2 - Fundamentals

Summary

Introduction

Polymer flow in any melt processing geometry is governed by three fundamental principles of physics: conservation of mass, conservation of linear momentum, and conservation of energy. Linear momentum is a vector quantity that must be conserved in each of three independent coordinate directions, so we must expect five conservation statements in the most general case. The natural language of these conservation statements is differential and integral calculus (recall that Newton invented the calculus to enable him to describe problems of motion); in particular, because we have four independent variables – time and three spatial variables – our language will employ partial derivatives, and the conservation equations will be stated as partial differential equations. The problems we will address in this text do not generally require familiarity with methods of solution of partial differential equations because the equations will usually simplify to forms that can be analyzed using elementary concepts of the calculus of one independent variable. (An apt linguistic analogy might be the contrast between understanding basic prose – our task here – and writing poetry.) Hence, the subject is open to any student who has completed a basic sequence in calculus.

The conservation equations are derived in many textbooks on fluid mechanics and transport phenomena, and we shall simply state them here, with an explanation of the meanings of terms where appropriate.