expression for an. wo initial concentration profile At time t= 0, the two walls suddenly become "sticky" (i.e. activated as adsorbents so that all solute molecules are captured on contact with the walls); this leads to the boundary conditions that the solute concentration w is zero at both walls for t > 0. (a) Show that the concentration w(x, t) is given byt xp(-n²n². D²) L an sin (7x) exp X The transport of solute molecules in the region 0 < x < L is characterized by a diffusivity D (assume no convective mass transport); the region is bounded by two walls (at x = 0 and x = L). Initially, the solute molecules are uniformly distributed at a concentration w=wo (see sketch). 00 w (x, t) = [ an 11=1 W Show all steps. (b) Give an expression for an. wo initial concentration profile At time t= 0, the two walls suddenly become "sticky" (i.e. activated as adsorbents so that all solute molecules are captured on contact with the walls); this leads to the boundary conditions that the solute concentration w is zero at both walls for t > 0. (a) Show that the concentration w(x, t) is given byt xp(-n²n². D²) L an sin (7x) exp X