There are many problems in which the motion of a small particle, bubble or drop in a non-Newtonian fluid differs in an important qualitative way from its corresponding motion in a Newtonian fluid. From a theoretical point of view such problems are conveniently separated into two groups. In the first, some aspect of the particle's motion only exists, for small Reynolds number, because the suspending fluid is non-Newtonian. Examples of this class include the cross-stream (or lateral) motion of spherical particles in a unidirectional shear flow, rotational motion of an orthotropic particle in sedimentation (leading to a deterministic equilibrium orientation), and cross-orbital drift in the rotation of an axisymmetric particle in shear flow. In these cases, a major change in the orientation or position of the particle can result from small instantaneous contributions of non-Newtonian rheology to the particle's motion, provided that these act “cumulatively” over a sufficiently long period of time. An analytical description of the fluid mechanics relevant to this process may thus be based on the asymptotic limit of a nearly-Newtonian fluid using the so-called “retarded-motion” expansion, and a relevant constitutive model for viscoelastic materials is the Rivlin—Ericksen nth-order fluid. Comparison between theory and experiment shows excellent qualitative (and frequently quantitative) agreement for such problems even when the flow is too rapid, in a rheological sense, for strict adherence to the requirements of a retarded-motion expansion. The second major class of problems is that in which the observed difference between Newtonian and non-Newtonian behavior is due to an important, O(1) change in the fluid motion at all times. In this case, the only possible theoretical description which is valid in more than an asymptotic sense is one based on a full non-linear constitutive model, including “memory”, and thus a solution of the equations of motion is generally possible only via numerical methods. Unlike the first class of problems, an important determining factor in successful match between experiment and theory is therefore a judicious (fortunate?) choice of the constitutive model. In the second part of this paper, I shall discuss some examples of numerical and experimental studies which pertain to particle motions in the regime of strongly viscoelastic flows.

The motion of small particles in non-Newtonian fluids

An experimental investigation is presented in which the velocity fields around sheres and bubbles moving in a cylinder have been measured by laser-Doppler anemometry (LDA). Instabilities in the flow field at rather low Deborah numbers have been discovered and these instabilities are damped by inertia forces. It is shown that the wall correction factor K is a rapidly decreasing function of the Deborah number. The experimental measurements have been compared with numerical simulations, and on the basis of this comparison it has been possible to identify a time constant and a zero-shear-rate viscosity for the test liquid.

Velocity fields around spheres and bubbles investigated by laser-doppler anemometry

When an air bubble rises in a viscoelastic fluid there is a critical capillary number for cusping and jump in velocity: when the capillary number is below critical, which is about 1 in our data, there is no cusp at the tail of a (smooth) air bubble. For larger volumes, a two-dimensional cusp, sharp in one view and broad in the orthogonal view, is in evidence. Measurements suggest that the cusp tip is in the generic form y = ax2/3 satisfied by analytic cusps. The intervals of volumes for which dramatic changes in air bubble shape take place is very small and the two to ten fold increase in the rise velocity which accompanies the small change of volume could be modelled as a discontinuity. A second drag transition and an orientational transition occurred when U/c > 1 where U is the rise velocity of an air bubble and c is the shear wave speed. For U/c 1 then U is proportional to d and the Deborah number does not change with U. Moreover the bubble shapes when U/c 1 when inertia is dominant. The formation of cusps occurs in all kinds of columns of different sizes and shapes. Cusping is generic but the orientation of the broad edge with respect to the sidewalls is an issue. There is no preferred orientation in columns with round cross-sections, or in the case of walls far away from the rising bubble. In columns with rectangular cross-sections, three relatively stable configurations can be observed: the cusp can be observed in the wide window and the broad edge in the narrow window; the cusp can be observed in the narrow window and the broad edge in the wide window or, less frequently, the broad edge lies along a diagonal. These orientational and drag alternatives are directly analogous to those which are observed in the settling of long or broad solid bodies (Liu & Joseph 1993).

A two-dimensional cusp at the trailing edge of an air bubble rising in a viscoelastic liquid

Using a finite-element program, the drag on an unbounded fluid in an (inelastic) power-law fluid is estimated. Comparison with upper and lower bounds, and with experimental data is given. Some remarks on wall effects are also made, and it is shown that wall effects are negligible forn ⩽ 0.5.

The drag on a sphere in a power-law fluid

The phenomenon of the negative wake behind a sphere sedimenting through a viscoelastic fluid is investigated. It is shown that there are two competing viscoelastic forces at work in this flow. The relaxation downstream of shear stresses generated near the side of the sphere drives a flow directed away from the sphere, giving rise to a negative wake. This force is opposed by the extensional stresses generated in the extensional flow at the rear of the sphere, which drives a flow towards the sphere producing an extended wake. The parameter controlling the balance between these forces is the extensibility of the polymer, which limits the extensional viscosity, with high extensibility producing an extended wake and smaller values giving negative wakes.

The negative wake behind a sphere sedimenting through a viscoelastic fluid

Comparison of the responses of viscoelastic fluids to a new rheometrical test

This paper contains experimental and theoretical work on a non-viscomethric flow with constant strain for non-Newtonian fluids. An experimental investigation of the laminar isothermal flow of moderately concentrated aqueous solutions of polymers (polyethylene oxide) around a spherical obstacle, which moves along the axis of a cylinder at low Reynolds number, is carried out. The sphere is free from any attachment and falls under the action of gravity. By means of a vizualisation method, velocity distributions are accurately measured and their dependence upon the three dimensionless parameters We (Weissenberg number), Re (Reynolds number) and λ (sphere-cylinder diameter ratio) is studied. A remarkable difference between Newtonian and viscoelastic velocity fields is pointed out. The drag on the sphere is also determined. The effects of finite boundaries are analyzed for a range of sphere-cylinder diameter ratios greater than 0.25. In particular, it is shown that the wall proximity increases the effects due to the fluid elastic behavior, while, on the other hand, it reduces the inertial effect. In order to complete the experimental results, a theoretical analysis is developed for a Maxwell constitutive equation. The lower terms of an expansion in power series of Re and We and simplified boundary conditions are used. The numerical data conveniently represent the experimentally observed phenomena.

Effect of finite boundaries on the slow laminar isothermal flow of a viscoelastic fluid around a spherical obstacle

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

D. Sigli

Author Tools

Chat about Author

Papers

Comparison of the responses of viscoelastic fluids to a new rheometrical test

Effect of finite boundaries on the slow laminar isothermal flow of a viscoelastic fluid around a spherical obstacle