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宾汉塑料

1922

Eugene C. Bingham

（图片仅供参考）

A Bingham plastic is a viscoplastic material that behaves as a rigid body at low stresses but flows as a viscous fluid at high 压力它以屈服应力τ₀为特征，即最小值 shear stress 需要达到一定的阈值才能开始流动。低于此阈值，它不会变形。常见的例子包括牙膏、蛋黄酱和粘土浆。

这 constitutive equation for a Bingham plastic is given by a two-part model. Below the yield stress ([latex]\tau \tau_0[/latex]), the material flows, and the relationship between stress and shear rate becomes linear: [latex]\tau – \tau_0 = \mu_p \dot{\gamma}[/latex]. Here, [latex]\mu_p[/latex] is the plastic 粘度, which represents the fluid’s resistance to flow once it has started moving.

这种行为是由于混凝土内部存在某种结构，例如颗粒或絮凝胶体网络，这些结构必须先分解才能流动。屈服应力与这种内部网络的强度相对应。对于牙膏来说，这种网络在牙刷上保持其形状。挤压牙膏管产生的压力大于屈服应力，使其流动。在土木工程中，新鲜混凝土的屈服应力对于防止其成分离析、确保其能够有效泵送以及在模具中保持形状而不坍塌至关重要。

增材制造, 土木工程, 制造业, 材料, 过程, 产品开发, Rheology

UNESCO Nomenclature: 2210

– Mechanics

类型

Material Model

中断

重大的

用法

广泛使用

前体

粘土浆和涂料的流动阈值研究
Hooke’s law for solids and Newton’s law for fluids, which Bingham’s model bridges
流变测量技术的发展

应用程序

牙膏留在牙刷上，挤压时会流出
钻井泥浆在循环停止时悬浮岩屑
可泵送但在浇筑后仍能保持形状的混凝土
留在食物上的蛋黄酱和芥末
涂漆后不会滴落

专利：

潜在创新理念

挤压后立即保持形状的建筑用3D打印材料
用于电子元件的直接书写油墨，可创建稳定、精细的电路
专为特定质地和货架稳定性而设计的食品
可注射但牢固固定的医用水泥
化妆品粉底液留在罐子里，但能顺滑地涂抹在皮肤上
防火密封剂易于涂抹，但在重力或高温下不会塌陷
土工灌浆可以泵入土壤，但可以阻止进一步移动
为艺术家提供易于操作且保留精细细节的雕刻材料

Related to: bingham plastic, yield stress, viscoplastic, rheology, toothpaste, drilling mud, concrete, non-newtonian.

历史背景

Electrochemical cell experiment demonstrating electron transfer in redox reactions.

氧化还原反应中的电子转移

氧化还原（还原-氧化）反应涉及化学物质之间的电子转移。一种物质发生氧化（失去电子），而另一种物质发生还原（获得电子）。这两个过程总是同时发生。失去电子的物质是还原剂，获得电子的物质是氧化剂。这一基本概念是电化学和许多生物过程的基础。

Laboratory experiment demonstrating Debye Force between polar and nonpolar molecules.

德拜力（偶极子诱导偶极子相互作用）

An attractive intermolecular force between a polar molecule (with a permanent dipole) and a nonpolar molecule. The electric field from the permanent dipole distorts the electron cloud of the nonpolar molecule, inducing a temporary dipole in it. The two dipoles then attract each other. The interaction potential energy is [latex]V \propto -\frac{\alpha \mu^2}{r^6}[/latex], where [latex]\alpha[/latex] is polarizability and [latex]\mu[/latex] is the permanent dipole moment.

Laboratory experiment demonstrating Keesom force with polar liquids and molecular models.

基森力量

An electrostatic interaction between molecules that possess permanent electric dipole moments, such as water or hydrogen chloride. The force arises from the tendency of these dipoles to align head-to-tail, resulting in a net attraction. This interaction is temperature-dependent, as thermal motion disrupts the alignment. The orientation-averaged potential energy varies as [latex]V \propto -\frac{1}{r^6 k_B T}[/latex].

宾汉塑料

Laboratory scene with scientist performing molecular dynamics simulations using Lennard-Jones potential.

伦纳德-琼斯潜力

A simple, widely used mathematical model that approximates the potential energy of interaction between two neutral atoms or molecules. It combines a long-range attractive term ([latex]\propto r^{-6}[/latex]) representing Van der Waals forces with a steep, short-range repulsive term ([latex]\propto r^{-12}[/latex]) representing Pauli repulsion. The formula is [latex]V_{LJ}(r) = 4\epsilon [(\frac{\sigma}{r})^{12} - (\frac{\sigma}{r})^6][/latex].

