## Consider the Navier-Stokes equations with constant density it their dimensional form: ## Consider the Navier-Stokes equations with constant density it their dimensional form:
## The Reynolds number *Re* is the only dimensionless parameter which is always important in simplifying the equations of fluid motion for various applications. ## The Reynolds number *Re* is the only dimensionless parameter which is always important in simplifying the equations of fluid motion for various applications. ## Reynoldsification helps in simplifying NS equations by ingnoring less important terms. ## This simplification helps in obtaining analytical solutions to engineering parameters like friction factor. ## Better understanding of the complexity of real fluid flow is achieved by fitting the situation into Reynolds frame work.
## These are flows with Reynolds number lower than unity, Re<< 1. ## extremely small length scales, or ## by treating flows of very small velocity, so-called creeping flows.
## The choice *Re << 1* is an very interesting and important assumption. ## The choice *Re << 1* is an very interesting and important assumption. ## It is relevant to many practical problems, especially in a world where fluid devices are shrinking in size. ## A particularly interesting application is to the swimming of micro-organisms. ## This assumption, unveils a special dynamical regime which is usually referred to as Stokes flow. ## To honor George Stokes, who initiated investigations into this class of fluid problems. ## We shall also refer to this general area of fluid dynamics as the Stokesian realm. ## This is of extreme contrast to the theories of ideal inviscid flow, which might be termed the Eulerian realm.
*Re* is indicative of the ratio of inertial to viscous forces. *Re* is indicative of the ratio of inertial to viscous forces.
## The assumption of small *Re *means that viscous forces dominate the dynamics. ## That suggests that to drop entirely the term *Dv/Dt *from the Navier-Stokes equations. ## This renders the linear system. ## The linearity of the problem will be a major simplification.
## Redefine the dimensionless pressure as *pL/(2μU) *instead of *p/(U2)*.
## The basic assumption of creeping flow was developed by Stokes (1851) in a seminal paper. ## The basic assumption of creeping flow was developed by Stokes (1851) in a seminal paper. ## This states that density (inertia) terms are negligible in the momentum equation. ## Under non-gravitational field.
## How does sedimentation vary with the size of the sediment particles? ## How does sedimentation vary with the size of the sediment particles? ## What electric field is required to move a charged particle in electrophoresis? ## What g force is required to centrifuge cells in a given amount of time. ## What is the effect of gravity on the movement of a monocyte in blood? ## How rapidly do enzyme-coated beads move in a bioreactor? ## The flow geometry of all above mentioned applications is flow past a sphere. ## Define the term vorticity in spherical coordinate system.
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