Skip to main content
SpringerLink
Log in

Dynamics, rheology, and applications of elastic deformable particle suspensions: a review

  • Review
  • Published:
Rheologica Acta Aims and scope Submit manuscript

Abstract

Suspensions with deformable solid inclusions have both scientific and industrial interest. Examples include microgel particle suspensions, biological fluids, and filled polymers. Due to the interplay of numerous factors (e.g., particle size, shape, and mechanical properties, suspending liquid rheology and flow conditions, flow cell shape, interactions between the particles and the flow channel and among the particles), these systems can show many different flow behaviors. The study of the flow behavior of soft particle suspensions is an open field and is attracting an increasing interest from the scientific community. As elastic beads are good models for biological cells, one reason for such interest is related to the possibility of exploiting particle mechanical-property-dependent flow behavior to diagnose diseases. On the other hand, in the recent years, suspensions of elastic microparticles are also proving useful in a completely different technological field, namely oil recovery from porous media. This paper gives an overview of the state of the art and envisages possible future perspectives on the dynamics, rheology, and applications of elastic particle suspensions.

Suspensions with deformable solid inclusions have both scientific and industrial interest. Examples include microgel particle suspensions, biological fluids, and filled polymers. in the recent years, suspensions of elastic microparticles are also proving useful in a completely different technological field, namely oil recovery from porous media.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Copyright Cambridge University Press 2013

Fig. 2
Fig. 3

Copyright The Royal Society of Chemistry 2010

Fig. 4

Copyright Elsevier B.V. 2014

Fig. 5

Copyright American Physical Society 2012

Fig. 6

Copyright American Physical Society 2015

Fig. 7

Copyright Elsevier 2016

Fig. 8

Copyright The Royal Society of Chemistry 2017

Fig. 9

Copyright The Royal Society of Chemistry 2013

Fig. 10

Adapted from Li et al. (2015)

Fig. 11

Copyright The Royal Society of Chemistry 2017

Fig. 12

Copyright Cambridge University Press 2013

Fig. 13

Copyright Cambridge University Press 2015

Fig. 14

Copyright American Physical Society 2012

Fig. 15

Copyright The Society of Rheology 2004

Fig. 16

Copyright The Society of Rheology 2004

Fig. 17

Copyright Cambridge University Press 2015

Fig. 18

Copyright The Royal Society of Chemistry 2010

Fig. 19

Copyright The Royal Society of Chemistry 2012

Fig. 20

Copyright American Physical Society 2017

Fig. 21

Copyright American Chemical Society 2012

Fig. 22

Copyright American Chemical Society 2015

Similar content being viewed by others

References

  • Abate AR, Han L, Jin L, Suo Z, Weitz DA (2012) Measuring the elastic modulus of microgels using microdrops. Soft Matter 8(39):10,032–10,035

    Article  CAS  Google Scholar 

  • Adams S, Frith WJ, Stokes JR (2004) Influence of particle modulus on the rheological properties of agar microgel suspensions. J Rheol 48(6):1195–1213

    Article  CAS  Google Scholar 

  • Ai Y, Mauroy B, Sharma A, Qian S (2011) Electrokinetic motion of a deformable particle: dielectrophoretic effect. Electrophoresis 32(17):2282–2291

    Article  CAS  Google Scholar 

  • Avazmohammadi R, Castañeda PP (2015) The rheology of non-dilute dispersions of highly deformable viscoelastic particles in newtonian fluids. J Fluid Mech 763:386–432

    Article  CAS  Google Scholar 

  • Avazmohammadi R, Castañeda PP (2016) Macroscopic rheological behavior of suspensions of soft solid particles in yield stress fluids. J Non-Newtonian Fluid Mech 234:139–161

    Article  CAS  Google Scholar 

  • Barthes-Biesel D (2016) Motion and deformation of elastic capsules and vesicles in flow. Annu Rev Fluid Mech 48:25–52

    Article  Google Scholar 

  • Butt HJ, Cappella B, Kappl M (2005) Force measurements with the atomic force microscope: technique, interpretation and applications. Surf Sci Rep 59(1–6):1–152

    Article  CAS  Google Scholar 

  • Chen L, Wang KX, Doyle PS (2017) Effect of internal architecture on microgel deformation in microfluidic constrictions. Soft Matter 13(9):1920–1928

    Article  CAS  Google Scholar 

  • D’Avino G, Greco F, Maffettone PL (2017) Particle migration due to viscoelasticity of the suspending liquid and its relevance in microfluidic devices. Annu Rev Fluid Mech 49:341–360

