- Email: [email protected]
Soft food microrheology
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ScienceDirect Soft food microrheology Jiakai Lu and Carlos M Corvalan Soft food materials, such as gels, pastes, emulsions and colloidal suspensions, are highly heterogeneous structures under constant dynamic interactions. For this reason, these materials frequently exhibit complicated rheological responses, many of which defy characterization by conventional techniques without disrupting their internal food microstructure. In this paper, we highlight recent advances in microrheological methods to probe rheological responses of delicate samples at the microscale. They offer a powerful new approach to characterize soft food materials in a direct and unobtrusive way. Microrheological methods promise to reveal a better fundamental understanding of the underlying structures and dynamics of soft food materials, inform novel constitutive models, and help develop new technological applications. Address Transport Phenomena Laboratory, Department of Food Science, Purdue University, West Lafayette, IN 47907, USA Corresponding author: Lu, Jiakai ([email protected])
Current Opinion in Food Science 2016, 9:112–116 This review comes from a themed issue on Food physics and material science Edited by Osvaldo Campanella For a complete overview see the Issue and the Editorial Available online 8th November 2016 http://dx.doi.org/10.1016/j.cofs.2016.10.004 2214-7993/# 2016 Elsevier Ltd. All rights reserved.
Introduction Food rheology is the study of how food materials deform in response to mechanical stresses. Food materials — and especially soft food materials — are typically composed of heterogeneous microstructures and metastable arrangements that lead to complicated responses when subjected to stress [1]. Moreover, experimental techniques able to quantify the rheology of food materials at small length scales can provide basic insight into their underlying structure and dynamics, and ultimately into their response during processing, storage and consumption. Microrheological techniques have been developed to complement and extend conventional bulk rheology by measuring local rheological properties of a material at the micron scale. In these techniques, the rheological information is extracted from the motion of microscopic probe Current Opinion in Food Science 2016, 9:112–116
particles embedded within the material. The embedded probe particles are driven by random thermal fluctuations in passive microrheology [2], or by an applied external force in active microrheology [3]. Both active and passive microrheology are increasingly been used to characterize challenging natural and synthetic materials, but these methods have not yet been fully exploited in food rheology. Here, we briefly discuss recent progress in microrheology, and highlight benefits of these techniques for studies of soft materials that play a critical role in food technology such as gels, colloids and biopolymers.
Active and passive microrheology Microrheology describes a wide collection of techniques used to quantify phenomena involved in the storage and dissipation of mechanical energy in a microscopic region of a material. In the last two decades there have been important developments in microrheological techniques, which can be broadly classified as passive or active depending on the forces underlying the measurements. Passive microrheology quantifies the mechanical properties of a sample by relating the diffusive fluctuations of an embedded probe particle to the shear modulus of the material (Figure 1). This technique is ideally suited for soft food materials because the weak thermal energy (kBT) required to fluctuate the particles provides a delicate probe of the internal food microstructure. And because there is no need to apply an external force, it only requires relatively simple instrumentation to trace the motion of the particles such as direct visualization [4,5], laser deflection tracking [6,7], diffusing wave spectroscopy [8,9] or dynamic light scattering [10]. The formalism to extract rheological information from thermal fluctuations employs the generalized Stokes– Einstein relation. In the simplest case of a purely viscous material, the mean-square displacement of the fluctuating particles hDr2i=6Dt depends linearly on time through the diffusion coefficient D. For a probe particle of (hydraulic) radius a, the diffusion coefficient is given by the Stokes– Einstein equation D = kBT/(6pha), which relates the desired sample viscosity h to the measured mean-square displacement [2]. In a seminal work for modern microrheology, Mason and Weitz [6] demonstrated that this approach could be generalized to characterize soft materials that exhibit viscoelastic behavior using the fluctuation-dissipation theorem [11,12]. By employing the fluctuationdissipation theorem, Mason and Weitz [6] generalized the Stokes–Einstein equation to relate the measured www.sciencedirect.com
Soft food microrheology Lu and Corvalan 113
Figure 1
(b)
< Δr 2 ( ) >
102 101
GSER
100
10–1 10–2 10–6 10–4 10–2
10
0
10
2
G′(ω), G″(ω)
(a)
106 105 104 103 102 102
104
ω
106
108
Current Opinion in Food Science
Passive microrheology. Passive microrheology uses the generalized Stokes–Einstein relation (GSER) and the fluctuation-dissipation theorem to relate the Brownian mean-square displacement hDr2i of a fluctuating probe particle embedded in a soft material as a function of time t (a) to the storage modulus G0 (v) (red) and loss modulus G00 (v) (blue) of the material (b).
