Is there a way to eliminate the disconnected elements of an image?

First, you could use morphological operations to ensure that the interesting edges are connected. You can read more about morphological operations in the web of OpenCV: https://docs.opencv.org/4.x/d9/d61/tutorial_py_morphological_ops.html.

The code would be:

import numpy as np
import cv2 as cv
import matplotlib.pyplot as plt
from scipy import ndimage

# Open the image
img = cv.imread('testim5.png', cv.IMREAD_GRAYSCALE)

# Note that `scipy.ndimage.filters.gaussian_filter` is deprecated, use `scipy.ndimage.gaussian_filter` instead
blurred = ndimage.gaussian_filter(img, 2, mode='nearest')
edges = cv.Canny(blurred,100,175)

# Apply morphological operation (closing) to the EDGES so they are connected
kernel = np.ones((5,3),np.uint8)
edges_closing = cv.morphologyEx(edges, cv.MORPH_CLOSE, kernel)

The result of this is that the vertical edges aren't so disjoint, as you can see in the following image.

The second step is to remove the pores. It can be seen as a problem of removing small connected objects and the solution of @Soltius in How to remove small connected objects using OpenCV works well.

The code in your case would be:

# Remove smallest connected components
# To understand the following lines, look the answer of @Soltius in https://stackoverflow.com/questions/42798659/how-to-remove-small-connected-objects-using-opencv
nb_blobs, im_with_separated_blobs, stats, _ = cv.connectedComponentsWithStats(edges_closing)
sizes = stats[:, -1]
sizes = sizes[1:]
nb_blobs -= 1

# Minimum size of particles we want to keep (number of pixels).
# Here, it's a fixed value, but you can set it as you want.
min_size = 80  

final_edges = np.zeros_like(im_with_separated_blobs)
for blob in range(nb_blobs):
    if sizes[blob] >= min_size:
        final_edges[im_with_separated_blobs == blob + 1] = 255

fig, axs = plt.subplots(ncols=3)
axs[0].imshow(img, cmap='gray')
axs[1].imshow(edges, cmap='gray')
axs[2].imshow(final_edges, cmap='gray')
axs[0].set_title('Original image')
axs[1].set_title('Original edges')
axs[2].set_title('New edges')
fig.tight_layout()
plt.show()

The final edges are: