In two-dimensional incompressible fluid flow, the continuity equation is essential for ensuring mass conservation, meaning that any change in fluid entering or exiting a region is balanced by a corresponding change elsewhere. For incompressible flow, where density remains constant, this requirement simplifies to the condition that the divergence of the velocity field must be zero. Mathematically, this is expressed as,

Downstream processing begins once fermentation is complete and involves a series of steps to recover and purify products such as acids, vitamins, antibiotics, or proteins.Cell HarvestingFor example, for intracellular protein-based products, the first step is harvesting the cells. This is typically achieved using centrifugation or filtration to separate the cells from the liquid phase.Cell Disruption for Intracellular ProductsIf the target product is intracellular, the harvested cells must be...

Transportation of samples from the collection point to the laboratory, as well as storage and preservation techniques, are crucial for maintaining sample integrity and ensuring accurate and reliable test results.
Samples should be transported carefully from collection points to the laboratory. They should be properly sealed and clearly labeled to prevent cross-contamination. To preserve the sample integrity, optimal temperature conditions during transport are essential. This could involve using...

Upstream processing represents a critical phase in biomanufacturing, wherein biological systems such as microorganisms, mammalian cells, or insect cells are cultivated to produce therapeutic proteins, vaccines, enzymes, or other biologically derived products. This phase encompasses all steps from the selection and genetic manipulation of the production organism to the cultivation of cells in bioreactors under tightly controlled environmental conditions.Host Selection and Genetic OptimizationThe...

Consider a control volume, such as a pipe with solid boundaries, through which fluid flows and changes direction due to the impulse exerted by the resulting force from the pipe walls. In steady flow, the mass of fluid entering the control volume at a given time, t, with velocity v1, is equal to the mass leaving after infinitesimal time dt, with velocity v2.
During this process, the momentum of the fluid within the control volume remains constant over the time interval dt. By applying the...

In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...