# Solids, liquids, what's the difference?

You've probably learned sometime in school that solids have a fixed shape and volume whereas liquids only have the latter. But why is that? In this chapter you will learn how a key liquid property; its viscosity - emerges from interactions between molecules. You will also learn why viscosity is fundamentally different from elasticity and why this is the underlying reason that liquids differ from solids. Read on for more!

# Shear stress

When you spread butter on toast you are effectively applying a force to 'shear' the butter. Similar to the concept of stress, the force per unit area applied is called shear stress. The difference for shear stress is that you are applying a force parallel to the area of contact. Whereas stress refers to when you are applying a force of compression or elongation both of which are perpendicular to the area of contact. But what is the difference whether you apply butter straight from the fridge vs after heating in the microwave for a few seconds? The latter is clearly easier to spread. In technical terms, you could apply the same shear stress on both butters and the heated butter spreads at a faster rate. We need another concept called strain rate to understand ease of spreading.

# Strain rate

Strain rate tells us how fast a liquid deforms relative to its height. Using the slice of butter analogy, heated butter will move at a faster rate for the same applied stress as compared to unheated butter. Fudamentally, the concept of strain rate arises from the top layer of molecules relative to the molecules below and so on until the bottom layer of butter atoms which are stuck to the bread underneath and are not moving. In liquids, molecules have a penalty for moving at a certain speed relative to neighboring molecules. This is a key difference between solids and liquids. In solids picture atoms connected by springs. Anytime you move a single atom, you stretch a spring, and need a force to do so. But liquids are different: there's no force required to displace molecules, instead you require a force to move molecules relative to other molecules; at a certain speed otherwise known as strain rate. Finally we have all the concepts in our bag to understand viscosity!

Note: I'm using atoms and molecules interchangably. I try to keep it consistent by referring to atoms in a solid and molecules in a liquid as most (crystalline) solids are made of atoms arranged in lattices whereas most liquids at room temperature are made of interacting molecules.

# Viscosity

Viscosity is the slope of the stress vs strain rate graph. Unheated butter has a higher viscosity than heated butter. This means that you need to apply a higher stress to spread unheated butter compared with heated butter at the same strain rate.

# Viscosity and Elasticity

Finally we come to the fundamental difference between elasticity and viscosity and consequently solids and liquids. Elasticity is determined by how much stress or force per unit area is required to strain (elongate or compress) an object by a certain amount. Once the stress is removed, the solid comes back to its original position, and this is called a temporary deformation. Think about stretching a rubber band. For liquids however, viscosity of a liquid is determined by how much stress or force per unit area is required to strain an object by a certain strain rate, equivalent to how fast the liquid spreads. Once the stress is removed, liquids do not return to their original state. Think about spreading butter. Once you spread it, it does not return back. Whereas if you try to spread a rubber, it might move a little bit but once you remove the knife it returns back as if nothing had disturbed it. Thus for solids how much you deform (strain) is critical whereas for liquids how fast you deform (strain rate) is the key factor. The image below shows stress vs time and strain vs time curves for solids and liquids. Notice how for solids the strain deformation follows the applied stress. But for liquids, the strain increases in time, and once the stress is removed, the strain still remains.

Is this the end of the story in understanding solids and liquids in everyday life? Not even close! First I told you all solids return back to their original state after the deformation, like a rubber band. However I neglected what happens when you apply enough force to permanently deform a solid or even fracture a solid like tearing a rubber band or a bridge falling down. Second, most everyday materials actually have a combination of both solid (elastic) and liquid (viscous) properties, and are aptly named viscoelastic materials. Think ketchup, shaving foam, ice cream - all the good stuff :). But now that we are familiar with the basics - solids, liquids, gases; we can delve in the next chapters into unlocking the science behind everyday materials!

# Slides