    Article  Google Scholar 

  • Desse M, Fraiseau D, Mitchell J, Budtova T (2010) Individual swollen starch granules under mechanical stress: evidence for deformation and volume loss. Soft Matter 6(2):363–369

    Article  CAS  Google Scholar 

  • Esmailzadeh H, Passandideh-Fard M (2014) Numerical and experimental analysis of the fluid-structure interaction in presence of a hyperelastic body. J Fluids Eng 136(11):111,107

    Article  Google Scholar 

  • Farahbakhsh I, Ghassemi H, Sabetghadam F (2016) A vorticity based approach to handle the fluid-structure interaction problems. Fluid Dyn Res 48(1):015,509

    Article  Google Scholar 

  • FitzGerald PA, Dupin D, Armes SP, Wanless EJ (2007) In situ observations of adsorbed microgel particles. Soft Matter 3(5):580–586

    Article  CAS  Google Scholar 

  • Fraldi M, Cugno A, Deseri L, Dayal K, Pugno NM (2015) A frequency-based hypothesis for mechanically targeting and selectively attacking cancer cells. J R Soc Interface 12(111):20150,656

    Article  CAS  Google Scholar 

  • Fröhlich A, Sack R (1946) Theory of the rheological properties of dispersions. Proc R Soc Lond A 185 (1003):415–430

    Article  Google Scholar 

  • Galaev I, Mattiasson B (eds) (2007) Smart polymers: applications in biotechnology and biomedicine. CRC Press, Boca Raton

    Google Scholar 

  • Gao T, Hu HH (2009) Deformation of elastic particles in viscous shear flow. J Comput Phys 228(6):2132–2151

    Article  CAS  Google Scholar 

  • Gao T, Hu HH, Castañeda PP (2011) Rheology of a suspension of elastic particles in a viscous shear flow. J Fluid Mech 687:209–237

    Article  Google Scholar 

  • Gao T, Hu HH, Castañeda PP (2012) Shape dynamics and rheology of soft elastic particles in a shear flow. Phys Rev Lett 108(5):058, 302

    Article  CAS  Google Scholar 

  • Gao T, Hu HH, Castañeda PP (2013) Dynamics and rheology of elastic particles in an extensional flow. J Fluid Mech 715:573–596

    Article  CAS  Google Scholar 

  • Gent AN (1996) A new constitutive relation for rubber. Rubber Chem Technol 69(1):59–61

    Article  CAS  Google Scholar 

  • Girardo S, Traeber N, Wagner K, Cojoc G, Herold C, Goswami R, Schluessler R, Abuhattum S, Taubenberger A, Reichel F et al (2018) Standardized microgel beads as elastic cell mechanical probes. bioRxiv p 290569

  • Goddard JD, Miller C (1967) Nonlinear effects in the rheology of dilute suspensions. J Fluid Mech 28 (4):657–673

    Article  Google Scholar 

  • Guo M, Wyss HM (2011) Micromechanics of soft particles. Macromol Mater Eng 296(3-4):223–229

    Article  CAS  Google Scholar 

  • Hashin Z, Shtrikman S (1963) A variational approach to the theory of the elastic behaviour of multiphase materials. J Mech Phys Solids 11(2):127–140

    Article  Google Scholar 

  • Hashmi SM, Dufresne ER (2009) Mechanical properties of individual microgel particles through the deswelling transition. Soft Matter 5(19):3682–3688

    Article  CAS  Google Scholar 

  • Hertz H (1881) Über die berührung fester elastischer körper. Journal fü,r die Reine und Angewandte Mathematik 92:156–171

    Google Scholar 

  • Hou HW, Li QS, Lee GYH, Kumar AP, Ong CN, Lim CT (2009) Deformability study of breast cancer cells using microfluidics. Biomed Microdevices 11(3):557–564

    Article  CAS  Google Scholar 

  • Hur SC, Henderson-MacLennan NK, McCabe ERB, Di Carlo D (2011) Deformability-based cell classification and enrichment using inertial microfluidics. Lab Chip 11(5):912–920

    Article  CAS  Google Scholar 

  • Hwang MY, Kim SG, Lee HS, Muller SJ (2017) Generation and characterization of monodisperse deformable alginate and pnipam microparticles with a wide range of shear moduli. Soft Matter 13(34):5785–5794

    Article  CAS  Google Scholar 

  • Hwang MY, Kim SG, Lee HS, Muller SJ (2018) Elastic particle deformation in rectangular channel flow as a measure of particle stiffness. Soft Matter 14(2):216–227

    Article  CAS  Google Scholar 

  • Ii S, Sugiyama K, Takeuchi S, Takagi S, Matsumoto Y (2011) An implicit full Eulerian method for the fluid–structure interaction problem. Int J Numer Methods Fluids 65(1-3):150–165

    Article  Google Scholar 

  • Ji X, Xu L, Zhou T, Shi L, Deng Y, Li J (2018) Numerical investigation of dc dielectrophoretic deformable particle–particle interactions and assembly. Micromachines 9(6):260

    Article  Google Scholar 

  • Kumachev A, Tumarkin E, Walker GC, Kumacheva E (2013) Characterization of the mechanical properties of microgels acting as cellular microenvironments. Soft Matter 9(10):2959–2965

    Article  CAS  Google Scholar 

  • Li Y, Kumacheva E, Ramachandran A (2013) The motion of a microgel in an axisymmetric constriction with a tapered entrance. Soft Matter 9(43):10,391–10,403

    Article  CAS  Google Scholar 

  • Li Y, Sarıyer OS, Ramachandran A, Panyukov S, Rubinstein M, Kumacheva E (2015) Universal behavior of hydrogels confined to narrow capillaries. Sci Rep 5:17,017

    Article  CAS  Google Scholar 

  • Liétor-Santos JJ, Sierra-Martín B, Fernández-Nieves A (2011) Bulk and shear moduli of compressed microgel suspensions. Phys Rev E 84(6):060,402

    Article  CAS  Google Scholar 

  • Liu Y, Hou J, Wang Q, Liu J, Guo L, Yuan F, Zhou K (2017) Flow of preformed particle gel through porous media: a numerical simulation study based on the size exclusion theory. Indus Eng Chem Res 56 (10):2840–2850

    Article  CAS  Google Scholar 

  • Matzelle TR, Geuskens G, Kruse N (2003) Elastic properties of poly (N-isopropylacrylamide) and poly (acrylamide) hydrogels studied by scanning force microscopy. Macromolecules 36(8):2926– 2931

    Article  CAS  Google Scholar 

  • Mietke A, Otto O, Girardo S, Rosendahl P, Taubenberger A, Golfier S, Ulbricht E, Aland S, Guck J, Fischer-Friedrich E (2015) Extracting cell stiffness from real-time deformability cytometry: theory and experiment. Biophys J 109(10):2023–2036

    Article  CAS  Google Scholar 

  • Mokbel M, Mokbel D, Mietke A, Traber N, Girardo S, Otto O, Guck J, Aland S (2017) Numerical simulation of real-time deformability cytometry to extract cell mechanical properties. ACS Biomater Sci Eng 3(11):2962–2973

    Article  CAS  Google Scholar 

  • Murata T (1980) On the deformation of an elastic particle falling in a viscous fluid. J Physical Soc Japan 48 (5):1738–1745

    Article  Google Scholar 

  • Murata T (1981) Deformation of an elastic particle suspended in an arbitrary flow field. J Physical Soc Japan 50(3):1009–1016

    Article  Google Scholar 

  • Nasouri B, Khot A, Elfring GJ (2017) Elastic two-sphere swimmer in stokes flow. Phys Rev Fluids 2(4):043,101

    Article  Google Scholar 

  • Nguyen VB, Wang CX, Thomas CR, Zhang Z (2009) Mechanical properties of single alginate microspheres determined by microcompression and finite element modelling. Chem Eng Sci 64(5):821–829

    Article  CAS  Google Scholar 

  • Niu Y, Zhang X, Si T, Zhang Y, Qi L, Zhao G, Xu RX, He X, Zhao Y (2017) Simultaneous measurements of geometric and viscoelastic properties of hydrogel microbeads using continuous-flow microfluidics with embedded electrodes. Small 13(48):1702,821

    Article  CAS  Google Scholar 

  • Oliver WC, Pharr GM (2004) Measurement of hardness and elastic modulus by instrumented indentation: advances in understanding and refinements to methodology. J Mater Res 19(1):3–20

    Article  CAS  Google Scholar 

  • Ottemann KM, Miller JF (1997) Roles for motility in bacterial–host interactions. Mol Microbiol 24(6):1109–1117

    Article  CAS  Google Scholar 

  • Pal R (2016) Fundamental rheology of disperse systems based on single-particle mechanics. Fluids 1(4):40