mean-squared displacement hDr2i of the particles (Figure 1a) directly to the sample frequency-dependent viscosity h*(v), and therefore to the sample complex shear modulus G*(v) = ivh*(v) = G0 (v) + iG00 (v) via integral transforms (Figure 1b). For a detailed discussion of the application of the generalized Stokes–Einstein relation to passive microrheology and conditions that can invalidate this generalization, see Squires and Mason [2] and DePuit and Squires [13,14]. Active microrheology, instead, extracts the mechanical properties of the material from the motion of embedded microscopic particles driven by an external force [3]. Therefore, besides instruments to trace the motion of the particles, active microrheology requires additional equipment to actively drive them within the material. Generally, the probe particles are pulled by a constant force using magnetic tweezers [15] or they are driven at constant speed using optical tweezers [16–18]. However, unlike passive techniques, active microrheology enables the characterization of the non-linear rheology of materials by using the applied force to perturb their microstructure far away from equilibrium [19,20,21]. Currently, a frontier research area in microrheology involves combining the benefits of both active and passive approaches. In active microrheology, probe particles are driven by external forces, whereas in passive microrheology the particles are driven by Brownian fluctuations. Combined methods involve the motion of an embedded probe that is actively pulled by internal but non-Brownian stresses (e.g. by capillarity). Recently, rigorous theories elucidating the interplay between endogenous capillary forces and the hydrodynamics of embedded microscopic pores and indentations have been www.sciencedirect.com
developed [22,23,24,25,26], and applied to relate the motion of the probe ‘micropores’ (Figure 2a) to the Newtonian (Figure 2b, black line), shear-thinning (Figure 2b, blue line), and viscoelastic rheology of the material [25,27].
Application to foods Microrheology is particularly attractive for the study of soft materials such as gels, colloids, and biopolymers that play a ubiquitous role in food science and food technology. Because of the small size of the embedded probe particles, it can measure local rheological properties that are necessarily lumped in macroscopic measurements [28]. And because of the low inertia of the particles, it can extract this information at a higher range of frequencies than allowed by conventional rheology [29]. Consequently, an important research area open to food microrheology concerns heterogeneous materials where the rheology changes from point to point. Either by successively tracking single probe particles or by simultaneously tracking multiple probe particles at various places in the sample, microrheology can provide insight into the spatial distribution of the internal microstructure for heterogeneous food systems — from dilute suspensions to arrested systems such as gels and colloidal glasses. Early works in this area include suspensions of wheat gliadin [30], a protein responsible for dough viscoelasticity, and suspensions of oat beta-glucan, a bioactive component credited with health benefits [31]. More recently, studies on suspensions of barley beta-glucan corroborated that microrheology can probe micro-heterogeneities in food samples that go unnoticed by macroscopic rheology [32]. Current Opinion in Food Science 2016, 9:112–116
114 Food physics and material science
Figure 2
(a)
(b)
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Δt
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r/H Current Opinion in Food Science
Combined microrheology. Example of a combined technique that relates the capillary velocity vm=s of an embedded contracting micropore used as a microrheological probe (a) to the shear-thinning rheological behavior of a soft material (blue line) in which the shear stress decreases (n < 1) with increasing shear rate (b). Here, Dt is the elapsed time, n the flow index of the material, r the radius of the micropore, and H the thickness of the fluid film.
Since the pioneering work by Mason and Weitz [6] on hard-sphere colloidal suspensions, the microrheology of colloidal systems has been extensively studied in both the dilute limit and the arrested limit close to the glass transition. In the dilute limit, colloidal suspensions have been studied using microrheological models based on the two-body solution of the Smoluchowski equation as an approximation to the many-body interactions between colloidal particles [21,33]. In this limit, microrheology enabled accurate characterization of both the loss modulus G00 , which generally dominates the dynamics, and the growth of the storage modulus G0 with the volume fraction [34]. Increasing the volume fraction of the colloidal particles may lead to dynamical arrest, and the suspensions may undergo a glass transition [34]. Close to their glass transition, dense colloidal suspensions have been studied using active and passive microrheological models based on the Mode-Coupling theory because many-body hydrodynamic interactions generally dominate the mechanical response [35–37]. In these conditions, colloidal suspensions frequently exhibit rheological behavior similar to other soft glassy materials of interest in food technology because of their shared metastable internal disorder. Measurements largely agree on a predominantly elastic behavior with a storage modulus G0 (v) scaling as a very weak power law of frequency v, and on the presence of a yield stress above which the material readily flows as a Herschel–Bulkley fluid [38]. For a review of recent work on the microrheology of colloidal systems, see Puertas and Voigtmann [34]. Current Opinion in Food Science 2016, 9:112–116
Microrheology enables not only simultaneous rheological measurements at different locations in a sample but also continuous measurements over time [39]. This makes this technique highly valuable for the study of food materials with evolving dynamic microstructures. Of particular importance for food technology is the use of microrheology to monitor the dynamics of aging [40–43] and the dynamics of gel formation [44]. Early research in food gels includes the gelation dynamics of pectin [45], fibrillar proteins [46], and milk gels [47]. And more recently, the gelation dynamics of beta-lactoglobulin [48], dairy proteins [49], and beta-glucan solutions [32]. For a recent review of the microrheology of food gels, see Moschakis [50]. Recent advances have enabled the rapid characterization of fast-forming gels, and further improved the ability of microrheology to characterize gelation reactions without disturbing the dynamics and assembly of the incipient network structure. Research by Gomez-Solano et al. [51] demonstrated the utility of microrheology to follow fast process associated to the rapid propagation of the gelation front into the sol phase during sol–gel transition, and Forde and collaborators [52,53] used microrheology to elucidate delicate mechanisms of self-assembly by following temporal changes in the shear modulus of gels of collagen fibrils since the very early phases of fibrillar growth.
Conclusion In this paper, we presented a few examples that provide a glimpse of what is now possible using microrheology, and www.sciencedirect.com
Soft food microrheology Lu and Corvalan 115
the unique benefits this technique can offer to food scientists beyond those provided by conventional bulk rheology. Potential applications of microrheology in food technology are by no means limited to these few examples. In addition to the clear advantage of microrheology to characterize minute amounts of sample (e.g. cells, proteins) [54,55], other potential applications include the use of microrheology to interrogate the mechanical properties of bacterial biofilms [56,57], and the viscoelastic properties of interfaces and emulsions stabilizers [58,59]. Microrheology has also been applied to characterize dynamical processes that modulate the release of the active ingredients in materials used for controlled release applications [60]. Moreover, leading research areas may soon enable automated microrheology instrumentation for highthroughput screening of food materials [61], as well as simpler and less expensive ways to characterize nonlinear food rheology by extending microrheology to different driving modes using micropores and indentations as embedded micro and nanorheological probes [26,62]. Clearly, food microrheology is still in its infancy and there is much interdisciplinary work to be done to further familiarize food scientists with this technique. But the possibilities for deciphering the mechanical response of food materials at an unprecedented level of detail, and using this information to develop better theoretical constitutive models [63] and new technological applications, are enormous.
6.
Mason TG, Weitz D: Optical measurements of frequencydependent linear viscoelastic moduli of complex fluids. Phys Rev Lett 1995, 74:1250.
7.
Du K, Liddle JA, Berglund AJ: Three-dimensional real-time tracking of nanoparticles at an oil-water interface. Langmuir 2012, 28:9181-9188.
8.
Mason T, Gang H, Weitz D: Diffusing-wave-spectroscopy measurements of viscoelasticity of complex fluids. J Opt Soc Am A 1997, 14:139-149.
9.
Oelschlaeger C, Cota Pinto Coelho M, Willenbacher N: Chain flexibility and dynamics of polysaccharide hyaluronan in entangled solutions: a high frequency rheology and diffusing wave spectroscopy study. Biomacromolecules 2013, 14:3689-3696.
10. Mason T, Gang H, Weitz D: Rheology of complex fluids measured by dynamic light scattering. J Mol Struct 1996, 383:81-90. 11. Landau LD, Lifshitz E: Statistical Physics. Oxford: ButterworthHeinemann 1980; 2000. 12. Evans DJ, Searles DJ, Williams SR: Fundamentals of Classical Statistical Thermodynamics: Dissipation, Relaxation and Fluctuation Theorems. John Wiley & Sons; 2016. 13. DePuit RJ, Squires TM: Micro-macro-discrepancies in nonlinear microrheology: I. Quantifying mechanisms in a suspension of Brownian ellipsoids. J Phys Condens Matter 2012, 24:464106. 14. DePuit RJ, Squires TM: Micro-macro discrepancies in nonlinear microrheology: II. Effect of probe shape. J Phys Condens Matter 2012, 24:464107. 15. Habdas P, Schaar D, Levitt AC, Weeks ER: Forced motion of a probe particle near the colloidal glass transition. EPL (Europhys Lett) 2004, 67:477. 16. Furst EM: Interactions, structure, and microscopic response: complex fluid rheology using laser tweezers. Soft Mater 2003, 1:167-185.
Acknowledgements
17. Sriram I, Meyer A, Furst EM: Active microrheology of a colloidal suspension in the direct collision limit. Phys Fluids (1994– Present) 2010, 22:062003.
This work was partially supported by the USDA National Institute of Food and Agriculture, Hatch projects 1008409 and 199888.
18. Meyer A, Marshall A, Bush BG, Furst EM: Laser tweezer microrheology of a colloidal suspension. J Rheol (1978– Present) 2006, 50:77-92.
References and recommended reading
19. Gomez-Solano JR, Bechinger C: Probing linear and nonlinear microrheology of viscoelastic fluids. EPL (Europhys Lett) 2014, 108:54008.
Papers of particular interest, published within the period of review, have been highlighted as: of special interest of outstanding interest 1.
Fischer P, Windhab EJ: Rheology of food materials. Curr Opin Colloid Interface Sci 2011, 16:36-40.
2. Squires TM, Mason TG: Fluid mechanics of microrheology. Annu Rev Fluid Mech 2010, 42:413. This work reviews the development and current state of various microrheological techniques, and their theoretical justification based on the generalized Stokes–Einstein relation, discussing their range of validity and key assumptions invoked. 3.
Wilson LG, Poon WC: Small-world rheology: an introduction to probe-based active microrheology. Phys Chem Chem Phys 2011, 13:10617-10630.
4.
Vadas E, Goldsmith H, Mason SG: The microrheology of colloidal dispersions: I. The microtube technique. J Colloid Interface Sci 1973, 43:630-648.
5.
Filipe V, Hawe A, Jiskoot W: Critical evaluation of nanoparticle tracking analysis (NTA) by nanosight for the measurement of nanoparticles and protein aggregates. Pharm Res 2010, 27:796-810.
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20. Gomez-Solano JR, Bechinger C: Transient dynamics of a colloidal particle driven through a viscoelastic fluid. New J Phys 2015, 17:103032. This work provides a novel method to measure transient microrheology of viscoelastic fluids by following an actively dragged colloidal particle with an optical trap. 21. Zia RN, Brady JF: Stress development, relaxation, and memory in colloidal dispersions: transient nonlinear microrheology. J Rheol (1978–Present) 2013, 57:457-492. 22. Backholm M, Benzaquen M, Salez T, Raphae¨l E, Dalnoki-Veress K: Capillary levelling of a cylindrical hole in a viscous film. Soft Matter 2014, 10:2550-2558. Extending the work by McGraw et al., this paper provides the required theoretical background, as well as experimental validation, for the application of microindentations to characterize local rheological properties. 23. Lu J, Corvalan CM: Free-surface dynamics of small pores. Chem Eng Sci 2015, 132:93-98. 24. Lu J, Yu J, Corvalan CM: Universal scaling law for the collapse of viscous nanopores. Langmuir 2015, 31:8618-8622. First theoretical and numerical demonstration of an universal scaling law during the contraction of viscous pores at the sub-micron scale, and its relationship with the rheological properties of the host material. Current Opinion in Food Science 2016, 9:112–116
116 Food physics and material science
25. McGraw JD, Jago NM, Dalnoki-Veress K: Capillary levelling as a probe of thin film polymer rheology. Soft Matter 2011, 7:7832-7838.
45. Vincent R, Pinder D, Hemar Y, Williams M: Microrheological studies reveal semiflexible networks in gels of a ubiquitous cell wall polysaccharide. Phys Rev E 2007, 76:031909.
26. Rahmani Y, Koopman R, Denisov D, Schall P: Visualizing the strain evolution during the indentation of colloidal glasses. Phys Rev E 2014, 89:012304.
46. Corrigan AM, Donald AM: Passive microrheology of solvent-induced fibrillar protein networks. Langmuir 2009, 25:8599-8605.
27. Roth CB, Dutcher JR: Hole growth as a microrheological probe to measure the viscosity of polymers confined to thin films. J Polym Sci B Polym Phys 2006, 44:3011-3021.
47. Cucheval AS, Vincent RR, Hemar Y, Otter D, Williams MA: Multiple particle tracking investigations of acid milk gels using tracer particles with designed surface chemistries and comparison with diffusing wave spectroscopy studies. Langmuir 2009, 25:11827-11834.
28. Schultz KM, Furst EM: Microrheology of biomaterial hydrogelators. Soft Matter 2012, 8:6198-6205. 29. Willenbacher N, Oelschlaeger C: Dynamics and structure of complex fluids from high frequency mechanical and optical rheometry. Curr Opin Colloid Interface Sci 2007, 12:43-49. 30. Xu J, Tseng Y, Carriere CJ, Wirtz D: Microheterogeneity and microrheology of wheat gliadin suspensions studied by multiple-particle tracking. Biomacromolecules 2002, 3:92-99. 31. Xu J, Chang T, Inglett GE, Kim S, Tseng Y, Wirtz D: Microheterogeneity and micro-rheological properties of highviscosity oat b-glucan solutions. Food Chem 2007, 103:1192-1198.
48. Balakrishnan G, Durand D, Nicolai T: Particle diffusion in globular protein gels in relation to the gel structure. Biomacromolecules 2010, 12:450-456. 49. Moschakis T, Murray BS, Dickinson E: On the kinetics of acid sodium caseinate gelation using particle tracking to probe the microrheology. J Colloid Interface Sci 2010, 345:278-285. 50. Moschakis T: Microrheology and particle tracking in food gels and emulsions. Curr Opin Colloid Interface Sci 2013, 18:311-323. 51. Gomez-Solano J, Blickle V, Bechinger C: Nucleation and growth of thermoreversible polymer gels. Phys Rev E 2013, 87:012308.
32. Moschakis T, Lazaridou A, Biliaderis CG: Using particle tracking to probe the local dynamics of barley b-glucan solutions upon gelation. J Colloid Interface Sci 2012, 375:50-59.
52. Shayegan M, Forde NR: Microrheological characterization of collagen systems: from molecular solutions to fibrillar gels. PLOS ONE 2013, 8:e70590.
33. Zia RN, Brady JF: Single-particle motion in colloids: forceinduced diffusion. J Fluid Mech 2010, 658:188-210.
53. Shayegan M, Altindal T, Forde NR: Investigating the mechanism of collagen self-assembly with microrheology. Biophys J 2014, 106:55a.
34. Puertas AM, Voigtmann T: Microrheology of colloidal systems. J Phys Condens Matter 2014, 26:243101. This work offers a comprehensive review of theoretical models available for both passive and active microrheology, with the focus on the application of single-probe motion microrheology in low- and high-density colloidal media. 35. Gazuz I, Puertas AM, Voigtmann T, Fuchs M: Active and nonlinear microrheology in dense colloidal suspensions. Phys Rev Lett 2009, 102:248302. 36. Gazuz I, Fuchs M: Nonlinear microrheology of dense colloidal suspensions: a mode-coupling theory. Phys Rev E 2013, 87:032304. 37. Voigtmann T, Fuchs M: Force-driven micro-rheology. Eur Phys J Spec Top 2013, 222:2819-2833. 38. Anderson D, Schaar D, Hentschel H, Hay J, Habdas P, Weeks ER: Local elastic response measured near the colloidal glass transition. J Chem Phys 2013, 138:12A520. 39. Larsen TH, Furst EM: Microrheology of the liquid–solid transition during gelation. Phys Rev Lett 2008, 100:146001. 40. Rich JP, Lammerding J, McKinley GH, Doyle PS: Nonlinear microrheology of an aging, yield stress fluid using magnetic tweezers. Soft Matter 2011, 7:9933-9943. 41. Gomez-Solano JR, Petrosyan A, Ciliberto S: Fluctuations, linear response and heat flux of an aging system. EPL (Europhys Lett) 2012, 98:10007. 42. Zia RN, Landrum BJ, Russel WB: A micro-mechanical study of coarsening and rheology of colloidal gels: cage building, cage hopping, and Smoluchowski’s ratchet. J Rheol (1978–Present) 2014, 58:1121-1157. 43. Peng X, McKenna GB: Physical aging and structural recovery in a colloidal glass subjected to volume-fraction jump conditions. Phys Rev E 2016, 93:042603. 44. Narita T, Indei T: Microrheological study of physical gelation in living polymeric networks. Macromolecules 2016.
