Exploring asymptotically-Fickian chemical transport in porous media

Matan Cohen1, Brian Berkowitz1

  • 1Department of Earth and Planetary Sciences, Weizmann Institute of Science, Rehovot 7610001, Israel.

PubMed

Related Concept Videos

Slant Asymptotes01:27

Slant Asymptotes

A function's behavior is often guided by asymptotic constraints, where one term dominates another, defining a limiting trend. In the given scenario, the mathematical pattern follows a rational function: a cubic term in the numerator is divided by a squared term in the denominator. This results in a function with distinct characteristics, including an oblique asymptote, critical points, and undefined regions.The function's validity is determined by the denominator, which must be nonzero. This...
157
Asymptotes in Rational Functions01:30

Asymptotes in Rational Functions

A rational function is defined as the quotient of two polynomials:  where Q(x)≠0, These functions often exhibit asymptotes, which are the lines that the graph approaches but never touches. These asymptotes are classified based on how the function behaves near specific values of the input.Vertical asymptotes occur where the denominator is zero, and the numerator is not, causing the function to be undefined. These are found by solving Q(x)=0. For example:  has a vertical...
280
Short-distance Transport of Resources02:12

Short-distance Transport of Resources

Short-distance transport refers to transport that occurs over a distance of just 2-3 cells, crossing the plasma membrane in the process. Small uncharged molecules, such as oxygen, carbon dioxide, and water, can diffuse across the plasma membrane on their own. In contrast, ions and larger molecules require the assistance of transport proteins due to their charge or size. Transport across membranes also occurs within individual cells, playing a variety of essential roles for the plant as a whole.
17.8K
Facilitated Transport01:19

Facilitated Transport

The chemical and physical properties of plasma membranes cause them to be selectively permeable. Since plasma membranes have both hydrophobic and hydrophilic regions, substances need to be able to transverse both regions. The hydrophobic area of membranes repels substances such as charged ions. Therefore, such substances need special membrane proteins to cross a membrane successfully. In  facilitated transport, also known as facilitated diffusion, molecules and ions travel across a...
152.1K
Primary Active Transport01:47

Primary Active Transport

In contrast to passive transport, active transport involves a substance being moved through membranes in a direction against its concentration or electrochemical gradient. There are two types of active transport: primary active transport and secondary active transport. Primary active transport utilizes chemical energy from ATP to drive protein pumps that are embedded in the cell membrane. With energy from ATP, the pumps transport ions against their electrochemical gradients—a direction...
201.1K
Secondary Active Transport01:55

Secondary Active Transport

One example of how cells use the energy contained in electrochemical gradients is demonstrated by glucose transport into cells. The ion vital to this process is sodium (Na+), which is typically present in higher concentrations extracellularly than in the cytosol. Such a concentration difference is due, in part, to the action of an enzyme “pump” embedded in the cellular membrane that actively expels Na+ from a cell. Importantly, as this pump contributes to the high concentration of...
138.3K