    Article  CAS  Google Scholar 

  • Pozrikidis C (2003) Modeling and simulation of capsules and biological cells. CRC Press

  • Pu W, Zhao S, Wang S, Wei B, Yuan C, Li Y (2018) Investigation into the migration of polymer microspheres (PMs) in porous media: implications for profile control and oil displacement. Colloids Surf A Physicochem Eng Asp 540:265–275

    Article  CAS  Google Scholar 

  • Rivlin RSl (1948) Large elastic deformations of isotropic materials. I. Fundamental concepts. Philoso Trans R Soc London A 240(822):459–490

    Article  Google Scholar 

  • Roscoe R (1967) On the rheology of a suspension of viscoelastic spheres in a viscous liquid. J Fluid Mech 28(2):273–293

    Article  Google Scholar 

  • Rosti ME, Brandt L (2018) Suspensions of deformable particles in a Couette flow. Journal of Non-Newtonian Fluid Mechanics

  • Rosti ME, Brandt L, Mitra D (2018) Rheology of suspensions of viscoelastic spheres: deformability as an effective volume fraction. Phys Rev Fluids 3(1):012,301

    Article  Google Scholar 

  • Segré G, Silberberg A (1961) Radial particle displacements in Poiseuille flow of suspensions. Nature 189 (4760):209

    Article  Google Scholar 

  • Sierra-Martin B, Frederick JA, Laporte Y, Markou G, Lietor-Santos JJ, Fernandez-Nieves A (2011a) Determination of the bulk modulus of microgel particles. Colloid Polym Sci 289(5-*6):721–728

    Article  CAS  Google Scholar 

  • Sierra-Martin B, Laporte Y, South AB, Lyon LA, Fernández-Nieves A (2011b) Bulk modulus of poly (N-isopropylacrylamide) microgels through the swelling transition. Phys Rev E 84(1):011,406

    Article  CAS  Google Scholar 

  • Subramaniam DR, Gee DJ (2016) Shape oscillations of elastic particles in shear flow. J Mech Behav Biomed Mater 62:534–544

    Article  Google Scholar 

  • Sugiyama K, Ii S, Takeuchi S, Takagi S, Matsumoto Y (2011) A full Eulerian finite difference approach for solving fluid–structure coupling problems. J Comput Phys 230(3):596–627

    Article  CAS  Google Scholar 

  • Takeuchi S, Yuki Y, Ueyama A, Kajishima T (2010) A conservative momentum-exchange algorithm for interaction problem between fluid and deformable particles. Int J Numer Methods Fluids 64(10–12):1084–1101

    Article  Google Scholar 

  • Tam CKW, Hyman WA (1973) Transverse motion of an elastic sphere in a shear field. J Fluid Mech 59 (1):177–185

    Article  Google Scholar 

  • Trofa M, Villone MM, D’Avino G, Hulsen MA, Netti PA, Maffettone PL (2016) Numerical simulations of the separation of elastic particles in a T-shaped bifurcation. J Non-Newtonian Fluid Mech 233:75–84

    Article  CAS  Google Scholar 

  • Villone MM, Greco F, Hulsen MA, Maffettone PL (2014a) Simulations of an elastic particle in Newtonian and viscoelastic fluids subjected to confined shear flow. J Non-Newtonian Fluid Mech 210:47–55

    Article  CAS  Google Scholar 

  • Villone MM, Hulsen MA, Anderson PD, Maffettone PL (2014b) Simulations of deformable systems in fluids under shear flow using an arbitrary lagrangian eulerian technique. Comput Fluids 90:88–100

    Article  Google Scholar 

  • Villone MM, D’Avino G, Hulsen MA, Maffettone PL (2015) Dynamics of prolate spheroidal elastic particles in confined shear flow. Phys Rev E 92(6):062,303

    Article  CAS  Google Scholar 

  • Villone MM, Greco F, Hulsen MA, Maffettone PL (2016) Numerical simulations of deformable particle lateral migration in tube flow of Newtonian and viscoelastic media. J Non-Newtonian Fluid Mech 234:105–113

    Article  CAS  Google Scholar 

  • Villone MM, Trofa M, Hulsen MA, Maffettone PL (2017) Numerical design of a T-shaped microfluidic device for deformability-based separation of elastic capsules and soft beads. Phys Rev E 96(5):053,103