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54. Wirtz D: Particle-tracking microrheology of living cells: principles and applications. Annu Rev Biophys 2009, 38:301-326. 55. Josephson LL, Furst EM, Galush WJ: Particle tracking microrheology of protein solutions. J Rheol (1978–Present) 2016, 60:531-540. 56. Rogers S, Van Der Walle C, Waigh T: Microrheology of bacterial biofilms in vitro: Staphylococcus aureus and Pseudomonas aeruginosa. Langmuir 2008, 24:13549-13555. 57. Galy O, Latour-Lambert P, Zrelli K, Ghigo J-M, Beloin C, Henry N: Mapping of bacterial biofilm local mechanics by magnetic microparticle actuation. Biophys J 2012, 103:1400-1408. 58. Mendoza AJ, Guzma´n E, Martı´nez-Pedrero F, Ritacco H, Rubio RG, Ortega F, Starov VM, Miller R: Particle laden fluid interfaces: dynamics and interfacial rheology. Adv Colloid Interface Sci 2014, 206:303-319. 59. Huang S, Gawlitza K, von Klitzing R, Gilson L, Nowak J, Odenbach S, Steffen W, Auernhammer GK: Microgels at the water/oil interface: in-situ observation of structural ageing and two-dimensional magnetic bead microrheology. Langmuir 2015. 60. Frith W, Donald A, Adams D, Aufderhorst-Roberts A: Gels formed from amino-acid derivatives, their novel rheology as probed by bulk and particle tracking rheological methods. J Non-Newton Fluid Mech 2015, 222:104-111. 61. Shindel MM, Furst EM: Frequency modulated microrheology. Lab Chip 2015, 15:2460-2466. This work provides an overview of the theory and experimental implementations of Frequency Modulated Microrheology, which enables characterization of the dynamic stress response of complex fluids over several frequency decades in a single experiment. 62. Lu J, Corvalan CM: Scaling laws for the contraction of nonNewtonian pores. 2016:. (in preparation). 63. Brader JM: Nonlinear rheology of colloidal dispersions. J Phys Condens Matter 2010, 22:363101.
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ScienceDirect Soft food microrheology Jiakai Lu and Carlos M Corvalan Soft food materials, such as gels, pastes, emulsions and colloidal suspensions, are highly heterogeneous structures under constant dynamic interactions. For this reason, these materials frequently exhibit complicated rheological responses, many of which defy characterization by conventional techniques without disrupting their internal food microstructure. In this paper, we highlight recent advances in microrheological methods to probe rheological responses of delicate samples at the microscale. They offer a powerful new approach to characterize soft food materials in a direct and unobtrusive way. Microrheological methods promise to reveal a better fundamental understanding of the underlying structures and dynamics of soft food materials, inform novel constitutive models, and help develop new technological applications. Address Transport Phenomena Laboratory, Department of Food Science, Purdue University, West Lafayette, IN 47907, USA Corresponding author: Lu, Jiakai ([email protected])
Current Opinion in Food Science 2016, 9:112–116 This review comes from a themed issue on Food physics and material science Edited by Osvaldo Campanella For a complete overview see the Issue and the Editorial Available online 8th November 2016 http://dx.doi.org/10.1016/j.cofs.2016.10.004 2214-7993/# 2016 Elsevier Ltd. All rights reserved.
Introduction Food rheology is the study of how food materials deform in response to mechanical stresses. Food materials — and especially soft food materials — are typically composed of heterogeneous microstructures and metastable arrangements that lead to complicated responses when subjected to stress [1]. Moreover, experimental techniques able to quantify the rheology of food materials at small length scales can provide basic insight into their underlying structure and dynamics, and ultimately into their response during processing, storage and consumption. Microrheological techniques have been developed to complement and extend conventional bulk rheology by measuring local rheological properties of a material at the micron scale. In these techniques, the rheological information is extracted from the motion of microscopic probe Current Opinion in Food Science 2016, 9:112–116
particles embedded within the material. The embedded probe particles are driven by random thermal fluctuations in passive microrheology [2], or by an applied external force in active microrheology [3]. Both active and passive microrheology are increasingly been used to characterize challenging natural and synthetic materials, but these methods have not yet been fully exploited in food rheology. Here, we briefly discuss recent progress in microrheology, and highlight benefits of these techniques for studies of soft materials that play a critical role in food technology such as gels, colloids and biopolymers.
