家 » 黛博拉·诺尔

黛博拉·诺尔

1960

Markus Reiner

The Deborah number is a dimensionless quantity in rheology, used to characterize the fluidity of materials. It is the ratio of the relaxation time, which is an intrinsic property of the material, to the characteristic time scale of the experiment or observation. The formula is [乳胶]De = \frac{t_c}{t_p}[/latex], where [latex]t_c[/latex] is the relaxation time and [latex]t_p[/latex] is the observation time.

The Deborah number provides a crucial framework for understanding whether a material will behave as a fluid or a solid under specific conditions. A high Deborah number ([latex]De >> 1[/latex]) indicates solid-like behavior, where the material does not have enough time to relax and flow before the deformation process is complete. In this regime, the material’s elastic properties dominate. A classic example is silly putty, which can be stretched slowly like a liquid ([latex]De <> 1[/latex]).

Conversely, a low Deborah number ([latex]De << 1[/latex]) signifies fluid-like behavior. The observation time is much longer than the material’s relaxation time, allowing molecular chains or particles to rearrange and flow in response to the applied stress. Most common liquids like water have extremely short relaxation times, so their Deborah number is almost always very low in everyday situations, and they behave as simple viscous fluids.

The concept was famously proposed by Markus Reiner, who named it after a line in a song by the prophetess Deborah in the Bible: “The mountains flowed before the Lord”. This poetic reference captures the essence of the concept: even seemingly solid materials like mountains can flow if observed over a sufficiently long timescale (geological time). The Deborah number is fundamental in process engineering, particularly for viscoelastic materials like polymers, where processing speeds (determining [latex]t_p[/latex]) must be carefully controlled relative to the material’s relaxation time ([latex]t_c[/latex]) to avoid defects like melt fracture.