    Article  CAS  Google Scholar 

  • Villone MM, Nunes JK, Li Y, Stone HA, Maffettone PL (2019) Design of a microfluidic device for the measurement of the elastic modulus of deformable particles. Soft Matter 15(5):880–889

    Article  CAS  Google Scholar 

  • Wang L, Shelton RM, Cooper PR, Lawson M, Triffitt JT, Barralet JE (2003) Evaluation of sodium alginate for bone marrow cell tissue engineering. Biomaterials 24(20):3475–3481

    Article  CAS  Google Scholar 

  • Wiedemair J, Serpe MJ, Kim J, Masson JF, Lyon LA, Mizaikoff B, Kranz C (2007) In-situ AFM studies of the phase-transition behavior of single thermoresponsive hydrogel particles. Langmuir 23(1):130–137

    Article  CAS  Google Scholar 

  • Willis JR (1977) Bounds and self-consistent estimates for the overall properties of anisotropic composites. J Mech Phys Solids 25(3):185–202

    Article  Google Scholar 

  • Wu J, Aidun CK (2010) Simulating 3D deformable particle suspensions using lattice Boltzmann method with discrete external boundary force. Int J Numer Methods Fluids 62(7):765–783

    Google Scholar 

  • Wyss HM, Franke T, Mele E, Weitz DA (2010) Capillary micromechanics: measuring the elasticity of microscopic soft objects. Soft Matter 6(18):4550–4555

    Article  CAS  Google Scholar 

  • Yao C, Lei G, Li L, Gao X (2012a) Selectivity of pore-scale elastic microspheres as a novel profile control and oil displacement agent. Energy & Fuels 26(8):5092–5101

    Article  CAS  Google Scholar 

  • Yao C, Lei G, Li W, Li L, Gao X (2012b) An experiment and simulation of elastic microspheres enhanced oil recovery (EMEOR). Energy Sources, Part A: Recovery, Utilization, and Environmental Effects 34(8):692–701

    Article  Google Scholar 

  • Yao C, Lei G, Cathles LM, Steenhuis TS (2014) Pore-scale investigation of micron-size polyacrylamide elastic microspheres (MPEMs) transport and retention in saturated porous media. Environ Sci Technol 48(9):5329–5335

    Article  CAS  Google Scholar 

  • Yao C, Lei G, Hou J, Xu X, Wang D, Steenhuis TS (2015) Enhanced oil recovery using micron-size polyacrylamide elastic microspheres: underlying mechanisms and displacement experiments. Indus Eng Chem Res 54 (43):10,925–10,934

    Article  CAS  Google Scholar 

  • Yuan M, Ju X, Xie R, Wang W, Chu L (2015) Micromechanical properties of poly (N-isopropylacrylamide) hydrogel microspheres determined using a simple method. Particuology 19:164–172

    Article  CAS  Google Scholar 

  • Zhao H, Freund JB, Moser RD (2008) A fixed-mesh method for incompressible flow–structure systems with finite solid deformations. J Comput Phys 227(6):3114–3140

    Article  Google Scholar 

  • Zhao S, Pu W, Wei B, Xu X (2019) A comprehensive investigation of polymer microspheres (PMs) migration in porous media: EOR implication. Fuel 235:249–258

    Article  CAS  Google Scholar 

  • Zhou T, Yeh LH, Li FC, Mauroy B, Joo SW (2016) Deformability-based electrokinetic particle separation. Micromachines 7(9): 170

    Article  Google Scholar 

  • Zhou K, Hou J, Sun Q, Guo L, Bing S, Du Q, Yao C (2017) An efficient LBM-DEM simulation method for suspensions of deformable preformed particle gels. Chem Eng Sci 167:288–296

    Article  CAS  Google Scholar 

  • Zhou T, Ge J, Shi L, Fan J, Liu Z, Woo Joo S (2018) Dielectrophoretic choking phenomenon of a deformable particle in a converging-diverging microchannel. Electrophoresis 39(4):590–596

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale, Università degli Studi di Napoli Federico II, P.le Tecchio 80, 80125, Napoli, Italy

    Massimiliano M. Villone & Pier Luca Maffettone

Authors
  1. Massimiliano M. Villone
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pier Luca Maffettone
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Massimiliano M. Villone.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Villone, M.M., Maffettone, P.L. Dynamics, rheology, and applications of elastic deformable particle suspensions: a review. Rheol Acta 58, 109–130 (2019). https://doi.org/10.1007/s00397-019-01134-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00397-019-01134-2

Keywords

Search

Navigation