# Basic Rheology for Biologists

In Chapter 1 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss ideal solids and ideal liquids. Ideal solids are covered in Section 1.10, which introduces stress, strain, and their relationship through an elastic modulus. Ideal fluids are discussed in Section 1.16, which introduces a Newtonian fluid where the shear force is related to the flow rate by the coefficient of viscosity.

In the book Cell Mechanics, the chapter “Basic Rheology for Biologists,” by Paul Janmey, Penelope Georges, and Søren Hvidt, focuses on materials that are not ideal solids or liquids.

Real materials are neither ideal solids nor ideal liquids nor even ideal mixtures of the two. There are always effects due to molecular rearrangements and other factors that complicate deformation, transforming elastic and viscous constants to functions of time, and extent of deformation. Real materials, and especially biological materials, exhibit both elastic and viscous responses and are therefore called viscoelastic. They are also often highlyanisotropic, showing different viscoelastic properties when deformed in one direction than when deformed in other directions. The goal of rheological experiments is to quantify the viscoelasticity of a material over as wide a range of time and deformation scales as possible, and ultimately to relate these viscoelastic properties to the molecular structure of the material.

IPMB examines only briefly the subject of rheology: the study of how nonideal materials deform and flow.

In some materials, the stress depends not only on the strain, but on the rate at which the strain is produced. It may take more stress to stretch the material rapidly than to stretch it slowly, and more stress to stretch it than to maintain a fixed strain. Such materials are called viscoelastic.

Some materials are even more complicated, and the stress is not proportional to the strain or flow, but instead the relationship is nonlinear, demonstrating strain softening or strain stiffening.

Most materials will exhibit strain softening with a smaller [elastic modulus] at large strains. However, some systems exhibit strain stiffening where [the elastic modulus] increases above a critical strain.

Russ and I show an example of strain softening in IPMB’s Fig. 1.21. When stress is plotted versus strain, the stress first rises linearly and then bends over and becomes flatter.

One rheological concept Russ and I never discuss is creep. Janmey et al. write

Many biological systems experience a sustained force such as gravity or blood pressure. It is therefore useful to monitor how such systems deform under a constant load or stress. This type of measurement is called a creep experiment, and in such an experiment the strain is monitored as a function of time for a fixed stress.

Another type of stress-relaxation experiment is to keep the strain constant and measure the stress.

Stress-relaxation measurements can be performed in both simple shear and simple elongation, and they are of special interest for viscoelastic systems. In a stress-relaxation experiment, the sample is rapidly deformed and the stress is monitored as a function of time, keeping the sample in the deformed state.

Janmey et al. point out that oscillatory behavior is particularly useful when studying nonideal materials.

Rheological information for viscoelastic systems is often obtained by applying small amplitude oscillatory strains or stresses to the sample rather than steady flows.

When a oscillating deformation is applied to a material, the part of the stress in phase with the strain contains information about the material’s elastic behavior and the out-of-phase part contains information about the viscosity.

Rheology is an advanced topic and probably doesn’t belong in an intermediate textbook like IPMB. Yet, in the messy, wet, and sticky world of biology, rheology can often play a major role. Janmey et al. conclude

As cell and tissue mechanics become more of an integral part of basic cell biologic studies, a comprehensive understanding of micro- and macrorheology may help develop a unified model for how specific structural elements are used to form the soft but durable and adaptable materials that make up most organisms. The results of these studies also have potential for developing materials and methods for wound healing, cell differentiation, artificial organ development, and many other applications in biomedical research.

Originally published at http://hobbieroth.blogspot.com.

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Professor of Physics at Oakland University and coauthor of the textbook Intermediate Physics for Medicine and Biology.