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An Unimaginable Diffusion Process: Why Is Diffusion in Porous Media So Unique?
In the discussion of physics and materials science, the process of "diffusion" is often accompanied by the development of various technologies and theories. In most cases, the diffusion process follows the classic Brownian motion model, which means that its mean square displacement (MSD) is linear in time. However, when we turn our perspective to more complex porous media, the characteristics of diffusion seem to be different, showing an "abnormal diffusion" phenomenon that is difficult to explain with classical theory.
Anomalous diffusion is a diffusion process in which there is a nonlinear relationship between mean square displacement and time, which is in sharp contrast to traditional Brownian motion.
Classification of abnormal diffusion
Abnormal diffusion can be classified according to the dynamic characteristics of diffusion. These classifications are not simple and clear, but imply more complex physical processes. Generally speaking, we can divide abnormal diffusion into the following categories:
- α < 1:
subdiffusion- In this case, due to crowding or obstacles, the pace of the random walker is restricted, forming a subdiffusion phenomenon. - α = 1:
Brownian motion- This is traditional Brownian motion, exhibiting linear characteristics of diffusion. - 1 < α < 2:
superdiffusion- Superdiffusion can be caused by active cellular transport processes or the hopping behavior of heavy-tailed distributions. - α = 2:
ballistic motion- Particles that move at a constant speed, such as in a straight line. - α > 2:
hyperballistic- Observed in optical systems showing uncharacteristic fast diffusion behavior.
In 1926, using a weather balloon, Louis Faure Richardson demonstrated the phenomenon of superdiffusion in the atmosphere, further expanding our understanding of diffusion processes.
Model of abnormal diffusion
In order to gain a deeper understanding of the origin and mechanism of abnormal diffusion, scientists have proposed a variety of mathematical models. Most of these models include operations related to long-range stochastic processes, such as continuous-time random walks (CTRW) and fractional Brownian motion (fBm). These advanced mathematical frameworks not only bring new understandings to physics, but also draw attention to the internal movement mechanisms of cells in biophysics.
Today, abnormal diffusion research in the field of cell biology has attracted increasing attention, because these studies have found that molecular movements in cells often exhibit abnormal diffusion behaviors that break formal assumptions.
The work of some researchers has proven that intracellular movements no longer follow the classic microcanonical system and the Wiener-Hutchinson theorem, which provides a new perspective for us to understand the molecular operations within cells.
Application scope of abnormal diffusion
In the real world, the phenomenon of abnormal diffusion also appears in many natural phenomena, including ultracold atoms, Hamington spring mass systems, scalar mixtures in the interstellar medium, and telomeres in the cell nucleus. These phenomena have prompted scientists to have a strong interest in the study of anomalous diffusion, and hope to unravel the complexity behind it through further experiments and theoretical explorations.
For example, in the moisture transport process in cement-based materials, the anomalous diffusion model helps us more accurately predict water vapor diffusion and its impact on material properties.
Conclusion
In short, abnormal diffusion is not just a simple physical phenomenon, it involves a wide range of application fields and profound scientific issues. We still need to further explore and understand in order to better utilize this natural phenomenon. Therefore, "In the future, in the process of studying abnormal diffusion, what unresolved issues will become key exploration points?"?
