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NUMERICAL DUAL-POROSITY MODEL OF SOLID-LIQUID EXPRESSION FROM ELECTROPORATED BIO-SOLIDS Samo MAHNIČ-KALAMIZA, Eugène VOROBIEV Université de Technologie de Compiègne Compiègne, FRANCE

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INTRODUCTION :: Numerical Dual-porosity Model of Solid-liquid Expression from Electroporated Bio-solids The "classical" approach (based on Terzaghi's soil consolidation theory) … 1/13 Sources: Shirato et al. 1971; Schwartzberg 1997; and other classical works in soil mechanics and mechanics of biological solids C… constant consolidation coefficient p L... liquid pressure k... hydraulic permeability of the particle bed E... Young‘s modulus (stress-deformation relation) ω... material coordinate, dω = (1 – ε)dz μ... liquid viscosity Terzaghi element coeff. E solid-liquid mixture z external pressure expressed liquid Particle rearrangement – secondary (creep) consolidation Terzaghi-Voigt element coeff. E 1, E 2, G

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2/13 INTRODUCTION :: Numerical Dual-porosity Model of Solid-liquid Expression from Electroporated Bio-solids...and the "dual-porosity" approach… Sources: Lanoisellé et al. 1996; Petryk and Vorobiev 2007; Petryk and Vorobiev 2013; Mahnič-Kalamiza and Vorobiev, 2014 bio-solid (biological tissue) z external pressure expressed liquid Various treatments exist for permeabilizing the cell membrane thus facilitating liquid expression SEM image schematic representation of vegetable tissue

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Electroporation......is a method of altering the permeability of a biological cell membrane using short, intense electrical pulses. 3/13 METHOD :: Numerical Dual-porosity Model of Solid-liquid Expression from Electroporated Bio-solids + - EP pulse generator - electrode+ electrode

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Sugar beet taproot slices before (left) and after (right) treatment with pulsed electric fields; illustration of spontaneous liquid release (below) from tissue due to force of turgor pressure relaxation in cells with permeabilised membranes (i.e. increased hydraulic permeability). 4/13 METHOD :: Numerical Dual-porosity Model of Solid-liquid Expression from Electroporated Bio-solids + - 2. pressure application 1. electroporation

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Some of the possible applications in food & environmental res.: Juice extraction (selective) Dehydration Cryoprotectant impregnation Extraction of valuable compounds Biorefinery... (suggestions?) 4/13 METHOD :: Numerical Dual-porosity Model of Solid-liquid Expression from Electroporated Bio-solids + - 2. pressure application 1. electroporation

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5/13 METHOD :: Numerical Dual-porosity Model of Solid-liquid Expression from Electroporated Bio-solids solid-liquid mixture z external pressure expressed liquid bio-solid (biological tissue) z external pressure expressed liquid Solid-liquid mixture; model of single porosityHeterogeneus material of two phases; model of double porosity ?

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6/13 METHOD :: Numerical Dual-porosity Model of Solid-liquid Expression from Electroporated Bio-solids The mathematical model – constituitive equations Mass balance equations for the system on the left ?

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6/13 extracellular space METHOD :: Numerical Dual-porosity Model of Solid-liquid Expression from Electroporated Bio-solids The mathematical model – constituitive equations accumulation or depletion filtr. flow gradient transmembrane flow p e, ε e qeqe ΨmΨm

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6/13 extracellular space METHOD :: Numerical Dual-porosity Model of Solid-liquid Expression from Electroporated Bio-solids The mathematical model – constituitive equations accumulation or depletion filtr. flow gradient transmembrane flow p i, ε i ΨmΨm intracellular space accumulation or depletion transmembrane flow

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6/13 extracellular space METHOD :: Numerical Dual-porosity Model of Solid-liquid Expression from Electroporated Bio-solids The mathematical model – constituitive equations accumulation or depletion filtr. flow gradient transmembrane flow intracellular space accumulation or depletion transmembrane flow

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7/13 METHOD :: Numerical Dual-porosity Model of Solid-liquid Expression from Electroporated Bio-solids The mathematical model – final model equations accumulation or depletion filtr. flow gradient transmembrane flow accumulation or depletion transmembrane flow This fairly stable system is readily solved using a stable implicit method of numerical integration of PDEs, e.g. Crank-Nicolson extracellular space intracellular space

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8/13 EXPERIMENT :: Juice expression from electroporated sugar beet taproot tissue samples

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RESULTS :: The respective phase liquid pressures z Intra- and extracellular pressure distribution ? 9/13

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extracellularintracellular t = 0 t = 8 s t = 20 s t = 100 s t = 200 s t = 400 s t = 3600 s t = 0 t = 8 s t = 20 s t = 100 s t = 200 s t = 400 s t = 3600 s impermeable piston porous support impermeable piston porous support RESULTS :: The respective phase liquid pressures retardation z

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10/13 varying membrane permeability (treatment intensity) RESULTS :: Simulated deformation (liquid expression) kinetics increasing voltage increasing electric field strength increasing delivered energy increasing permeability of cell membrane completely destroyed and homogenised tissue, "blancmange" intact and partially permeabilised cells in tissue

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11/13 sugar beet taproot juice expression following electroporation due to assumed constant permeabilities* RESULTS :: A real-world example (from in silico to ex vivo) various treatment intensities *permeability of reversibly permeabilised membranes changes dramatically over time - resealing

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12/13 IN SUMMARY... Subject to some modifications, the model just presented is applicable: to mixtures of liquid and semi-solid particles themselves containing a solid- liquid mixture (e.g. biological sludges?); to solid-liquid mixtures with highly deformable solid particles (model should be upgraded with a Voigt element to account for secondary-creep consol.). TAKE-HOME MESSAGE(S) The mathematical model used to describe a bio-physical or bio-mechanical process should be built from the morphology up, not forced to conform to existing models. We should not be afraid to try and develop new models, even in cases where the object is complex!

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...we will all be there. 1 st World Congress on Electroporation and Pulsed Electric Fields in Biology, Medicine and Food and Environmental Technologies September 6-10, 2015 Portoroz, Slovenia visit the Congress website at wc2015.electroporation.netwc2015.electroporation.net Thank you for attention!

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