Active and passive microrheology Microrheology describes a wide collection of techniques used to quantify phenomena involved in the storage and dissipation of mechanical energy in a microscopic region of a material. In the last two decades there have been important developments in microrheological techniques, which can be broadly classified as passive or active depending on the forces underlying the measurements. Passive microrheology quantifies the mechanical properties of a sample by relating the diffusive fluctuations of an embedded probe particle to the shear modulus of the material (Figure 1). This technique is ideally suited for soft food materials because the weak thermal energy (kBT) required to fluctuate the particles provides a delicate probe of the internal food microstructure. And because there is no need to apply an external force, it only requires relatively simple instrumentation to trace the motion of the particles such as direct visualization [4,5], laser deflection tracking [6,7], diffusing wave spectroscopy [8,9] or dynamic light scattering [10]. The formalism to extract rheological information from thermal fluctuations employs the generalized Stokes– Einstein relation. In the simplest case of a purely viscous material, the mean-square displacement of the fluctuating particles hDr2i=6Dt depends linearly on time through the diffusion coefficient D. For a probe particle of (hydraulic) radius a, the diffusion coefficient is given by the Stokes– Einstein equation D = kBT/(6pha), which relates the desired sample viscosity h to the measured mean-square displacement [2]. In a seminal work for modern microrheology, Mason and Weitz [6] demonstrated that this approach could be generalized to characterize soft materials that exhibit viscoelastic behavior using the fluctuation-dissipation theorem [11,12]. By employing the fluctuationdissipation theorem, Mason and Weitz [6] generalized the Stokes–Einstein equation to relate the measured www.sciencedirect.com
Soft food microrheology Lu and Corvalan 113
Figure 1
(b)
< Δr 2 ( ) >
102 101
GSER
100
10–1 10–2 10–6 10–4 10–2
10
0
10
2
G′(ω), G″(ω)
(a)
106 105 104 103 102 102
104
ω
106
108
Current Opinion in Food Science
Passive microrheology. Passive microrheology uses the generalized Stokes–Einstein relation (GSER) and the fluctuation-dissipation theorem to relate the Brownian mean-square displacement hDr2i of a fluctuating probe particle embedded in a soft material as a function of time t (a) to the storage modulus G0 (v) (red) and loss modulus G00 (v) (blue) of the material (b).
mean-squared displacement hDr2i of the particles (Figure 1a) directly to the sample frequency-dependent viscosity h*(v), and therefore to the sample complex shear modulus G*(v) = ivh*(v) = G0 (v) + iG00 (v) via integral transforms (Figure 1b). For a detailed discussion of the application of the generalized Stokes–Einstein relation to passive microrheology and conditions that can invalidate this generalization, see Squires and Mason [2] and DePuit and Squires [13,14]. Active microrheology, instead, extracts the mechanical properties of the material from the motion of embedded microscopic particles driven by an external force [3]. Therefore, besides instruments to trace the motion of the particles, active microrheology requires additional equipment to actively drive them within the material. Generally, the probe particles are pulled by a constant force using magnetic tweezers [15] or they are driven at constant speed using optical tweezers [16–18]. However, unlike passive techniques, active microrheology enables the characterization of the non-linear rheology of materials by using the applied force to perturb their microstructure far away from equilibrium [19,20,21]. Currently, a frontier research area in microrheology involves combining the benefits of both active and passive approaches. In active microrheology, probe particles are driven by external forces, whereas in passive microrheology the particles are driven by Brownian fluctuations. Combined methods involve the motion of an embedded probe that is actively pulled by internal but non-Brownian stresses (e.g. by capillarity). Recently, rigorous theories elucidating the interplay between endogenous capillary forces and the hydrodynamics of embedded microscopic pores and indentations have been www.sciencedirect.com
developed [22,23,24,25,26], and applied to relate the motion of the probe ‘micropores’ (Figure 2a) to the Newtonian (Figure 2b, black line), shear-thinning (Figure 2b, blue line), and viscoelastic rheology of the material [25,27].
Application to foods Microrheology is particularly attractive for the study of soft materials such as gels, colloids, and biopolymers that play a ubiquitous role in food science and food technology. Because of the small size of the embedded probe particles, it can measure local rheological properties that are necessarily lumped in macroscopic measurements [28]. And because of the low inertia of the particles, it can extract this information at a higher range of frequencies than allowed by conventional rheology [29]. Consequently, an important research area open to food microrheology concerns heterogeneous materials where the rheology changes from point to point. Either by successively tracking single probe particles or by simultaneously tracking multiple probe particles at various places in the sample, microrheology can provide insight into the spatial distribution of the internal microstructure for heterogeneous food systems — from dilute suspensions to arrested systems such as gels and colloidal glasses. Early works in this area include suspensions of wheat gliadin [30], a protein responsible for dough viscoelasticity, and suspensions of oat beta-glucan, a bioactive component credited with health benefits [31]. More recently, studies on suspensions of barley beta-glucan corroborated that microrheology can probe micro-heterogeneities in food samples that go unnoticed by macroscopic rheology [32]. Current Opinion in Food Science 2016, 9:112–116
114 Food physics and material science
Figure 2
(a)
(b)
101
υμ /σ
Δt
(n - 1) / n
100
10–1 10–4
10–3
10–2
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Combined microrheology. Example of a combined technique that relates the capillary velocity vm=s of an embedded contracting micropore used as a microrheological probe (a) to the shear-thinning rheological behavior of a soft material (blue line) in which the shear stress decreases (n < 1) with increasing shear rate (b). Here, Dt is the elapsed time, n the flow index of the material, r the radius of the micropore, and H the thickness of the fluid film.
