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Basic Principles of Mass Transfer

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Molecular Diffusion versus Convective Mass Transfer

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Molecular diffusion involves the random movement of molecules, whereas convective mass transfer is the movement of molecules with the flow of the fluid they are in. Example of molecular diffusion: Sugar dissolving in still water. Example of convective mass transfer: Sugar carried away by stirring the water.

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Stripping

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Stripping is a mass transfer operation where impurities are removed from a liquid by passing a gas through it. Example: Removal of volatile organic compounds (VOCs) from wastewater.

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Henry's Law

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Henry's Law states that the amount of dissolved gas in a liquid is proportional to its partial pressure above the liquid, represented by C=kHPC = k_H \cdot P, where CC is the concentration of the dissolved gas, kHk_H is Henry's law constant, and PP is the partial pressure of the gas.

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Membrane Separation

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Membrane separation utilizes semi-permeable membranes to separate components in a mixture based on differences in permeability. Example: Reverse osmosis for desalination of seawater.

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Mass Transfer Coefficient

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Mass transfer coefficient is a measure of the mass transfer rate of a species per unit area to a fluid across a phase boundary, often used in the context of convective mass transfer. Example: Oxygen transfer from air to blood in the lungs.

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Rayleigh Equation

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The Rayleigh Equation relates the amount of material distilled to the compositions of the residue and distillate, represented by

xd=x0(1W)Wx_d = \frac{x_0 \cdot (1-W)}{W}
, where xdx_d is the mole fraction of the distillate, x0x_0 is the initial mole fraction, and WW is the fraction of the total amount remaining.

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Sherwood Number

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Sherwood Number is a dimensionless number used in mass transfer, representing the ratio of convective to diffusive mass transfer rates, and is given by

Sh=kLDSh = \frac{kL}{D}
, where kk is the mass transfer coefficient, LL characterizes the length, and DD is the diffusion coefficient.

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Distillation

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Distillation is a mass transfer process of separating components or substances from a liquid mixture by using selective boiling and condensation. Example: Separation of ethanol from water in the production of spirits.

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Absorption

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Absorption is the process in which a substance captures and transforms energy or particles from a substance. Example: Removal of CO2 from industrial gases using a solvent like water or amine solutions.

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Two-film Theory

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Two-film Theory describes mass transfer across a phase boundary considering a stagnant film on each side of the interface where all resistance to mass transfer occurs. Example: Absorption of a gas into a liquid where each has its own respective film resistance.

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McCabe-Thiele Method

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The McCabe-Thiele Method is a graphical design technique used to determine the number of theoretical stages required for binary distillation. Example: The separation of ethanol and water in a distillation column.

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Diffusion

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Diffusion is the movement of particles from a region of higher concentration to a region of lower concentration, driven by a concentration gradient. Example: The spreading of a perfume scent in the air.

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Fick's First Law of Diffusion

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Fick's First Law quantifies diffusion, stating that the molar flux due to diffusion is proportional to the concentration gradient, represented by

J=DdϕdxJ = -D \frac{d\phi}{dx}
where JJ is the diffusive flux, DD is the diffusion coefficient, and dϕdx\frac{d\phi}{dx} is the concentration gradient.

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Equilibrium Stage Concepts

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In mass transfer operations, an equilibrium stage is where the mass transfer between phases occurs until equilibrium is reached. Example: Each tray in a distillation column represents an equilibrium stage.

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Wetted Wall Column

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A wetted wall column is a type of equipment used to study mass transfer where a liquid film flows down a wall and gas is passed over it. Example: Absorption of gases in liquid films for research and laboratory experimentation.

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