Demonstration of shear-thinning behavior in a laboratory with ketchup.

剪切稀化（假塑性）

剪切稀化，或称假塑性，是一种非牛顿行为，指流体的粘度随剪切应力的增加而降低。许多常见物质，例如番茄酱或油漆，都表现出这种特性。静止状态下，它们很稠，但在摇晃、搅拌或摊开时更容易流动。这通常用奥斯特瓦尔德-德瓦勒幂律关系来描述。

Physicist's workspace with Schrödinger Equation and quantum mechanics materials.

薛定谔方程

This is a fundamental equation in quantum mechanics that describes how the quantum state of a physical system changes over time. It is a linear partial differential equation for the wavefunction, [latex]\Psi(x, t)[/latex]. The time-dependent version is [latex]i\hbar\frac{\partial}{\partial t}\Psi = \hat{H}\Psi[/latex], where [latex]\hat{H}[/latex] is the Hamiltonian operator, representing the total energy of the system.

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1919-05-29

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Albert Einstein discussing gravitational lensing in a historical laboratory setting.

引力透镜

广义相对论预测光的路径会因引力而弯曲。当来自遥远光源的光经过星系或恒星等巨大物体时，其路径会发生偏转。这种现象被称为引力透镜，它可以放大、扭曲背景光源，或创建其多重图像，就像一台宇宙望远镜，用于观察遥远的宇宙。

Chemist balancing redox reactions using the half-reaction method in analytical chemistry.

半反应法

复杂的氧化还原反应可以用半反应法配平。整个反应被拆分成两个独立的半反应：一个氧化反应，一个还原反应。每个半反应的原子和电荷都独立配平，通常是通过在水溶液中添加H+、OH-和H2O来实现的。最后，平衡电子数，并将两个半反应合并。

Chemist studying autocatalysis in a laboratory setting with glassware and chemical reactions.

自催化

自催化是一种化学反应，其中一种反应产物同时也是同一反应或偶联反应的催化剂。这形成了一个正反馈回路，导致反应速率加快。反应速率最初较慢，但随着产物（催化剂）浓度的增加而加快，通常形成S形动力学曲线。

Laboratory scene with scientist analyzing spectrometer for quantum mechanics research.

Landé g因子

The Landé g-factor ([latex]g_J[/latex]) is a dimensionless proportionality constant that relates an atom's total magnetic moment to its total angular momentum in the weak-field limit. It is crucial for quantitatively explaining the anomalous Zeeman effect. Its value is given by the formula: [latex]g_J = 1 + \frac{J(J+1) + S(S+1) - L(L+1)}{2J(J+1)}[/latex], where L, S, and J are the quantum numbers.

Laboratory experiment demonstrating wave-particle duality in quantum physics.

波粒二象性

All quantum entities, such as photons and electrons, exhibit both particle and wave properties. Depending on the experimental setup, they can behave like a localized particle or a distributed wave. The de Broglie hypothesis states that any particle with momentum [latex]p[/latex] has an associated wavelength [latex]\lambda = h/p[/latex], where [latex]h[/latex] is Planck's constant.

Laboratory pH measurement with a digital meter in analytical chemistry.

pH is formally defined as the negative decimal logarithm of the hydrogen ion activity, [latex]a_{H^+}[/latex]. The formula is [latex]pH = -\log_{10}(a_{H^+})[/latex]. Activity is the effective concentration of hydrogen ions, accounting for intermolecular forces, and is dimensionless. For dilute solutions, activity is approximately equal to the molar concentration of [latex]H^+[/latex] ions, simplifying the calculation.

Laboratory experiment on lanthanide elements in inorganic chemistry.

镧系收缩

镧系收缩是指镧系元素（从镧到镥）的原子半径和离子半径随着原子序数的增加而逐渐减小的现象。这种效应是由于4f电子对核电荷的屏蔽作用较弱造成的。这导致镧系元素之后的第六周期元素意外地小，与第五周期元素相似。

Quantum Statistics

Quantum statistics modifies classical statistical mechanics to account for the indistinguishability of identical particles. It splits into two types: Fermi-Dirac statistics for fermions (half-integer spin particles like electrons), which obey the Pauli exclusion principle, and Bose-Einstein statistics for bosons (integer spin particles like photons), which can occupy the same quantum state. This distinction is crucial at low temperatures and high densities.

（如果日期未知或不相关，例如“流体力学”，则提供其显著出现的近似估计）