Since the pioneering work by Mason and Weitz [6] on hard-sphere colloidal suspensions, the microrheology of colloidal systems has been extensively studied in both the dilute limit and the arrested limit close to the glass transition. In the dilute limit, colloidal suspensions have been studied using microrheological models based on the two-body solution of the Smoluchowski equation as an approximation to the many-body interactions between colloidal particles [21,33]. In this limit, microrheology enabled accurate characterization of both the loss modulus G00 , which generally dominates the dynamics, and the growth of the storage modulus G0 with the volume fraction [34]. Increasing the volume fraction of the colloidal particles may lead to dynamical arrest, and the suspensions may undergo a glass transition [34]. Close to their glass transition, dense colloidal suspensions have been studied using active and passive microrheological models based on the Mode-Coupling theory because many-body hydrodynamic interactions generally dominate the mechanical response [35–37]. In these conditions, colloidal suspensions frequently exhibit rheological behavior similar to other soft glassy materials of interest in food technology because of their shared metastable internal disorder. Measurements largely agree on a predominantly elastic behavior with a storage modulus G0 (v) scaling as a very weak power law of frequency v, and on the presence of a yield stress above which the material readily flows as a Herschel–Bulkley fluid [38]. For a review of recent work on the microrheology of colloidal systems, see Puertas and Voigtmann [34]. Current Opinion in Food Science 2016, 9:112–116
Microrheology enables not only simultaneous rheological measurements at different locations in a sample but also continuous measurements over time [39]. This makes this technique highly valuable for the study of food materials with evolving dynamic microstructures. Of particular importance for food technology is the use of microrheology to monitor the dynamics of aging [40–43] and the dynamics of gel formation [44]. Early research in food gels includes the gelation dynamics of pectin [45], fibrillar proteins [46], and milk gels [47]. And more recently, the gelation dynamics of beta-lactoglobulin [48], dairy proteins [49], and beta-glucan solutions [32]. For a recent review of the microrheology of food gels, see Moschakis [50]. Recent advances have enabled the rapid characterization of fast-forming gels, and further improved the ability of microrheology to characterize gelation reactions without disturbing the dynamics and assembly of the incipient network structure. Research by Gomez-Solano et al. [51] demonstrated the utility of microrheology to follow fast process associated to the rapid propagation of the gelation front into the sol phase during sol–gel transition, and Forde and collaborators [52,53] used microrheology to elucidate delicate mechanisms of self-assembly by following temporal changes in the shear modulus of gels of collagen fibrils since the very early phases of fibrillar growth.
Conclusion In this paper, we presented a few examples that provide a glimpse of what is now possible using microrheology, and www.sciencedirect.com
Soft food microrheology Lu and Corvalan 115
the unique benefits this technique can offer to food scientists beyond those provided by conventional bulk rheology. Potential applications of microrheology in food technology are by no means limited to these few examples. In addition to the clear advantage of microrheology to characterize minute amounts of sample (e.g. cells, proteins) [54,55], other potential applications include the use of microrheology to interrogate the mechanical properties of bacterial biofilms [56,57], and the viscoelastic properties of interfaces and emulsions stabilizers [58,59]. Microrheology has also been applied to characterize dynamical processes that modulate the release of the active ingredients in materials used for controlled release applications [60]. Moreover, leading research areas may soon enable automated microrheology instrumentation for highthroughput screening of food materials [61], as well as simpler and less expensive ways to characterize nonlinear food rheology by extending microrheology to different driving modes using micropores and indentations as embedded micro and nanorheological probes [26,62]. Clearly, food microrheology is still in its infancy and there is much interdisciplinary work to be done to further familiarize food scientists with this technique. But the possibilities for deciphering the mechanical response of food materials at an unprecedented level of detail, and using this information to develop better theoretical constitutive models [63] and new technological applications, are enormous.
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Acknowledgements
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This work was partially supported by the USDA National Institute of Food and Agriculture, Hatch projects 1008409 and 199888.
18. Meyer A, Marshall A, Bush BG, Furst EM: Laser tweezer microrheology of a colloidal suspension. J Rheol (1978– Present) 2006, 50:77-92.
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Papers of particular interest, published within the period of review, have been highlighted as: of special interest of outstanding interest 1.
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