Mass transfer co-efficient varies as D_AB^0.5, according to the __________ theory.

ANS:B - surface renewal

Surface renewal theory is a concept in chemical engineering and fluid dynamics that describes the renewal or refreshing of the interface between two phases, typically a gas and a liquid or two immiscible liquids. The theory proposes that the rate of mass transfer at the interface is determined by the frequency at which fresh or unexposed surface is brought into contact with the bulk fluid. Here's how surface renewal theory works:

1. Interface Renewal: In systems involving mass transfer between two phases, such as gas-liquid or liquid-liquid systems, the efficiency of mass transfer depends on the availability of fresh interface. When a new surface area is exposed to the bulk fluid, it allows for renewed contact and exchange of mass between the phases.
2. Frequency of Renewal: Surface renewal theory suggests that the rate of mass transfer is primarily controlled by the frequency at which the interface is renewed. This renewal can occur through various mechanisms such as turbulence, agitation, or other fluid dynamics phenomena that disrupt the interface and expose fresh surface area to the bulk fluid.
3. Enhanced Mass Transfer: By increasing the frequency of surface renewal, the mass transfer rate can be enhanced. This is because fresh interface provides more opportunities for molecules to transfer between the phases, leading to higher mass transfer coefficients and faster rates of mass transfer.
4. Applications: Surface renewal theory is applied in various processes where mass transfer between phases is critical, such as absorption, distillation, extraction, and chemical reactions occurring at interfaces. Engineers use this theory to design and optimize equipment and processes to maximize mass transfer efficiency.